DEVELOPMENT AND APPLICATION OF A STATISTICAL APPROACH TO ESTABLISH
EQUIVALENCE OF UNABBREVIATED MASS SPECTRA
By
Melissa Anne Bodnar Willard

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Chemistry- Doctor of Philosophy
2013

ABSTRACT
DEVELOPMENT AND APPLICATION OF A STATISTICAL APPROACH TO ESTABLISH
EQUIVALENCE OF UNABBREVIATED MASS SPECTRA
By
Melissa Anne Bodnar Willard
In many regulatory applications, identification is based on mass spectral comparisons of
a compound to a reference standard or library; however, no confidence level associated with the
match is determined. Described herein is a means for determining statistical equivalence to the
mass spectral identification of an unknown compound. A statistical model was developed to
predict standard deviations, which were used in an unequal variance t-test to compare spectra at
every m/z ratio over the entire scan range. If determined to be statistically indistinguishable at
every m/z ratio, the random-match probability (RMP) was calculated, assessing the probability
that the characteristic fragmentation pattern of the mass spectra would occur by random chance
alone.
Due to the challenge of differentiating similar mass spectra, the method was initially
developed using alkane and alkylbenzene standards of varying concentrations. Using the
developed method, replicate spectra were successfully associated at the 99.9% confidence level,
with RMP values ranging from 10

-29

to 10

-46

. Despite the similarity in fragmentation patterns,

spectra were distinguished from others in the homologous series. Moreover, the alkane spectra
were appropriately associated to, and discriminated from, normal and branched alkanes in a
standard reference library at the 99.9% confidence level.
The statistical method was further investigated using salvinorin A, the hallucinogenic
compound in the plant Salvia divinorum. Spectra of salvinorin A were statistically associated to

those of salvinorin A standards, with RMP values ranging from 10

-126

to 10

-134

, and were

distinguished from spectra of salvinorins B, C, and D at the 99.9% confidence level. Statistical
association of salvinorin A spectra from eight different geographical locations was possible at
90.0 to 99.9% confidence levels, with RMP values ranging from 10

-37

to 10

-126

, while

discrimination was possible at the 99.9% confidence level for salvinorins B and C and 99.0 to
99.9% for salvinorin D. In addition, 441 different Salvia species and varieties were screened for
salvinorin A using the developed method. Mass spectra of compounds with similar retention
times were statistically discriminated from salvinorin A at the 99.9% confidence level.
Lastly, mass spectra of amphetamine, methamphetamine, 3,4methylenedioxyamphetamine (MDA), 3,4-methylenedioxymethamphetamine (MDMA),
phentermine, and psilocin case samples (n = 36) were collected by an accredited forensic
laboratory using their routine procedures. Using the developed method, these spectra were
statistically associated to corresponding reference standards at the 99.9% confidence level, with
RMP values ranging from 10

-37

to 10

-41

. The spectra of the case samples were discriminated

from other reference standards at the 99.0% or 99.9% confidence level. Moreover, the case
samples were appropriately associated to, and discriminated from, spectra in a standard reference
library at the 99.0% or 99.9% confidence level.
Therefore, a method was developed for assigning statistical significance to the
comparison of mass spectra that is simple and rapid. This method may be useful for industrial
quality control as well as for many regulatory applications, such as identification of
environmental pollutants, food and drug contaminants, and controlled substances.

ACKNOWLEDGMENTS

“Life, we learn to late, is in the living, in the tissue of every hour and every day.”
-Stephan Leacock
I would like to thank those who walked beside me in life and shaped me through
relationships and interactions: first my husband, Tristan, without whom I would have lost
focus of the bigger picture of life many times along this journey. He reminded me that life is
for the living now, not after you finish the next paper or spreadsheet. To my sister, Amanda,
who was an invaluable help in the last leg of the journey- may all the milk Seth spilled on
you be a blessing on your own journey. To my Father and Mother who initiated in me a
deep desire to learn and appreciate the intricacies of our universe. To those who offered
daily support, encouragement, and perspective- Megan, Beth, David, Amy and the rest of
the Wkyes Family, Betsy, the rest of my siblings and countless others. To both my sons,
Soren and Seth, whom are gifts I’m sure God gave to teach me how to laugh. And special
thanks to my two principle investigators Ruth Waddell Smith and Victoria McGuffin who
challenged me to continue to learn, to truly think critically, and who encouraged me to keep
going during the times I was uncertain I could finish.

iv

TABLE OF CONTENTS

LIST OF TABLES

viii

LIST OF FIGURES

xiii

CHAPTER 1-INTRODUCTION
1.1 Existing Methodologies for Forensic Identification of Controlled Substances
1.1.1 Limitations of Existing Methodologies
1.2 Review of Prior Research on Statistical Matching
1.2.1 Similarity Indices for Spectral Matching
1.2.2 Deoxyribonucleic Acid Profiling
1.3 Research Objectives
REFERENCES

1
3
6
7
7
21
24
27

CHAPTER 2- DEVELOPMENT AND APPLICATION OF A STATISTICAL
APPROACH TO ESTABLISH EQUIVALENCE OF UNABBREVIATED MASS
SPECTRA

31

2.1 Introduction
2.2 Statistical Theory
2.2.1 Unequal Variance t-Test
2.2.2 Random-Match Probability
2.2.3 Pearson Product Moment Correlation Coefficients
2.3 Experimental
2.3.1 GC-MS Analysis
2.3.2 Data Analysis
2.4 Results and Discussion
2.4.1 Similarity of Spectra
2.4.2 Match Determination of the Same Alkane
2.4.3 Match Determination of Different Alkanes
2.4.4 Match Determination of Alkylbenzenes
2.4.5 Effect of Ionizing Voltage on Association and Discrimination
2.4.6 Effect of Concentration on Association and Discrimination
2.4.7 Effect of Predicted Standard Deviation on Association and Discrimination
2.4.8 Retention Time Differentiation
2.4.9 Comparison to NIST Standard n-Alkanes
2.4.10 Comparison to NIST Standard Branched Alkanes
2.4.11Comparison of SAEEUMS to NIST Library Search Algorithm
2.5 Conclusions
2.6 Summary of Final Method
2.6.1 Considerations
2.6.2 Data Analysis
2.6.3 Output
REFERENCES

31
32
32
34
36
37
37
38
41
41
44
46
50
50
53
61
71
71
73
81
82
83
83
83
87
89

v

CHAPTER 3- STATISTICAL COMPARISON OF MASS SPECTRA FOR
FORENSIC IDENTIFICATION OF AMPHETAMINE-TYPE STIMULANTS
3.1 Introductions
3.2 Materials and Methods
3.2.1 Sample Preparation
3.2.2 GC-MS Analysis
3.2.3 Data Analysis
3.3 Results and Discussion
3.3.1 Similarity of Amphetamine-type Stimulants
3.3.2 Differentiation of Case Samples Based on Retention Time
3.3.3 Statistical Association of Case Samples to Reference Standards
3.3.4 Statistical Discrimination of Reference Standards and Case Samples
3.3.5 Comparison to NIST Standards
3.4 Conclusions
REFERENCES
CHAPTER 4- STATISTICAL COMPARISON OF MASS SPECTRA FOR
FORENSIC IDENTIFICATION OF SALVINORIN A
4.1 Introduction
4.2 Materials and Methods
4.2.1 Salvinorin A Standards
4.2.2 S. divinorum Samples
4.2.3 Other Salvia Samples
4.2.4 Extraction Methods
4.2.5 GC-MS Analysis
4.2.6 Data Analysis
4.3 Results and Discussion
4.3.1 Statistical Association of Salvinorin A
4.3.2 Statistical Discrimination of Salvinorin A from Salvinorins B, C, and D
4.3.3 Statistical Association of Salvinorin A from Different Geographical Locations
4.3.4 Statistical Discrimination of Salvinorin A from Compounds Present in Other
Salvia Species
4.4 Conclusions
4.5 Acknowledgements
REFERENCES
CHAPTER 5- CONCLUSIONS AND FUTURE WORK
5.1 Development and Validation of a Statistical Approach to Establish Equivalence of
Unabbreviated Mass Spectra
5.2 Statistical Comparison of Mass Spectra for Forensic Identification of AmphetamineType Stimulants
5.3 Statistical Comparison of Mass Spectra for Forensic Identification of Salvinorin A
5.4 Future Work
REFERENCES

vi

91
91
93
93
94
96
99
99
101
101
104
112
116
118

121
121
124
124
125
127
127
128
130
133
133
135
140
146
153
154
155
158
158
160
162
165
168

APPENDICES
Appendix A- Confidence Level Consideration for the Unequal Variance t-Test
Appendix B- Normalization
Appendix C- Threshold Determination
Appendix D- Supplemental Data Tables for Chapter 2
Appendix E- Retention Time Differentiation
Appendix F- Supplemental Data Tables for Chapter 3
REFERENCES

vii

170
171
175
177
187
211
214
218

LIST OF TABLES

Table 1.1 The probability-based matching (PBM) abundance, Aj, and dilution, D, factors based
on relative abundance ranges of either the reference spectrum or the abundance of the reference
spectrum base peak relative to the sample spectrum base peak, respectively [7].
13
Table 2.1. Average Pearson product moment correlation (PPMC) coefficients summarizing
the comparison of the alkane mass spectra from Sets 1 and 2. Each comparison of the same
alkane is an average of 45 PPMC coefficients, while each comparison of different alkanes is
an average of 100 PPMC coefficients (1770 total comparisons). The full tables are in
Appendix D, Table A4.
42
Table 2.2. Average Pearson product moment correlation (PPMC) coefficients summarizing
the comparison of propylbenzene, butylbenzene, amylbenzene, and hexylbenzene mass
spectra from Sets 1 and 2. Each comparison of the same alkylbenzene is an average of 45
PPMC coefficients, while each comparison of different alkylbenzenes is an average of 100
PPMC coefficients (780 total comparisons). The full tables are in Appendix D, Table A5. 43
Table 2.3. Random-match probability (RMP) for comparison of the same alkane in Set 1
and Set 2 using a t-test at the lowest confidence level (CL) for which association was
maintained. Confidence levels of 98.0, 99.0, and 99.9% were investigated.

45

Table 2.4 Ions responsible for discrimination of alkanes (t-test, 99.9% CL) in Set 1 and Set
2
47
Table 2.5. Number of discriminating ions for comparison of alkylbenzenes in Set 1 and Set
2 (t-test, 99.9% CL). Zero discriminating ions indicate complete association and the
corresponding random-match probability is shown in parentheses.
51
Table 2.6. Effects of ionizing voltage on the total number of ions at 1 mM concentration.

52

Table 2.7. Effects of ionizing voltage on the number of discriminating ions of Set 1 alkanes
compared to the corresponding alkane in Set 2 (t-test, two tailed, 99.9%) at 1 mM
concentration. Zero discriminating ions indicate complete associations and the
corresponding random-match probability is shown in parentheses. Entries in red highlight
dissociation where not expected. For interpretation of the references to color in this and all
other tables or figures, the reader is referred to the electronic version of this dissertation.
54
Table 2.8. Effect of concentration and base peak abundance on the number of discriminating
ions for the comparison of C10 in Set 1 to all alkanes in Set 2 (t-test, 99.9% CL). Zero
discriminating ions indicate complete association and the corresponding random-match

viii

probability is shown in parentheses. Entries in red highlight unexpected association or
discrimination.

56

Table 2.9. Effect of lower concentration and base peak abundance on the number of
discriminating ions for the comparison of C10 in Set 1 to all alkanes in Set 2 (t-test, 99.9%
CL). Zero discriminating ions indicate complete association and the corresponding randommatch probability is shown in parentheses. Entries in red highlight unexpected association
or discrimination.
57
Table 2.10. Average Pearson product moment correlation (PPMC) coefficients summarizing
the effect of concentration on Set 1 alkane mass spectra at five concentrations (0.05, 0.1,
0.5, 1.0, 5.0 mM). Each comparison of the same concentration is an average of 3 PPMC
coefficients, while each comparison of different concentration is an average of 9 PPMC
coefficients (630 total comparisons). The full tables are in Appendix D, Table A6.
60
Table 2.11. Effect of concentration and base peak abundance on the number of
discriminating ions for comparison of C10 in Set 1 compared to all alkanes in Set 2 (t-test,
99.9% CL) using predicted standard deviation. Zero discriminating ions indicate complete
association and the corresponding random-match probability is shown in parentheses. The
full tables are in Appendix D, Table A7.
67
Table 2.12. Effect of confidence level (CL) on the number of discriminating ions (# Ions) in
the comparison of 1 mM C10 (Set 1) to 1 mM C11 (Set 2).
70
Table 2.13. The number of discriminating ions for the pair-wise comparison of Set 1 alkanes
to the National Institute of Standards and Technology (NIST) database alkanes (one sample
t-test, 99.9% CL unless otherwise specified). Zero discriminating ions indicate complete
association and the corresponding random match probability is shown in parentheses.
Entries in red highlight unexpected association or discrimination.
72
Table 2.14. The number of discriminating ions for the pair-wise comparison of 1 mM Set 1
normal (n) alkanes to the National Institute of Standards and Technology database branched
alkanes (one sample t-test, 99.9% CL unless otherwise specified, 180 total comparisons).
74
Table 2.15. Representative examples of m/z values and general trends of ions responsible for
discrimination of 1 mM Set 1 normal alkanes to C10 branched alkane isomers from the
National Institute of Standards and Technology database, using a two-tailed Student’s t-test
at the 99.9% confidence level.
78
Table 2.16. Pearson product moment correlation (PPMC) coefficients comparing 1 mM Set
1 normal alkanes to branched alkane isomers from the National Institute of Standards and
Technology (NIST) database (180 total comparisons).
80
Table 2.17. The SAEEUMS random-match probability (RMP), after the t-test indicated
complete association at the 99.9% confidence level, and the corresponding Match Factor
and Probability from the NIST library search database for the comparison of Set 1 alkanes at
1mM compared to the NIST n-alkane standards.
82
ix

Table 3.1. Date of analysis and retention time (tR) of reference standards and case samples
of amphetamine, methamphetamine, MDMA, MDA, phentermine, and psilocin mass
spectra.
95
Table 3.2. A summary of Pearson product moment correlation (PPMC) coefficients for 1128
total comparisons of case samples and reference standards of amphetamine (Amp),
methamphetamine (Meth), MDMA, MDA, phentermine (Phent), and psilocin mass spectra.
The maximum (Max), minimum (Min), average (Avg) ± standard deviation, and number of
comparisons (n) are shown.
102
Table 3.3. Random-match probability for reference standards of amphetamine,
methamphetamine, MDMA, MDA, phentermine, and psilocin compared to respective case
samples, using a two-tailed Student’s t-test at the 99.9% confidence level. The sample case
identity is that assigned by the forensic laboratory.
105
Table 3.4. Number of ions responsible for discrimination of amphetamine,
methamphetamine, MDA, MDMA, phentermine, and psilocin case samples from reference
standards (t-test, two tailed) at the highest confidence level (CL) that discrimination was
maintained, 99.9% CL unless otherwise specified.
107
Table 3.5. Representative examples of m/z values and general trends of ions responsible for
discrimination of amphetamine, methamphetamine, MDA, MDMA, phentermine, and
psilocin case samples from reference standards, using a two-tailed Student’s t-test at the
99.9% confidence level (unless otherwise specified).
110
Table 3.6. The number of discriminating ions for the pair-wise comparison of case samples
to standards from the National Institute of Standards and Technology (NIST) database (one
sample t-test, 99.9% CL unless otherwise specified). Zero discriminating ions indicate
complete association and the corresponding random-match probability is shown in
parentheses. Entries in red highlight unexpected association or discrimination.
113
Table 4.1. Sample information for S. divinorum used in this study.

126

Table 4.2. Gas chromatography-mass spectrometry parameters used throughout this study. 129
Table 4.3. Random-match probability (RMP) calculated for pair-wise comparisons of
salvinorin A extracted from S. divinorum and five salvinorin A reference standards (t-test,
two tailed, 99.9%).

134

Table 4.4. Ions responsible for discrimination in the comparison of salvinorin A from
Extract 1 to salvinorins B, C, and D from Extract 1 (t-test, 99.9% confidence level).

139

Table 4.5. Random-match probability (RMP) of salvinorin A extracted from S. divinorum
samples at the lowest confidence level (CL) that association was maintained. Average
number of ions in the triplicate spectra and the number of ions present just above the
instrumental threshold in one spectrum and below it in the other (Above/Below Threshold)
are also shown. The t-test was performed at confidence levels of 90.0, 95.0, 98.0, 99.0, and
99.9%. Extract and analysis information is provided in Tables 4.1 and 4.2.
142
x

Table 4.6 Number of discriminating ions for pair-wise comparisons of Extracts 6 - 12 at the
lowest confidence level that association was maintained (99.9% confidence level unless
otherwise specified). The t-test was performed at confidence levels of 80.0, 90.0, 95.0, 98.0,
99.0, and 99.9%. Zero discriminating ions indicate complete association and the
corresponding random-match probability is shown in parentheses. Extracts 6 and 7 were
analyzed on the same instrument and Extracts 8 - 12 were analyzed on the same instrument
(Table 4.2).
143
Table 4.7. Number of ions responsible for discrimination in the comparison of salvinorin A
from Extracts 1 - 13 to salvinorins B, C, and D from Extract 1 (t-test, two tailed) at the
highest confidence level (CL) that discrimination was maintained. The t-test was performed
at the 99.9% CL, unless otherwise specified. Extract and analysis information is provided in
Tables 4.1 and 4.2.
145
Table 4.8. Salvia species and number of discriminating ions (# Ions) of compounds eluting
within ± 0.2 min of salvinorin A (retention time, Tr, 17.142 min). The t-test was performed
at the 99.9% confidence level, unless otherwise specified.
147
Table A1. Average PPMC coefficients (n = 16) for C10, C11, C12, C13, C14, and C16 at 05% thresholds. Bolded average, maximum value (Max) and standard deviation (SD) are
representative of all pair-wise comparisons of different alkanes (240 total comparisons).

180

Table A2. Average PPMC coefficients of pair-wise comparisons of the same alkane (n = 10
each) for C10, C11, C12, C13, C14, and C16 at 4% threshold (60 total comparisons).
183
Table A3. The threshold versus the number of ions for each alkane models a first order
logarithmic decay relationship (Equation A4). Variable A relates to the number of ions in
2
the spectrum, B is the offset, t-value is the rate of exponential decay, and R is the degree of
fit.
185
Table A4. Pearson product moment correlation (PPMC) coefficients comparing different
alkane mass spectra from Sets 1 and 2 at five concentrations (0.05, 0.1, 0.5, 1.0, 5.0 mM).
Set 1 mass spectra are italicized.

188

Table A5. Pearson product moment correlation (PPMC) coefficients comparing
propylbenzene (P), butylbenzene (B), amylbenzene (A), and hexylbenzene (H) mass spectra
from Sets 1 and 2 at five concentrations (0.05, 0.1, 0.5, 1.0, 5.0 mM). Set 1 mass spectra are
italicized.
197
Table A6. Pearson product moment correlation (PPMC) coefficients comparing the effect of
concentration on three replicates (a, b, c) of C10 mass spectra at five concentrations (0.05,
0.1, 0.5, 1.0, 5.0 mM) from Set 1.
202
Table A7. Effect of concentration on the number of discriminating ions for pair-wise
comparison of Set 1 alkanes compared to all alkanes in Set 2 (t-test, 99.9% CL) using
predicted standard deviation. Zero discriminating ions indicate complete association and the
xi

corresponding random-match probability is shown in parentheses. Entries in red highlight
unexpected association or discrimination.

208

Table A8. Retention time of replicates (n = 21) of alkanes and the tolerance accepted by the
Arkansas Forensic Laboratory [4].
213
Table A9. Pearson product moment correlation (PPMC) for 1128 total pair-wise
comparisons of case samples and reference standards of amphetamine (Amp),
methamphetamine (Meth), MDMA, MDA, phentermine (Phent), and psilocin mass spectra. 215

xii

LIST OF FIGURES

Figure 2.1 Logarithmic graph of standard deviation versus abundance for all ions in
replicate mass spectra of alkanes (90 spectra, 1237 ions). Solutes C10, C11, C12, C13, C14,
and C16; concentrations 0.05, 0.1, 0.5, 1.0, 5.0 mM; ionizing voltage 70 eV.

63

Figure 2.2. Logarithmic graph of standard deviation versus abundance for all ions in
replicate mass spectra of alkanes (90 spectra, 1237 ions). Solutes C10, C11, C12, C13, C14,
and C16; concentrations 0.05, 0.1, 0.5, 1.0, 5.0 mM; ionizing voltage 70 eV. Manual fit of
two linear equations with a slope of 0.5525 and intercept of 0.9211 for the data with lower
standard deviations and a slope of 0.8405 and an intercept of and -0.2311 for the data with
higher standard deviations.
64
Figure 2.3. Logarithmic graph of standard deviation versus abundance for all ions in
replicate mass spectra of alkanes (90 spectra, 1237 ions). Solutes C10, C11, C12, C13, C14,
and C16; concentrations 0.05, 0.1, 0.5, 1.0, 5.0 mM; ionizing voltage 70 eV. Linear best fit
line of slope 0.6900 ± 0.0332 and intercept 0.0440 ± 0.0093.
65
Figure 2.4. Relative abundance mass spectra of C10 isomers (A) n-decane, (B) 3methylnonane, (C) 2,3-dimethyloctane, (D) 2,4,6-trimethylheptane, (E) 2,2,5,5tetramethylhexane, and (F) 4-ethyloctane. Chemical structures shown as inserts.

76

Figure 3.1. Logarithmic graph of mean abundance versus standard deviation for mass
spectra of MDMA (15 spectra, 502 ions). Linear best fit line with slope 0.6922 ± 0.0156 and
intercept 0.3238 ± 0.0632.
97
Figure 3.2. Logarithmic graph of mean abundance versus standard deviation for mass
spectra of MDMA (16 spectra, 855 ions). Linear best fit line with slope 0.7139 ± 0.0210 and
intercept 0.1086 ± 0.0839.
98
Figure 3.3. Relative abundance mass spectra of (A) amphetamine, (B) methamphetamine,
(C) MDA, (D) MDMA, (E) phentermine, and (F) psilocin. Chemical structures shown as
inserts.

100

Figure 4.1. Chemical structure of salvinorins A, B, C, and D. Salvinorin A (R = OCOCH3),
salvinorin B (R = OH), salvinorin C (R1 = OCOCH3; R2 = OCOCH3), salvinorin D (R1 =
OH; R2 = OCOCH3).

123

Figure 4.2. Logarithmic graph of mean abundance versus standard deviation for mass
spectra of salvinorin A extracts and reference standards (36 spectra, 5136 ions). Linear best
fit line with slope 0.5327 ± 0.0045 and intercept 0.8107 ± 0.0180.
131

xiii

Figure 4.3. Logarithmic graph of mean abundance versus standard deviation for mass
spectra of salvinorin A extracts and reference standards (34 spectra, 7084 ions). Linear best
fit line with slope 0.5123 ± 0.0063 and intercept 0.7482 ± 0.0251.
132
Figure 4.4. Mass spectra of A) Salvinorin A, B) Salvinorin B, C) Salvinorin C, and D)
Salvinorin D.

136

Figure A1. Area under normal distribution density curves for two populations, 1 and 2, at
various confidence levels, where Z is the z-score, x is the respective sample value, μ is the
sample mean, and σ is the standard deviation.

173

Figure A2. Decay relationship of number of ions versus threshold for C10, C11, C12, C13,
C14, and C16 spectra.

184

xiv

CHAPTER 1
INTRODUCTION
In many legal and regulatory applications, evidence must be presented with statistical
assessment of its validity. Statistical methods are well established for the comparison of
deoxyribonucleic acid (DNA) samples, which are routinely used in court testimony [1]. For other
types of evidence, statistical assessment is not yet available, as highlighted in a report published
by the National Academy of Sciences National Research Council (NRC) [2]. In particular, mass
spectrometry (MS) is extensively used for the identification of controlled substances, ignitable
liquid residues, and other types of chemical evidence in forensic science [1]. In addition, the
Environmental Protection Agency (EPA) and the Food and Drug Administration use mass
spectrometry for the identification of contaminants in the environment, food, tobacco,
pharmaceuticals, etc [3,4]. Yet, in current methods, the identification is not supported by
statistical assessment of the veracity by means of confidence levels or error rates. Such an
assessment would address the NRC recommendations and be a timely advance not only for legal
and regulatory applications, but for any application in which objective validation is desired.
Figures of merit to describe the similarity of mass spectra are well established. For
example, indices based on the dot product, composite similarity, probability-based matching,
Hertz similarity, as well as Euclidean and absolute value distances have been developed [5-9].
These indices can rapidly identify the most likely identity of an unknown or questioned sample
by comparison to standard mass spectra in a database. A single number, a similarity index (SI),
is provided as a measure of the similarity of the mass spectra, however, no confidence level or
error rate associated with the mass spectral identification is included. In forensic science,
caution is advised against using the SI to evaluate the accuracy of the identification [10]. Such
1

indices do not provide a statistical confidence in the identification of the compound, as required
by the Daubert standard for the admissibility of evidence [11]. Therefore, for legal or regulatory
purposes, a further statistical test is needed to establish whether the tentative identification, as
indicated by the SI, is correct. In addition, when a questioned sample is compared to a reference
standard, the same type of statistical test is needed. This test must answer the question “is the
mass spectrum of the unknown or questioned sample identical to (i.e., statistically
indistinguishable from) that of the database or reference standard, at a given confidence level?”
In the present work, a method, called the statistical approach to establish equivalence of
unabbreviated mass spectra, is developed to serve this purpose.
The proposed method is composed of two major phases. Initially, statistical hypothesis
testing, in the form of an unequal variance t-test, is applied to the mean abundances, normalized
to the base peaks, at every mass-to-charge (m/z) value acquired in the mass spectra This t-test is
used to determine if the spectra are statistically indistinguishable at a given confidence level.
Then, if the spectra are indistinguishable, the random-match probability (RMP) is calculated
based on the frequency of ion occurrence at each m/z value in a selected database. Randommatch probabilities, calculated in a related manner, are conventionally used in forensic science
for DNA profiling and are already accepted for use in court testimony [1]. In the present case,
the RMP assesses the probability that the characteristic fragmentation pattern of the two mass
spectra would occur by random chance alone, which may provide a helpful context for a jury.
The proposed method utilizes every m/z value in the mass spectrum to establish the
identity of the unknown or questioned sample. This method allows for a direct comparison of
every data point in the two mass spectra, without a loss of information. Accordingly, low
abundance ions, including characteristic high-mass ions such as the molecular ion, can provide

2

vital information to discriminate spectra [12]. The proposed method can reduce false positive
and negative identification and provide stronger statistically based interpretation of evidence for
court testimony. In addition, this objective comparison of mass spectra and the associated
confidence level will provide the error rate required by the Daubert standard and begin to
address the recommendations in the NRC report [2,11]
This chapter discusses the existing methods used in spectral matching for one evidentiary
application: forensic controlled substance identification. As similarity indices are the most
common metric used for spectral matching, a review of the applicable literature and the
advantages and disadvantages of this approach are also discussed. As DNA profiling is an
already accepted example of using probability statistics, specifically random-match probabilities,
in a judicial setting, this approach is also explained in detail. Finally, the research objectives and
an overview of the work described in this dissertation are presented.
1.1

Existing Methodologies for Forensic Identification of Controlled Substances
Controlled substance analysis procedures and requirements for identification are not

currently standardized across forensic laboratories. However, the Scientific Working Group for
the Analysis of Seized Drugs (SWGDRUG) is working towards standardized recommendations
[13]. In addition, laboratories have the option of becoming accredited through the American
Society of Crime Laboratory Directors/Laboratory Accreditation Board (ASCLD/LAB), which
requires standard operating procedures (SOPs) be in place for each laboratory and be reviewed
annually [14]. Summarized below are general requirements and examples of SOPs from forensic
laboratories controlled substance divisions.

3

The positive results of at least two analytical techniques are recommended by
SWGDRUG for reporting the definitive forensic identification of a controlled substance [13].
Identification is generally accomplished through either a presumptive test (identifies the class of
substance) or a selective test (tentative identification of substance), combined with a
confirmatory test (definitive identification). Gas chromatography is classified as a selective test
and mass spectrometry as a confirmatory test; hence, the combination of GC-MS is suitable for
the identification of most controlled substances that are sufficiently volatile to be analyzed using
this technique. In forensic science, GC-MS is considered the “gold standard” and is a near
universal test for controlled substance identification [2,14].
The specific requirements for the definitive mass spectral identification of a controlled
substance sample vary depending on the SOPs of the individual forensic laboratory and the
controlled substance in question. In general, however, the questioned sample and reference
standard are analyzed by GC-MS using the same instrument parameters (stationary phase, flow
rate, temperature program, etc.). Depending on the SOP, the mass spectrum of the questioned
sample and/or retention time are either visually compared to the mass spectrum and retention
time of the reference standard and/or to the mass spectrum of a library database. An in-house or
commercially available library database can be used to assist the analyst in identification.
However, in most cases, caution is advised against using a similarity index (SI) calculated by the
library search algorithm as an evaluation of the match for reasons discussed in Section 1.2.1 [11].
Summaries of SOPs for three ASCLD/LAB accredited laboratories are given below as
demonstrations of the variability in match determination requirements among forensic
laboratories. For example, the Arkansas State Laboratory specifies that the retention time of the
questioned sample can be compared to the retention time of the reference standard if the signal4

to-noise (S/N) ratio of the analyte peaks in both chromatograms are greater than 10 [15]. The
relative retention times are considered a match when they are within ± 2% if the retention time is
≤ 3 minutes or ± 1% if the retention time is > 3 minutes [15]. The mass spectrum of the
questioned sample and the reference standard are considered a match if a) the analyte peak in the
chromatogram was not present in the solvent blank, b) both the questioned sample and reference
standard spectra show the molecular ion of the analyte, if normally seen for that substance, c) all
the ions greater than 10% of the base peak of the reference standard spectrum are also present in
the questioned sample spectrum, and d) no additional peaks greater than 10% the base peak are
present in the questioned sample spectrum that are not in the reference standard spectrum [15].
Please note, it is rare in forensic laboratory SOPs to describe the means of selection or means of
validation for parameters, such as the criteria reported in the above SOP.
The most reliable statistical comparisons are obtained when spectra are collected
sequentially from the same instrument using the same experimental conditions. This minimizes
experimental and instrumental variations, thereby allowing the chemical variations in the spectra
to be more apparent. In some forensic laboratories however, the questioned sample and reference
standard may not be analyzed sequentially or even on the same day [16]. For example, in the San
Francisco Crime Laboratory, reference standards are analyzed once upon arrival in the
laboratory, and the corresponding GC-MS data are placed in a logbook. The questioned sample
is compared to a spectral library database for identification of the questioned sample. Visual
comparison to the reference standard spectra in the logbook occurs if no match was found in the
library database [16]. Again, the criteria for an acceptable match in the library database were not
specified in the SOP and may be determined by the individual analyst.

5

In other laboratories, the analyst may choose whether to compare to a spectral library
database or to reference standards analyzed within the same 24 hour period as the questioned
sample [17]. Spectra of the questioned sample are to be compared with either 1) a reference
standard spectrum run under the same conditions and within a 24-hour period, 2) to an in-house
or reputable library spectrum, or 3) to a published spectrum. For definitive mass spectral
identification, all major peaks must have associated

13

C isotope peaks present above the

threshold. Some specific controlled substance are required to have the molecular ion [M]+
present (e.g.,cocaine, heroine, lysergic acid diethylamide) while others are required to have the
[M-H]+ ion present (e.g.,amphetamines) [17]. If each of these criteria is fulfilled, the questioned
sample is considered a positive identification with the reference standard.
1.1.1 Limitations of Existing Methodologies
Lack of standardization in the requirements for analysis and the subjectivity in
identification of controlled substances is a problem that is receiving attention in forensic science
after the NRC Report [2]. As demonstrated in the SOPs described above, controlled substance
laboratories may not be required to analyze a reference standard sequentially with the questioned
sample for comparison. However, sensitivity loss and instrumental drift in ion abundances are
common in GC-MS systems, which can lead to mass spectra that vary considerably when
analyzed over time [6,18]. The variations that result from non-sequential analysis of the
questioned sample and reference standards mass spectra could result in inaccurate mass spectral
identification.
Even in the SOPs with the most rigorous requirements for identification, the spectra are
visually compared, which introduces subjectivity into the identification. Yet subjectivity in the
6

interpretation of mass spectral results is a basis for rejection of scientific testimony [19]. In
addition, controlled substance laboratories may not be required to compare a reference standard
mass spectrum to the questioned sample. For some laboratories, the comparison to a library
database using the SI algorithm evaluation is considered sufficient [16]. However SIs are not
optimal for sole evaluation of a questioned sample or for reporting statistical comparisons in
forensic science, and a discussion of the inherent limitations are given in Section 1.2.1.
1.2

Review of Prior Research on Statistical Matching
No method currently exists in forensic science for assigning a statistical confidence for

the mass spectral comparison of a questioned sample to a reference standard. However, a related
approach for scoring the quality of a match between an unknown spectrum and a spectrum in a
reference database has been well established in the field of mass spectrometry [5-9,21-24]. In
this section, select methods will be introduced and the advantages and limitations for reporting a
statistical measure for mass spectral identification of controlled substances will be discussed. In
addition, DNA profiling is an already accepted use of RMP in court testimony, therefore
applicable to this work. The relevant research on each of these topics will be discussed in more
detail below.
1.2.1 Similarity Indices for Spectral Matching
Three main approaches have been developed to minimize the effort needed for
identification of an unknown based on its mass spectrum: learning machines, artificial
intelligence, and library searching [6,18]. The learning machine and artificial intelligence
methods are primarily for identifying molecular substructures from spectra and are used in
proteomics for the assignment of protein and peptide identities, where the substructural diversity
7

is largely limited to 20 amino acids [6,18]. Of more interest to this work is the library searching
method, in which an unknown spectrum is matched to a spectrum in a reference database and a
SI is calculated to evaluate that match. The search algorithm is used to identify the spectra in the
database that most closely resemble the unknown spectrum based on the SI, and the “matching”
spectra are listed in numerical order from highest to lowest SI. This latter approach is more
common for identification of small molecules such as natural products, drugs of abuse, and
volatile petroleum products that are amenable to separation by gas chromatography.
The initial mass spectral search algorithms, developed in the 1950s and 1960s, were
designed to minimize storage requirements and search time because of limitations of the existing
computer processing power. Mass spectra were often abbreviated to a certain number of peaks,
commonly the most abundant ions. Several similar methods have compared the presence or
absence of specific m/z values among the n most abundant ions of an unknown spectrum and a
reference spectrum [8,9,20,21]. For example, Abrahamsson et al. compared the five most
abundant mass spectral ions in both an unknown and reference spectrum and calculated a SI by a
sum of the difference of the abundances, normalized to the base peak, of the two spectra at each
m/z value [20]. However, if only the most abundant ions are used to calculate the SI,
discriminatory low abundance ions, such as the molecular ion, may not be included in the
comparison. Crawford et al. calculated a SI in a similar manner using the six most abundant
mass spectral peaks and using various normalization procedures for all observed peak
abundances [9]. When spectra are normalized by using a single peak (e.g. base peak
normalization), the effect of random and/or systematic error in peak abundance is increased, as
any error in that peak will be applied to the entire normalized spectrum. However, when the
spectra are normalized by using the sum of all peak abundances, the relevance of lower
8

abundance peaks is increased and the effect of random and/or systematic error in peak
abundance is minimized [9].
Another variation for calculating the SI is to divide the spectrum into sections of 14 mass
unit intervals (the mass of a methylene group). The two most abundant peaks in each interval are
retained to form an abbreviated spectrum [8]. The benefit of this method is that the molecular ion
(if present) is more likely to be included, as it may be among the highest abundance peaks in the
relevant interval. Hertz et al. calculated the SI by taking the ratio of the abundances at matching
m/z values in the abbreviated known and unknown mass spectra [8]. In this manner, ratios
ranged from 1.00 for complete agreement to 0.00 for complete disagreement. The ratios were
weighted by factors of 1, 4, and 12 depending on whether the larger abundance making up the
ratio was < 1%, 1 - 10%, or > 10% relative abundance, respectively. The authors state that the
weighted factors were empirically determined, but gave no further details. The weighted ratios
were then divided by the fraction of the peak abundances that did not have corresponding m/z
values in the reference spectrum over the sum of the abundances in the unknown spectrum.
Knock et al. developed and compared four methods for matching an unknown spectrum
to a reference spectrum [21]. In the first method, the m/z values of the user-defined n most
abundant peaks are compared and the SI given by

SI =

(1.1)

where M is the number of common m/z values between the two spectra. In the second method, to
increase the specificity, the m/z values in each mass spectrum are ranked in order of decreasing

9

relative abundance (i.e., the base peak of each mass spectrum would have rank 1). The SI is
given by

SI =

(1.2)

where s and t are the respective ranks in the unknown and reference spectra, at m/z value, j. The
third method involves dividing the spectrum into R equal m/z intervals. The SI is then given by

SI =

(1.3)

The fourth method combines the interval sectioning of the mass spectrum of Method 3 and a
compensating factor for the differences in the order of the matches of Method 2, and the SI is
given by

SI =

(1.4)

Methods 3 and 4 were designed to compensate for possible mass spectral differences, such as
abundances of specific ions, due to different instruments. Knock et al. reported that tests of
unknown compounds against a reference database containing 8000 spectra resulted in the correct
compound matched first with 93% of the trials when Methods 1 and 3 were used, whereas every
trial was successful using Methods 2 (n = 20) and 4 (n = 3 and m = 20) [21]. Several variations
for the values of n and m were investigated but were not found to have significantly different
results.
Each of the methods for calculating SI described to this point have been based on the
most abundant ions in the mass spectra. In addition, most of these methods use an abbreviated
10

spectrum to increase computing efficiency. However, using an abbreviated spectrum of only the
most abundant ions assumes that such ions are the most characteristic and, hence, representative
of the compound. This is not always the case, as higher mass ions are often more characteristic,
even at lower abundances, as explained below [12].
McLafferty et al. developed a probability-based matching (PBM) system for examining a
mass spectrum of a mixture for the presence of a specific compound [7]. Each m/z value in an
abbreviated spectrum was weighted according to the uniqueness of the m/z value and the relative
abundance of ions with the m/z value in the reference database [7]. A database of 18,806
compounds was examined and the probability of an abundance occurring was found to follow a
log-normal distribution. Under the energetic conditions of 70 eV electron ionization, high
molecular mass ions usually fragment to produce ions at lower m/z values. Therefore, high m/z
value ions were found to be less common and more characteristic of the compound. In addition,
the probability of a particular m/z value occurring in a spectrum decreases by a factor of two
approximately every 130 u [7].
The probability that the mass spectrum was due to the specific compound was calculated
as
SI =

(1.5)

where Uj is a value representing the uniqueness of the m/z value of peak j, Aj is a value
representing the abundance of the peak in the reference spectrum, D is the purity of the mass
spectrum, and Wj is the window factor which is a measure of the agreement between the
abundance of the peak in the unknown spectrum and the reference spectrum. The uniqueness
11

value, Uj, was calculated by dividing the number of spectra in the database by the number of
spectra that had m/z value, j, at abundance greater than an arbitrary 50% of the base peak. For
m/z 30 - 150, Uj varied from 2 to 10 with most around U = 7, while higher m/z values had higher
Uj values. For peaks < 50% abundance, Aj was assigned (from Table 1.1, based on the relative
abundance of each m/z value in the reference spectrum) to decrease the U value of the peak. In
this manner, both the uniqueness of the m/z value, U, and the uniqueness of the corresponding
relative abundance, A, were incorporated in the SI.
The values of U and A, however, are based on the spectra of pure compounds. However,
if co-elution should occur in GC-MS, the target compound is diluted and the abundance, and
hence the uniqueness, is reduced. Therefore a dilution factor, D, was assigned (from Table 1.1,
based on the abundance of the base peak in the reference spectrum relative to the base peak in
the sample spectrum) to adjust for absolute compound concentration. The dilution factor can be
calculated from user knowledge of the concentration of the target compound in the mixture or
from a default setting (for no co-elution D = 0). The window tolerance, Wj, reflects the range of
the peak abundances allowed in the comparisons of ion abundances. The value for Wj is set in
relation to the reproducibility of the analysis [7]. The PBM algorithm is the default search engine
used in Agilent’s ChemStation software; however, the algorithm has difficulty discriminating
certain compounds, such as aliphatic amines [7,22]. This difficulty could be due to similar
fragmentation patterns and spectra that are dominated by low m/z ions that, as previously
mentioned, may be less discriminating than high m/z ions.

12

Table 1.1 The probability-based matching (PBM) abundance, Aj, and dilution, D, factors based
on relative abundance ranges of either the reference spectrum or the abundance of the reference
spectrum base peak relative to the sample spectrum base peak, respectively [7].
Aj /D
0
1
2
3
4
5

Relative Abundance
Range
50 - 100%
19 - 50%
7.1 - 19%
2.7 - 7.1%
1.0 - 2.7%
0.38 - 1.0%

13

While PBM uses an abbreviated spectrum, a method for calculating a SI called the dotproduct algorithm uses the entire spectrum [6,23]. The dot-product algorithm was developed
from the idea of representing the mass spectrum as an n-dimensional vector, normalized to unit
length. Each m/z value in the spectrum represents a dimension and the corresponding
abundances represent the lengths in that dimension. The magnitude of each normalized vector
then represents a coordinate in multidimensional hyperspace and is therefore represented by a
single point in hyperspace. When two identical spectra are compared, the point representation in
hyperspace will be identical. As the spectra decrease in similarity the point representations will
increase in distance from one another. The SI (known as the Match Factor) is then the inverse of
the distance between the point representations of the two spectra being compared. This concept
was initially given as a technical report [23] but was then developed further into the dot-product
algorithm [6].
The dot-product algorithm calculates the cosine of the angle between the unknown and
library spectral vectors by the scalar product of the two vectors [6]. A scalar product can be
calculated as [24]:

cos θ
where

and

(1.6)

are the lengths of the vectors x and y and θ is the angle between the two

vectors. The length of the vectors can then be calculated as

(1.7)

(1.8)

14

at m/z value, j. The scalar product and the lengths can be calculated using the respective
components of the vectors:
(1.9)

Hence

cos θ

(1.10)

In this manner, the cosine of the angle (dot product) of the vector representations of the spectra
yields a measure of similarity [6].
The dot-product algorithm is used as a measure of spectrum similarity in the National
Institute of Standards and Technology (NIST) Mass Spectral Search Program and the Automated
Mass Spectrometry Deconvolution and Identification System (AMDIS) [25,26]. In addition to
the dot-product algorithm, the NIST Search Program weights each ion by the square root of its
abundance, normalized to the base peak, and compares ratios of adjacent peaks in the unknown
and reference spectra [25]. For an identity search, a further scaling is used where ions are
weighted by the square of their m/z value. In this manner the importance of the ion in the search
increases with higher m/z values, which, as previously discussed, are often more characteristic of
a compound than ions of lower m/z values. The match factors for the NIST Search Program
range from 999 – 0 (i.e., a “perfect” match is defined as 999, > 900 is an “excellent” match, 800 900 is a “good” match, 700 - 800 is a “fair” match, and < 600 is a “very poor” match) [25]. In
addition to a match factor, the NIST Search Program also reports a relative probability of
correctness for each match of an unknown spectrum to the library spectrum. This probability is
15

calculated assuming that the compound is present in the library, from the difference in match
factors between adjacent hits in the match list [25]. Compounds with few similar mass spectra
will have a higher probability than compounds with a greater number of similar mass spectra in
the library [25]. For example, a search for 'decane' will have low probabilities (e.g. < 50%)
because many similar spectra exist in the library database.
Wan et al. compared a SI previously derived by their group to the SI determined using
the dot-product algorithm to differentiate the mass spectra of three pentadeoxynucleotide
structural isomers (TGTTT, TTGTT, TTTGT) and nine artificially generated spectra [5]. Since
nucleotides do not evaporate without decomposition, a soft ionization method, electrospray, was
employed that primarily yields pseudomolecular ions with minimal fragmentation. Multistage
MS, in negative ion mode, was then used to generate fragment ions. Isomers are often
undifferentiable based on their single stage mass spectra, however, each of the isomers
investigated gave a product-ion spectrum that distinguished it from other isomers. The eleven
most abundant peaks (m/z 321, 625, 650, 705, 849, 874, 929, 954, 1009, 1034, and 1178) of eight
replicate spectra were investigated. The SI was calculated for all combinations by

SI =

(1.11)

where x and y are the relative abundances at m/z value, j, for two compounds and n is the
number of peaks compared. The spectral contrast angle (θ) was calculated for all combinations
using Equation 1.10.

16

If the spectra could not be differentiated then θ was equal to zero, while maximum
differentiation was indicated by θ equal to 90˚. In general, the dot-product method had a higher
differentiating ability than the SI method with a lower margin of error. For example in the
comparison of two isomers, the dot product average θ ± the standard deviation was 18.5° ± 0.8°
and the average SI ± the standard deviation was 12.0 ± 1.0 [5].
The SIs previously described and the dot-product method of Wan et al. are still limited by
using only a few of the most abundant ions for characterization of the spectrum. Wan et al. did
not explain why a limited number of ions were used to calculate the dot product, given that
traditionally the entire spectrum is used. In addition, the product-ion spectra were used for
differentiation, which increase the discrimination ability but are not commonly available in
forensic laboratories. Multistage mass spectrometry, while used in this case to discriminate
isomers, is expensive and not routinely used for controlled substance analysis; therefore a
comparison based on product-ion spectra will limit the applicability of the technique in
conventional forensic science.
Olson et al. developed a method to provide a statistical confidence in mass spectral
comparison using the dot-product algorithm [27]. Consensus spectra of 30 replicate MALDI
mass spectra, collected in negative ion mode, of rat and bovine brain tubulin and bovine
testicular tubulin peptides were created [27]. The initial consensus spectra contained only peaks
above a S/N ratio of 5. While this S/N ratio may remove noise ions, the possibility also exists
that low abundance discriminatory ions may also be eliminated. The dot-product algorithm was
applied to all spectra and then, each dot product was converted to a normally distributed variable
via a Fisher transformation

17

(1.12)

where f(x) is a dot product and f(y) is the normally distributed variable [24]. The 95% confidence
interval was calculated for the resulting variables between each of the replicate spectra and the
respective initial consensus spectrum. A second consensus spectrum was created including only
the spectra within the 95% confidence interval of the original consensus spectrum dot product,
thereby filtering out spectra with high background noise. A pair-wise comparison was then
performed between the second consensus spectra dot-product values of rat brain, bovine brain,
and bovine testicular tissue extracts. The dot products of the rat brain compared to the bovine
brain tubulin peptides were found to be within the 95% confidence interval, whereas either of the
brain peptides compared to the testicular peptides were not. The authors noted that brain tubulin
is known to have similar sequencing across species, but different sequencing across tissues in the
same species (e.g. brain and testicular) [27].
Although this method provides a statistical assessment of association, a relatively large
number of replicates (≥ 30) is required for this method, which is impractical for forensic
laboratories. While the use of MALDI would decrease the replicate sampling time, it is not
commonly available in forensic laboratories. In addition, the method of Olson et al. is based on
comparison of spectra using the dot-product algorithm. However, there are limitations in using
any SI algorithm for spectral comparison, as discussed below.
Library searches and their corresponding SI, while useful for a fast comparison of an
unknown spectrum with large databases of reference spectra, are not appropriate for reporting
statistical comparisons in forensic science. The first issue with a library search is that a high SI
does not necessarily mean the compound was identified correctly. A study illustrating this point
18

was performed by Stein et al., who investigated five library searching algorithms (dot product,
Euclidean and absolute value distances, PBM, and Hertz) [6]. A test set of 12,592 spectra (8000
compounds) from the NIST- EPA National Institutes of Health Mass Spectral Database were
searched using these algorithms against reference standards in the database (62,235 compounds)
[6]. The two most common commercially available algorithms are PBM and dot product [6].
The dot-product algorithm uses the spectral contrast angle method described previously, while
the Euclidian distance and absolute value distance are algorithms similar to those proposed by
Crawford et al. [9] and Abrahamsson et al. [20]. Using the dot-product algorithm, the true
identity of the searched compounds was returned as the first compound on the match list in 75%
of cases. Euclidian distance returned the true identity first in 72% of cases, absolute value
distance in 68% of cases, PBM in 65% of cases, and Hertz in 64% of cases [6]. The presence of
sterioisomers in the library database had only a small effect on the search results (~5%).
Differences in experimental and instrumental parameters in the spectra being compared and
limitations in the search algorithms were assumed to be the main contributions to
misidentification. It should be noted that this study was performed prior to the removal of poor
quality spectra in the NIST database during the late 1990s. However, the spectra used in this
study had been selected, according to the authors, on the basis of quality by an experienced
evaluator. No further information on the criteria used for spectral selection was reported;
however this pre-selection narrows the significance of the study to only the “best case”
circumstances [6]. Therefore, even using optimal spectra, database searching may not result in
the true identity of the compound in 25% or more of searches.
In reality, spectra of the same compound could vary considerably when obtained under
different analysis conditions or using different instruments, as is often the case when an
19

unknown spectrum is compared to a reference spectrum. Substantial variations in ion
transmittance can occur when the ion source and lenses become contaminated with material that
acts as a dielectric. In addition, when too many ions are introduced into the source (as occurs
with air leaks), space charge effects cause lower mass ions to be pushed away from the exit
apertures, leading to reduced ion transmission. Differences in the relative ion abundances can
originate from changing or aging of the components (i.e. filament, electron multiplier, etc.) and
contamination of the system (the ionization chamber and focusing lenses in particular), which
can also alter the ion transmittance and lead to spectra that appear different over time [18,22].
These changes can severely affect the ability of an algorithm to match the unknown spectrum to
the corresponding spectrum in the reference database.
In addition, the ability of an algorithm to match an unknown spectrum can be influenced
by coelution, impurities in the solvent, and/or column or septum bleed from the GC or LC. If two
substances elute at similar retention times and are not baseline resolved, there will be overlap in
the mass spectra of the compounds, potentially leading to poor library search results.
Concentration discrepancies between the unknown sample and the database standard, often
observed when crude mixtures are analyzed, can also affect the ability of the algorithm to return
a correct identity. When samples at very low concentrations are analyzed, the mass spectrum
may not be representative as fragment ions of interest may be below the instrument threshold or
masked by background or column bleed. When excessively high concentrations are analyzed,
fragmentation in the ionization chamber of the mass spectrometer may vary due to space charge
effects, leading to a spectrum that is significantly different than the normal spectrum [18]. In
addition, if the concentration is too high, the linear range of the detector may be exceeded,
resulting in variation of the relative abundances of individual ions. Many of these factors are
20

more problematic when comparing spectra collected on different instruments (e.g. unknown
compared to library database spectrum) than when comparing spectra collected sequentially on
the same instrument. For example, impurities in the solvent, column/septa bleed, sensitivity loss,
and instrumental drift are minimized or eliminated when the reference standard and unknown
spectra are prepared and analyzed sequentially under the same experimental and instrumental
conditions.
Errors in mass spectral databases, where spectra are mislabeled or incorrect, are also
known to occur, although extensive work has been conducted to identify and correct these errors
[28]. If errors exist in the database, this would, of course, compromise the accuracy of the match.
Additionally, if the library does not contain a spectrum for the compound of interest, an accurate
match will not be possible. Examples of this are often observed in forensic science with the
occurrence of new synthetic drugs, (e.g. synthetic cannabinoids).
In summary, SIs do not establish whether the tentative mass spectral identification is
objectively correct and are generally not applicable for reporting a statistical assessment of mass
spectral comparisons by regulatory agencies. A method for evaluating the confidence in the
mass spectral identification of a compound using the entire spectrum and probability-based
statistics would circumvent some of the weaknesses of the SI approach. An example of a familiar
forensic application of probability statistics, deoxyribonucleic acid (DNA) profiling, is explained
in detail below.
1.2.2 Deoxyribonucleic Acid Profiling
DNA profiles are used to eliminate or match evidence found at a crime scene to potential
suspects. A DNA profile is a specific sequence of four repeating base nucleotides, adenine (A),
21

thymine (T), guanine (G), and cytosine (C), that combine to form organized and linear sequences
of DNA. Polymerase Chain Reaction-Short Tandem Repeat Testing (PCR-STR) is used to
measure specific loci that differ in sequence of bases and are characteristic to an individual [29].
These DNA profiles or markers consist of a range of DNA fragments with known numbers of
base pairs. Using PCR, short regions of the DNA are selectively amplified. The resulting
products are then separated using gel electrophoresis, and visualized by staining. The Combined
DNA Index System (CODIS) maintained by the Federal Bureau of Investigation is a national
database containing DNA profiles based on 13 distinct markers (CSF1PO, D3S1358, D5s818,
D7s820, D8S1179, D13s317, D16s539, D18s51, D21s11, FGA, THO1, TPOX, vWA), as well as
a marker called AMEL to determine if the suspect is male or female. The profiles are generally
divided into three broad ethnic groups of Caucasian, Hispanic, and African-American, although
some laboratories include additional groups (e.g. Southwestern Hispanic, Southeastern Hispanic,
East Asian, American Indian, etc.). DNA profiles in CODIS are obtained from convicted
offenders or arrestees (offender profiles), missing persons, or from state databases of crime scene
DNA profiles (forensic profiles). As of October 2012, the CODIS database had 9,993,800
offender profiles and 457,700 forensic profiles [30].
A forensic analyst will compare a suspect DNA profile to one collected from a crime
scene or to CODIS and estimate a random-match probability based on the presence or absence of
alleles. In order to report this probability match, the frequency of each allele, at a particular locus
among the various racial groups, is first determined from the database. The frequency of each
genotype (or pair of alleles) is then estimated by taking the product of the probability of each
allele and the number of ways a person can inherit a genotype, which is either one or two, as a
person inherits one from the mother and one from the father. Genotypes are sequence specific,

22

for example, alleles a and b could have been inherited as ab or ba, while alleles b and b could
only have been received as bb. Lastly, the frequency of each genotype that matched between the
suspect and evidentiary profile is multiplied together to estimate the frequency of the overall
DNA profile [31]. The probability of this profile occurring by chance is the random-match
probability.
This method of calculating the RMP relies on the product rule of probabilities, the
assumptions of which will be further discussed in Chapter 2. In general, however, this formula
assumes that the frequencies of the two alleles in a genotype are statistically independent of one
another (if so, the population is said to be in Hardy-Weinberg equilibrium). In addition, the
formula also assumes the frequencies of each genotype are statistically independent of one
another (if so, the population is said to be in linkage equilibrium).
The product rule is not accurate if the frequency of alleles or genotypes are statistically
dependent. Briefly, Hardy-Weinberg equilibrium for statistical independence is based on the
assumption that the population is isolated, infinitely large with random mating, and without
significant natural selection or recent mutations in the DNA [32]. Balding et al. make the
argument that few data have been reported to justify the Hardy-Weinberg equilibrium of a
population and the corresponding assumptions [32]. Balding et al. statistically show that if the
alleles are not independent then the RMP will be significantly overestimated, thereby
exaggerating the apparent strength of the evidence. However, DNA profiling is considered
indisputably sound and reliable by the scientific and legal communities [33].

23

1.3 Research Objectives
The objectives of this research are 1) to develop a probability-based method for assigning
statistical confidence to mass spectral comparisons, and 2) to validate this method using mass
spectra of forensically important samples.
Compounds that have similar mass spectra pose the greatest difficulty for visual
discrimination by the analyst. Therefore, this statistical method, referred to as statistical approach
to establish equivalence of unabbreviated mass spectra (SAEEUMS), will be developed using
straight-chain alkane and simple alkylbenzene compounds. These compounds have spectra that
are often similar, containing common fragment ions, such as m/z 43, 57, 71 and 85 which are
alkyl ions of formula CnH2n+1+. The developed method will then be further investigated and
validated using more complex mass spectra, namely, spectra from amphetamine-type stimulants
and the hallucinogen, salvinorin A.
In order to determine if the mass spectrum of the unknown sample is statistically
equivalent to that of the standard, an unequal variance t-test will be calculated at every m/z value
to compare the abundances of the ions. If, at any m/z value the abundances are statistically
different, then the two spectra will not be considered a match and no further statistical
calculations will be performed. Alternatively, the spectra will be considered a match if the
abundances at every m/z value are statistically equivalent.
The NIST Mass Spectral Search Program will be used to determine the frequency of
detected fragment ions occurring in the NIST database of GC-MS spectra. The probability of the
appearance of each m/z value can then be calculated by the number of times it is observed. The

24

random-match probability of the fragmentation pattern occurring by chance can then be
calculated.
The PBM method, developed by McLafferty [7], used some of the same reasoning as the
RMP calculations proposed in this work: that a probability can be calculated for the frequency of
occurrence of each ion in a mass spectrum. However, the PBM method does not provide a
confidence level in the identification. In addition, many of the other SI methods use only a
portion of the spectrum, and the disadvantages of this type of comparison were discussed
previously. The method proposed herein will provide a confidence level and is performed on the
entire spectrum in order to utilize the discrimination available from low abundance ions.
The method of Olson et al. [27] also used similar reasoning as that proposed in this work;
that is, a statistical confidence can be calculated for the comparison of mass spectra. However,
Olson et al. used an abbreviated spectrum and required a large number of replicates to calculate a
z-score, which it is impractical for routine forensic application. In addition, as only a single
value, the dot product, is used to represent the entire mass spectrum, it is not a detailed and
comprehensive comparison. The strength of the method proposed herein is the direct comparison
of the entire spectrum, which has not previously been reported. In addition, the number of
replicates of each sample is greatly reduced in the proposed method through the use of a tstatistic (n ≥ 2) rather than the z-statistic (n ≥ 30), which was employed by Olson et al. [27].
These improvements increase the ease and applicability for assigning a statistical confidence to
the comparison of mass spectra.
The statistical approach to establish equivalence of unabbreviated mass spectra is a proofof-concept work to provide a simple and rapid method for assigning a statistical confidence to

25

the comparison of any two mass spectra. This method could be implemented without expensive
software and should be broadly applicable across many fields of environmental, food, and
forensic chemistry.

26

REFERENCES

27

REFERENCES
[1]

Scientific Working Group on DNA Analysis Methods, Interpretation Guidelines for
Autosomal STR Typing by Forensic DNA Testing Laboratories, National Institute of
Justice, Washington, DC, 2010.

[2]

Strengthening Forensic Science in the United States: A Path Forward. National Research
Council of the National Academies. The National Academies Press, Washington D.C.
2009.

[3]

Brumley WC. Tools of the trade-separations and detections. US Environmental
Protection Agency. http://www.epa.gov/esd/chemistry/org-anal/home.htm, (retrieved
June 26, 2012).

[4]

Brumley WC, Sphon JA (1981) Regulatory mass spectrometry. Biomed Mass Spectrom
8: 390-396.

[5]

Wan KX, Vidavsky I, Gross ML (2002) Comparing similar spectra: from similarity index
to spectral contrast angle. J Am Soc Mass Spectrom 13: 85-88.

[6]

Stein SE, Scott DR (1994) Optimization and testing of mass spectral library search
algorithms for compound identification. J Am Soc Mass Spectrom 5: 859-866.

[7]

McLafferty FW, Hertel RH, Villwock RD (1974) Probability based matching of mass
spectra, rapid identification of specific compounds in mixtures, Org Mass Spectrom 9:
690-702.

[8]

Hertz HS, Hites RA, Biemann K (1971) Identification of mass spectra by computersearching a file of known spectra Anal Chem 43: 681-691.

[9]

Crawford JD, Morrison JD (1968) Computer methods in analytical mass spectrometry
identification of an unknown compound in a catalog. Anal Chem 40: 1464-1469.

[10]

Burns M (2007) Medical-legal aspects of drugs. Tucson Arizona: Lawyer and Judges
Publishing.

[11]

Daubert v. Merrell Dow Pharmaceuticals, Inc., 43 f.3d 1311 (9th cir. 1995).

[12]

McLafferty FW (1959) Mass spectrometric analysis molecular rearrangements. Anal
Chem 31: 82-87.

[13]

Scientific Working Group for the Analysis of Seized Drugs (2011) SWGDRUG
recommendations, Edition 6.0.

[14]

American Society of Crime Laboratory Directors/Laboratory Accreditation Board (April
2008) Proficiency test provider program.
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[15]

Forensic chemistry section quality manual (2009) Document DRG‐DOC‐01. Little Rock,
AR: Arkansas State Crime Laboratory.

[16]

Controlled substances standard operating procedure (2005). San Francisco, CA: San
Francisco Police Department Criminalistics Laboratory.

[17]

Controlled substances procedures manual (2012) Document 221-D100. Richmond, VA:
Virginia Department of Forensic Science.

[18]

Hoffmann E, Stroobant V (2007) Mass Spectrometry: Principles and applications. West
Sussex England: John Wiley and Sons.

[19]

Heller D (2002) Prescription and process for achieving acceptable methods of
confirmation [abstract]. In: 224th American Chemical Society National Meeting; 2002
Aug 18-22; Boston, MA. Cape Girardeau, MO: American Chemical Society, Division of
Environmental Chemistry, Inc; p 637. Abstract nr 30.

[20]

Abrahamsson S, Haggstrom G, Stenhagen E (1966) An information retrieval system for
organic mass spectrometry. the American Society for Mass Spectrometry: Fourteenth
annual conference on Mass Spectrometry and Allied Topics; 1966 May 22-27; Dallas,
TX; 522.

[21]

Knock BA, Smith IC, Wright DE, Ridley RG (1970) Compound identification by
computer matching of low resolution mass spectra. Anal Chem 42: 1516-1520.

[22]

Smith RM (2004) Understanding mass spectra: a basic approach. Hoboken, New Jersey:
John Wiley and Sons.

[23]

Sokolow S, Kamofsky J, Guston P (1978) The Finnigan library search program; Finnigan
application report 2. San Jose, CA: Finnigan Corp.

[24]

Alfassi ZB, Boger Z, Ronen Y (2005) Statistical treatment of analytical data. Boca Raton,
FL: CRC Press

[25]

Stein SE (2008) NIST standard reference database 1A. Users guide. National Institute of
Standards and Technology, Gaithersburg, MD

[26]

Stein SE (1999) An integrated method for spectrum extraction and compound
identification from GC/MS data. J Am Soc Mass Spectrom 10: 770-781

[27]

Olson MT, Blank PS, Sackett DL, Yergey AL (2008) Evaluating reproducibility and
similarity of mass and intensity data in complex spectra- applications to tubulin. J Am
Soc Mass Spectrom 19: 367-374.

29

[28]

Ausloos P, Clifton CL, Lias SG, Mikaya AI, Stein SE, Tchekhovskoi DV, Sparkman OD,
Zaikin V, Zhu D (1999) The critical evaluation of a comprehensive mass spectral library.
J Am Soc Mass Spectrom 10: 287-299.

[29]

Riley D (April 6, 2005) DNA testing: an introduction for non-scientists
an illustrated explanation. scientific testimony. Seattle, WA: University of Washington.

[30]

Federal Bureau Investigation (Accessed December 8, 2012) Combined DNA index
system: fact sheet—CODIS and the national DNA index system.

[31]

Fung WK, Hu Y (2008) Statistical DNA forensics: theory, methods and computational
statistics in practice. San Francisco, CA: John Wiley.

[32]

Balding DJ, Nichols RA (1994) DNA profile match probability calculations: how to
allow for population stratification, relatedness, database selection and single bands.
Forensic Sci Int 64: 125-140.

[33]

United States v. Jakobetz, 955 f. 2d 786. Federal Court of Appeals (2nd circuit 1992).

30

CHAPTER 2
DEVELOPMENT AND APPLICATION OF A STATISTICAL APPROACH TO
ESTABLISH EQUIVALENCE OF UNABBREVIATED MASS SPECTRA
2.1

INTRODUCTION
In many regulatory applications, mass spectrometry (MS) is used to identify compounds

through spectral comparison to a reference standard or library database. As discussed in Chapter
1, neither of the current comparison methods, similarity indices (SI) nor visual examination of
spectra, provide a statistical assessment, such as a confidence level or error rate, for the mass
spectral identification of an unknown compound. Reported herein is the development of a
statistical approach to establish equivalence of unabbreviated mass spectra (SAEEUMS), which
is a simple and rapid method to assign statistical significance for the comparison of mass spectra.
Compounds that have similar mass spectra pose the greatest difficulty for identification.
Therefore, SAEEUMS was developed using straight chain alkanes. These compounds have
spectra that are often visually similar, containing common fragment ions, such as m/z 43, 57, 72,
85, etc. As mass spectra of alkanes are among the most difficult to differentiate, this choice of
compound provides a challenging means to demonstrate the effectiveness of the proposed
method. The method was also applied to alkylbenzenes as an example of simple aromatic
compounds.

31

2. 2
2.2.1

STATISTICAL THEORY
Unequal Variance t-Test
The mean relative ion abundances and associated standard deviations at every m/z value

in the mass spectra are required prior to calculating the statistical confidence of a match between
two mass spectra, 1 and 2. The mean abundance and standard deviation can be calculated from
replicate mass spectra. Alternatively, standard deviations can be predicted by using the counting
statistics of the mass spectrometer detector. In this approach, the statistical response of the
electron multiplier provides an independent means of determining the variance inherent in the
ion abundance and, for this purpose, may prove to be more robust and accurate than the
traditional calculation of standard deviations from replicates.
The statistical confidence of a match between 1 and 2 can then be determined using
hypothesis testing for each ion in the spectrum. Statistically, the null hypothesis, H0, is stated as

(2.1)

where the mean abundance, µ1 and µ2, of each ion in 1 and 2 are statistically indistinguishable.
The alternative hypothesis, Ha, is stated as

(2.2)

where µ1 and µ2 of the respective ions are statistically distinguishable.

Two types of errors can arise in hypothesis testing, Type I and Type II errors. Type I
errors arise if H0 is accepted when it is false (i.e., 1 and 2 are considered a match when, in truth,
32

they are not the same compound) and Type II errors arise if H0 is rejected when it is true (i.e., 1
and 2 are not considered a match when, in truth, they are the same compound). The confidence
level at which the statistical test is performed relates to the probability of these errors occurring;
for example, a two-tailed t-test at the 99.9% confidence level indicates the analyst is 99.9%
confident there is not a Type I error [1]. Consideration of the confidence level at which the t-test
is performed must be taken into account prior to the calculation (Appendix A).
To determine which hypothesis is verified, an unequal variance t-test is used at each m/z
value to determine if that ion abundance in the mass spectra of 1 and 2 is statistically
indistinguishable (H0 accepted) or if it is statistically distinguishable (H0 rejected) [1]. Standard
deviations and averages for replicate mass spectra of 1 and 2 are calculated at each m/z, to
determine the variance inherent in the fragmentation pattern of the respective spectra. A t-test
assuming unequal variance is then calculated as

tcalc =

(2.3)

where n1 and n2 are the number of spectra used to calculate the standard deviations, σ1 and σ2, of
1 and 2 respectively [1]. An approximation of the degrees of freedom, df, is calculated by

df =

(2.4)

33

This equation generally leads to a degree of freedom that is not an integer and, therefore, to be
conservative, should be rounded down to the nearest integer [1].

To determine if Ho is true at a given confidence level, the values of the Welch t-statistic,
tcalc, is compared to a table of critical values, tcrit, at the desired level of statistical significance.
When tcalc is less than or equal to tcrit, the Ho is verified. Alternatively, Ha is verified when tcalc
is greater than tcrit. This process is repeated for each m/z in the two spectra. If, at every m/z
value, H0 is accepted, then the two spectra are considered statistically associated (i.e., a match).
Alternatively, the spectra are statistically differentiated (i.e., not a match) if Ha is accepted for
any ion in the spectra.
2.2.2 Random-Match Probability
In mass spectral databases, it is commonly known that some mass fragments occur with
greater frequency than others [2]. The less common fragments are thereby more characteristic of
a compound. The frequency that a certain fragment occurs in a set of known mass spectra can be
used to calculate a chemical probability. For this approach, the frequency of detected fragment
ions was determined using the National Institute of Standards and Technology (NIST) Mass
Spectral Search Program (version 2.0d) as a reference database. This database contains
approximately 150,000 spectra, collected using electron ionization (EI), with an ionizing voltage
of 70 eV. Other databases, including those generated in house, could be used as the reference.
There are two ways in which a total probability may be calculated: assuming the presence
or absence of an ion is an independent random event or assuming it is dependent. The choice
34

between the two is difficult as the calculation for ion independence would require complex
knowledge of the interrelated fragmentation of dependent ions. In many cases this prior
knowledge would be compound specific or chemical class specific, thereby narrowing the
applicability of the calculation to known compounds. The calculation assuming ion
independence, however, is straightforward and can be implemented without prior knowledge of
the identity of the compound. In addition, the assumption of ion independence has precedence in
the literature and is central to the calculations of existing peptide-scoring algorithms [3,4]. Given
this rational, ion independence was also assumed in this research [3,4]. As this assumption is not
valid when charge may be transferred to one of two ions formed by fragmentation, or when one
ion is formed as a product from another precursor ion, the RMP calculated herein are estimates.
Assuming ion independence, basic rules of probability theory are used to calculate the
likely occurrence of each ion in the mass spectrum [1]. If an ion A is present in the mass
spectrum, the probability P(A) of occurrence is calculated by

P(A) =

(2.5)

where N(A) is the number of compounds containing ion A in a database of T spectra. Conversely,
if ion A is not present in the mass spectrum, the probability of non-occurrence is calculated by

P(A) = 1

(2.6)

The total random-match probability of a particular sequence of ions appearing in the mass
spectrum is calculated using the multiplicative rule [1].

RMP =

(Aj) = P(A(m/z)i) × P(A(m/z)i+1 ) ×…× P(A(m/z)f)
35

(2.7)

where (m/z)i and (m/z)f are the initial and final mass-to-charge ratios, respectively, in the mass
scan range.
2.2.3 Pearson Product Moment Correlation Coefficients
As a means of comparing the similarity of mass spectra, Pearson product moment
correlation (PPMC) coefficients can be calculated for pair-wise comparisons of mass spectra.
PPMC coefficients (r) are calculated as

r1, 2 =

(2.8)

where x1j and x2j correspond to the abundances at m/z value j in two mass spectra, 1 and 2, μ1
and μ2 are the average abundances, and (m/z)i and (m/z)f are the initial and final mass-to-charge
ratios, respectively, in the mass scan range [1].
A coefficient of ± 0.80 or greater indicates strong correlation, coefficients ranging from ±
0.50 to ± 0.79 indicates moderate correlation, coefficients of ± 0.49 or less indicate weak
correlation, and coefficients close to zero indicate no correlation [1]. The PPMC coefficients
between replicate mass spectra of the same compound should have values close to one.
Deviation from one is a measure of the lack of precision of the analysis, i.e. greater deviation
indicates less precision. Conversely, mass spectra from different samples, such as different
alkanes, should have lower PPMC values. In this manner, PPMC coefficients can be used as a
measure of the similarity or dissimilarity of mass spectra.

36

2.3

EXPERIMENTAL

2.3.1 GC-MS Analysis

Five standards (0.05, 0.1, 0.5, 1.0, 5.0 mM) containing decane (C10), undecane (C11),
dodecane (C12), tridecane (C13), tetradecane (C14), hexadecane (C16), and the alkylbenzenes
propylbenzene, butylbenzene, amylbenzene, and hexylbenzene, all purchased from Sigma (Saint
Louis, MO), were prepared in dichloromethane (Honeywell Burdick and Jackson, 99.9% purity,
Morristown, NJ). All compounds were present at the same concentration in each standard.
Two sets of replicate (n = 3) standards (Set 1 and Set 2) were analyzed sequentially over
a 16-hour period, on the same day. Both sets were analyzed using an Agilent 6890N gas
chromatograph (Agilent Technologies, Santa Clara, CA) equipped with a DB-5MS column (30
m x 0.25 mm i.d. x 0.25 µm film thickness) (Agilent Technologies) and an Agilent 7683B
automatic liquid sampler (Agilent Technologies). Ultra-high purity helium (Airgas Great Lakes,
Independence, OH) was used as the carrier gas at a nominal flow rate of 1 mL/min. The inlet
was maintained at 250 °C and 1 μL of the standard was injected in splitless mode. The oven
temperature program was as follows: 40 °C for 2 min, 15 °C/min to 280 °C, with a final hold at
280 °C for 2 min. The transfer line to the Agilent 5975C mass selective detector (Agilent
Technologies) was maintained at 250 °C. Electron ionization (70 eV) was used and the
quadrupole mass analyzer was operated in the full scan mode (m/z 40 - 550) with a scan rate of
2.86 scans/s and an instrumental peak threshold of 150. The 1 mM standard was also analyzed
using ionizing voltages of 50 and 90 eV under the same conditions.

37

2.3.2 Data Analysis
The mass spectra of the alkane standards examined in this work had minimal
contribution from background ions. However, depending on the GC temperature program used or
type and age of the column, background and noise ions may be more prevalent. In these cases,
background subtraction would be crucial to ensure statistical differentiation of spectra is not due
to background variation.
The mass spectra were exported from ChemStation Software (version E01.02.16, Agilent
Technologies, Santa Clara, CA) to Microsoft Excel (version 2007, Microsoft Corp., Redmond,
WA). All calculations and logical functions were performed in Microsoft Excel. The exported
data from ChemStation contains only the abundances of the ions present in the spectrum above
the instrumental peak threshold. Therefore, to create a complete mass spectrum, the m/z value
for each ion was rounded to its integer value and the corresponding abundance was tabulated for
the entire mass scan range. For any ion not present in the mass spectrum, an abundance of 0 was
entered. The normalized abundance of each ion relative to the base peak in the spectrum was
then calculated.
Both the traditional method of calculating standard deviations and the predicted standard
deviations previously mentioned were investigated. For the traditional method, the mean
abundance and standard deviation were calculated for each ion in the triplicate mass spectra for
each compound at each concentration. For the predicted standard deviation method, a
logarithmic graph of mean abundance versus standard deviation for all mass spectra was created
in Microsoft Excel. In so doing, each ion abundance was represented by a total of 90 mass
spectra, thereby providing a more robust statistical approach than the traditional method.
Comparisons were made between fitting the data manually and using an automatic fitting
38

function in Excel. The linear least squares regression line was then calculated and used to predict
the standard deviations for all ions. For any ion at or below the instrumental threshold (150
counts), the standard deviation was predicted at an abundance of 150. The mean abundances and
standard deviations were then normalized to the base peak for both methods.
Other normalization methods were also investigated (Appendix B). In addition, a
threshold was investigation to determine the point at which variance due to low abundance noise
in the mass spectra is minimized, while the discrimination provided by lower abundance ions is
retained (Appendix C). Although these other methods were investigated, they were not included
in the final SAEEUMS method for reasons discussed in the appropriate Appendix.
All comparisons, unless otherwise stated, were based on the triplicate mass spectra in
Sets 1 and 2. Comparisons were made between the same compound (e.g., C10 in Set 1 compared
to C10 in Set 2) to examine statistical association. Comparisons were also made between
different compounds (e.g., C10 in Set 1 compared to C11 in Set 2) to examine statistical
differentiation.
For these comparisons, an unequal variance student t-test was performed in which the
Welch t-statistic, tcalc, and the associated degrees of freedom were calculated at each m/z value.
These were compared to the critical values, tcrit, at various confidence levels using a two-tailed
table. Using an IF function in Excel, a value of 1 was returned if the mean abundance for each
m/z value was statistically indistinguishable (tcalc ≤ tcrit), and a value of 0 was returned if
statistically different (tcalc > tcrit) at the specified confidence level. The two spectra were

39

considered statistically associated if the product of these values was 1 (i.e., if values of 1 were
returned for every m/z value) and were considered statistically different if the product was 0 (i.e.,
if a value of 0 was returned for any m/z value).
If the two spectra were statistically associated, the random-match probability (RMP) was
calculated. A binary consolidated array, C, of the two spectra was created, in which a value of 1
was returned at that m/z value if an ion was present in both spectra. Conversely, a value of 0 was
returned if the ion was absent in both spectra. Although the spectra are statistically equivalent, it
is still possible for an ion to be present in one spectrum (i.e., near the threshold) but not in the
other (i.e., below the threshold). In such cases, to be conservative, a value of 0 was returned to
eliminate that ion from the RMP calculation.
The NIST Mass Spectral Search Program (version 2.0d, Gaithersburg, MD), which
contains 147,198 mass spectra, was used as a representative database to determine the frequency
of fragment ions. The number of spectra in the database containing each ion in the mass scan
range above 1% threshold (the lowest threshold allowed) was tabulated using the search function
in the NIST program. The probability of each ion in C with a value of 1 was calculated by
Equation 2.5, while the probability of each ion in C with a value of 0 was calculated by Equation
2.6. The total probability of array C was then calculated by Equation 2.7 to obtain the RMP.
This represents the probability that the pattern of ions occurs by random chance alone.
Ions that are known to be chemically irrelevant were removed from the RMP calculations
in two ways. The mass scan range, 40 - 550 m/z, was chosen to avoid common atmospheric
compounds (such as H2O, N2, etc.) that are not removed completely by the vacuum pump. In
addition, common contaminant ions from column or septum degradation (e.g., m/z 73, 147, 207,

40

221, 281, 295, 355, 429) or fluorinated hydrocarbons used for mass tuning (e.g., m/z 69, 219,
502) were ignored in the RMP calculations if below a user-defined value (e.g., 5% of the base
peak). If above this value, the ions were assumed to be chemically relevant to the compound and
were included in the calculation.
2.4

RESULTS AND DISCUSSION

2.4.1 Similarity of Spectra
As noted previously, homologous series of alkanes and alkylbenzenes were chosen to
develop and validate this method. Each series has very similar mass spectra, as evidenced by
their Pearson product moment correlation (PPMC) coefficients. PPMC coefficients were
calculated for all the alkane mass spectra at five concentrations (0.05, 0.1, 0.5, 1.0, 5.0 mM) in
Set 1 and Set 2 (1770 total comparisons). A table summarizing the results is given in Table 2.1
and the full tables are in Appendix D, Table A4. The coefficients for pair-wise comparisons of
the same alkane (Set 1 and Set 2) ranged from 0.9611 to 1.000, whereas those for different
alkanes ranged from 0.9189 to 0.9973. The coefficients of different alkanes decreased as the
difference in carbon number of the alkanes being compared increased. For example, the average
coefficient for the comparison of C16 to C16 was 0.9909, while the average coefficient for the
comparison of C10 to C16 was 0.9523.

PPMC coefficients were calculated for all the alkylbenzene mass spectra at five
concentrations (0.05, 0.1, 0.5, 1.0, 5.0 mM) in Set 1 and Set 2 (780 total comparisons). A table
summarizing the results is in Table 2.2 and the full tables are in Appendix D, Table A5. The

41

Table 2.1. Average Pearson product moment correlation (PPMC) coefficients summarizing the comparison of the alkane mass spectra
from Sets 1 and 2. Each comparison of the same alkane is an average of 45 PPMC coefficients, while each comparison of different
alkanes is an average of 100 PPMC coefficients (1770 total comparisons). The full tables are in Appendix D, Table A4.

C10

C11

C12

C13

C14

C16

Maximum

Minimum

Same Alkane

1.000

0.9611

0.9973

0.9189

C10

0.9892 ± 0.0089

C11

0.9853 ± 0.0081

0.9866 ± 0.0125

C12

0.9784 ± 0.0089

0.9849 ± 0.0108

0.9915 ± 0.0078

Different Alkanes

C13

0.9705 ± 0.0105

0.9805 ± 0.0117

0.9885 ± 0.0078

0.9913 ± 0.0080

C14

0.9647 ± 0.0101

0.9766 ± 0.0116

0.9871 ± 0.0071

0.9905 ± 0.0064

0.9939 ± 0.0055

C16

0.9523 ± 0.0132

0.9673 ± 0.0133

0.9802 ± 0.0196

0.9862 ± 0.0085

0.9901 ± 0.0076

a

one standard deviation

42

0.9909 ± 0.0086

Table 2.2. Average Pearson product moment correlation (PPMC) coefficients summarizing the comparison of propylbenzene,
butylbenzene, amylbenzene, and hexylbenzene mass spectra from Sets 1 and 2. Each comparison of the same alkylbenzene is an
average of 45 PPMC coefficients, while each comparison of different alkylbenzenes is an average of 100 PPMC coefficients (780 total
comparisons). The full tables are in Appendix D, Table A5.

Propylbenzene
Propylbenzene 0.9965 ± 0.0031
0.8717 ± 0.0095
Butylbenzene
0.8428 ± 0.0129
Amylbenzene
0.7871 ± 0.0167
Hexylbenzene
a
one standard deviation

Butylbenzene
0.9949 ± 0.0044
0.9382 ± 0.0055
0.9210 ± 0.0102

Amylbenzene

0.9968 ± 0.0027
0.9362 ± 0.0095

43

Hexylbenzene
Same Alkylbenzene
Different Alkylbenzene
0.9902 ± 0.0098

Maximum
1.000
0.9542

Minimum
0.9679
0.7580

coefficients for pair-wise comparisons of the same alkylbenzene (Set 1 and Set 2) ranged from
0.9679 to 1.000, whereas those for different alkylbenzenes ranged from 0.7580 to 0.9542. The
coefficients of different alkylbenzenes decreased as the difference in carbon number side chain
of the alkylbenzenes being compared increased. For example, the average coefficient for the
comparison of hexylbenzene to hexylbenzene was 0.9902, while the average coefficient for the
comparison of propylbenzene to hexylbenzene was 0.7871.
These values indicate a strong correlation for all comparisons of alkane spectra, and a
moderate to strong correlation for all comparisons of alkylbenzene spectra. Many comparisons of
different alkane spectra had higher coefficients than comparisons of the same alkane. Hence,
these compounds provide a rigorous test of the ability of the proposed method to associate and
discriminate mass spectra.
2.4.2 Match Determination of the Same Alkane
The spectra of corresponding alkanes in Sets 1 and 2 were compared at a concentration of
1 mM and an ionizing voltage of 70 eV. All pair-wise statistical comparisons (6 total) were made
using a t-test at confidence levels of 98.0, 99.0, and 99.9%. Corresponding alkanes were
statistically indistinguishable at the 99.9% confidence level and, therefore, were considered to be
associated. However, this confidence level is the least rigorous in regards to statistical
association (Appendix C). The lowest confidence level at which association was maintained for
corresponding alkanes is reported in Table 2.3. In these comparisons, C13 did not associate with
one ion responsible for the discrimination (m/z 85), discussed further in Section 2.4.7. Alkanes
C11 and C14 were associated only at the 99.9% confidence level, while C12 was also associated
at the 99.0% confidence level. Alkanes C10 and C16 maintained association at all confidence
44

Table 2.3. Random-match probability (RMP) for comparison of the same alkane in Set 1 and Set 2 using a t-test at the lowest
confidence level (CL) for which association was maintained. Confidence levels of 98.0, 99.0, and 99.9% were investigated.
Alkane

CL

RMP

C10

98.00% 2.0 x 10

C11

99.90% 2.4 x 10

C12

99.00% 2.6 x 10

C14

99.90% 3.1 x 10

C16

98.00% 1.1 x 10

-39
-41
-42
-44
-45

45

levels investigated. This indicates that association was possible for most alkanes, with the
exception of C13, but the degree of rigorousness varied.

The RMPs were calculated for all spectra that were statistically associated (Table 2.3)
and represent the probability that the specific ion pattern occurs by chance. As an example, the
RMP for C10 alkanes was 2.0 x 10

-39

, indicating that the occurrence of this ion pattern is

infinitesimally small. As carbon number increases, the RMP decreases (e.g., for comparison of
45

C16 spectra, the RMP is 1.1 x 10- ). The larger alkanes have a greater number of discriminating
ions and, therefore, a lower probability that the specific ion pattern occurs by chance.
2.4.3 Match Determination of Different Alkanes
The spectra of different alkanes in Sets 1 and 2 were compared at a concentration of 1
mM and an ionizing voltage of 70 eV. All pair-wise statistical comparisons (30 total) were made
using a t-test at confidence levels of 98.0, 99.0, and 99.9%. Each alkane was statistically
distinguishable from all others at the 99.9% confidence level, which is the most rigorous test for
statistical discrimination (Appendix A). Hence, despite the similarity of the spectra (as
evidenced by the Pearson correlation coefficients above), these alkanes were still distinguishable
using the unequal variance t-test.
The number and m/z of ions responsible for discriminating the alkane spectra are reported
in Table 2.4 at the 99.9% confidence level. The number of discriminatory ions ranged from 1 to
24 ions, depending on the alkanes being compared. This number is somewhat surprising, given
the similarity of the fragmentation patterns and the total number of ions that comprise the alkane
spectra (46 to 71 for C10 to C16, respectively). Additionally, 54% of the discriminating ions were
46

Table 2.4 Ions responsible for discrimination of alkanes (t-test, 99.9% CL) in Set 1 and Set 2.
Set 1/Set 2
C10

C11

% Even
m/z
67%

Ions m/z
3
83, 142, 156

% Low
a
Abundance
33%

M+. Ions
C10, C11

C12

C10, C12

15

42, 43, 71, 82, 83, 84, 85, 97, 112, 126, 127, 140, 141, 142, 184

53%

67%

C10, C13

18

61%

67%

C10, C14

18

42, 43, 56, 70, 71, 82, 83, 84, 85, 96, 97, 112, 126, 127, 140, 141, 142,
198
42, 43, 56, 69, 70, 71, 72, 82, 83, 84, 85, 96, 111, 112, 125, 140, 141, 142

56%

50%

C10

1

71

0%

0%

C10
---

C12

3

140, 141, 170

67%

33%

C12

C13

6

55, 83, 85, 140, 142, 184

50%

50%

C13

C14

11

41, 71, 83, 85, 97, 99, 111, 113, 140, 155, 198

18%

64%

C16

12

41, 53, 55, 69, 71, 83, 85, 97, 99, 111, 125, 155

0%

67%

C14
---

C10

10

56, 68, 70, 71, 82, 84, 85, 97, 126, 127

60%

50%

---

C11

3

71, 97, 156

33%

67%

C11

C13

2

126, 184

100%

50%

C13

C14

9

71, 85, 86, 96, 99, 125, 126, 140, 198

56%

44%

C16

16

41, 42, 55, 56, 67, 69, 71, 82, 85, 97, 98, 99, 111, 113, 125, 140

31%

69%

C14
---

C10

7

42, 71, 84, 85, 97, 141, 155

29%

57%

---

C11

4

85, 141, 155, 156

25%

50%

C11

C12

4

42, 83, 155, 170

50%

75%

C12

C14

3

99, 125, 198

33%

67%

C16
a

63%

C16

C13

38%

C14

C12

42, 43, 71, 83, 85, 141, 142, 170

C13

C11

8

5

97, 99, 111, 125, 154

20%

40%

C14
---

≤ 5% of base peak
47

Table 2.4 (cont’d)

Set 1/Set 2
C14

C10

Ions
15

C11
C12

% Low
a
Abundance
53%

M+. Ions
--C11, C14

33%

44%

C12, C14

6

99, 110, 140, 169, 184, 198

67%

50%

C13, C14

5

56, 71, 99, 125, 198

40%

80%

C14

C10

23

52%

C16

24

50%

63%

C11, C16

C12

15

40, 41, 42, 43, 56, 67, 69, 70, 71, 72, 82, 83, 84, 85, 97, 99, 111,
125, 140, 168, 182, 183, 226
41, 42, 43, 56, 67, 69, 71, 82, 83, 85, 97, 98, 99, 100, 113, 125, 126,
140, 154, 156, 168, 182, 183, 226
41, 42, 43, 83, 85, 97, 99, 100, 113, 125, 140, 170, 182, 183, 226

48%

C11

40%

67%

C12, C16

C13

a

56%

C16

%

44%

9

42, 69, 71, 81, 84, 85, 97, 98, 111, 126, 140, 141, 155, 156, 169,
198
83, 85, 111, 140, 141, 155, 169, 170, 198

C13
C16

16

m/z
42, 68, 69, 71, 83, 84, 85, 97, 111, 112, 126, 140, 141, 155

% Even
m/z
40%

13

83, 85, 97, 99, 100, 111, 140, 154, 168, 182, 183, 184, 226

54%

46%

C13, C16

C14
Total

10

83, 97, 113, 125, 168, 170, 182, 183, 198, 226

50%

60%

C14, C16

44 %

54%

≤ 5% of base peak

48

low abundance ions, which was defined as < 5% of the base peak in this research. Lower
abundance ions may be more characteristic of the compound and, therefore, contribute to
discrimination. This emphasizes the importance of using the full spectra rather than abbreviated
spectra composed of only the most abundant ions.
The ions responsible for discrimination among the spectra were further examined for
general trends (Table 2.4). The number of discriminating ions increased as the difference in
carbon number of the alkanes being compared increased. Ions with even m/z values represented
44% of the total discriminating ions, while odd m/z values represented 56%. In non-nitrogen
containing compounds such as the alkanes, even-numbered fragments are less common and
generally result from multiple-bond cleavage, indicating that rearrangement may have occurred
[5]. Therefore, the presence of these fragments indicates that, in 44% of the comparisons,
differentiation was based on rearrangement and other less common cleavage patterns.
In most comparisons, the molecular ion was among the fragments leading to
discrimination of the alkanes. However, as electron ionization is a hard ionization technique, it
often does not result in a high abundance of the molecular ion. Therefore, the molecular ion is
not always present among the discriminating ions, and was not observed in most comparisons
involving C10 [5].

This application of the t-test for the spectral comparison appears to be extremely rigorous
with regard to discrimination, thereby minimizing false positives (Type I errors). However, it is
less rigorous with regard to association of spectra of the same compound, and could potentially
result in false negatives (Type II error).

49

2.4.4 Match Determination of Alkylbenzenes
To investigate the effectiveness of SAEEUMS for simple aromatic compounds, the mass
spectra of alkylbenzenes were compared at a concentration of 1 mM and an ionizing voltage of
70 eV. Again, all pair-wise comparisons (16 total) were made using a t-test at confidence levels
of 98.0, 99.0, and 99.9%. When spectra of corresponding alkylbenzenes in Set 1 and Set 2 were
compared, association was possible at the 99.9% confidence level. When spectra of different
alkylbenzenes were compared, discrimination was possible at the 99.9% confidence level, with 8
to 18 ions responsible for discrimination (Table 2.5). Approximately 56% of the discriminating
ions were low abundance (< 5% of the base peak), which is comparable to those in the alkane
spectra (54%) discussed above. This further emphasizes that the full spectra are essential for
successful comparisons.
Electron ionization of aromatic compounds generally leads to stable and characteristic
molecular ions, which were, in almost all cases, among the discriminating ions [5]. In addition,
common fragments for alkylbenzenes, such as the McLafferty rearrangement of the tropylium
ion (m/z 92) and methyl-substituted tropylium ion (m/z 105), were also among the discriminating
ions [5].
2.4.5 Effect of Ionizing Voltage on Association and Discrimination
As noted above, spectra being compared should always be acquired under the same
instrumental conditions. However, small variations in the ionizing voltage of the mass
spectrometer are possible over time. To investigate the effect of changes in ionizing voltage, the
1 mM alkane standard was analyzed in replicate at voltages of 50, 70, and 90 eV (Table 2.6).
Spectra of each compound collected at 50 eV typically had 5 to 9 fewer ions than those collected
50

Table 2.5. Number of discriminating ions for comparison of alkylbenzenes in Set 1 and Set 2 (t-test, 99.9% CL). Zero discriminating
ions indicate complete association and the corresponding random-match probability is shown in parentheses.
Propyl
Propyl
Butyl

Butyl
-39

0 (8.6 x 10
10

)

Amyl

Hexyl

12

13

17

39

0 (1.2 x 10- )

Amyl

17

10

Hexyl

18

14

8

13
-40

0 (2.8 x 10
11

)

8
39

0 (2.8 x 10- )

51

Table 2.6. Effects of ionizing voltage on the total number of ions at 1 mM concentration.
Voltage

C10

C11

C12

C13

C14

C16

50 eV

37

42

47

53

59

63

70 eV

46

50

53

58

65

69

90 eV

44

46

55

57

62

68

52

at 70 eV. In contrast, spectra collected at 90 eV were more comparable, with 4 fewer to 2 more
ions than those collected at 70 eV.
When spectra collected at voltages of 70 and 90 eV were compared using the t-test at the
99.9% confidence level (Table 2.7), statistical association of corresponding alkanes in Set 1 and
Set 2 was maintained in all cases but one. For C12, the spectra were differentiated by one low
abundance ion at m/z 51, which was not observed at 70 eV and was only 0.4% of the base peak at
90 eV. The higher ionizing voltage appears to have caused additional fragmentation for C12 that
led to this additional ion.
In contrast, spectra collected at voltages of 50 and 70 eV were statistically distinct, with 1
to 5 ions responsible for discrimination of corresponding alkanes (Table 2.7). Distinction was
mainly due to variation in ion abundance relative to the base peak. For all alkanes, this was most
noticeable at m/z 43, for which the relative abundance was more than 13% greater at 50 eV than
at 70 eV. For C10, this variation in abundance caused a change in the base peak, which was m/z
43 at 50 eV, but m/z 57 at 70 eV.
These results indicate that statistical association of spectra is relatively insensitive to
voltage increases up to 20 eV greater than 70 eV, but is sensitive to decreases up to 20 eV.
These variations are far greater than would be expected in normal operation.
2.4.6 Effect of Concentration on Association and Discrimination
The alkane standards at different concentrations were analyzed at an ionizing voltage of
70 eV. The concentrations ranged from 0.5 to 5.0 mM, with the base peak abundance (m/z 57)
ranging from 50,000 to 1,500,000 counts, respectively. Pair-wise statistical comparisons (150
53

Table 2.7. Effects of ionizing voltage on the number of discriminating ions of Set 1 alkanes compared to the corresponding alkane in
Set 2 (t-test, two tailed, 99.9%) at 1 mM concentration. Zero discriminating ions indicate complete associations and the corresponding
random-match probability is shown in parentheses. Entries in red highlight dissociation where not expected. For interpretation of the
references to color in this and all other figures, the reader is referred to the electronic version of this dissertation.

Voltage
90 eV
50 eV

C10
0 (1.3 x 10
1

70 eV
C12

C11
-28

)

0 (1.16 x 10
2

-28

)

1

C13
0 (2.8 x 10

3

3

54

C14
-34

)

0 (4.0 x 10
5

C16
-36

)

0 (3.5 x 10
5

-36

)

total) of C10 spectra in Set 1 are compared to all alkane spectra in Set 2 using the t-test at the
99.9% confidence level (Table 2.8).

In each case, when C10 spectra in Sets 1 and 2 were compared at the same concentration,
association was possible. In contrast, when C10 spectra were compared at different
concentrations, association of the spectra was not possible in most cases (vide infra), with 1 to 3
discriminating ions. However, the C10 spectra were statistically distinct from the other alkanes at
all concentrations, with 1 to 44 ions responsible for discrimination.
Spectra of alkane standards at lower concentration of 0.05 and 0.1 mM were also
investigated (Table 2.9). For these concentrations, the abundance of the base peak (m/z 57)
ranged from 1500 to 4000 counts, respectively. Spectra with base peaks below 5000 counts could
not be accurately associated or discriminated, which is potentially due to the smaller number of
ions in the spectra. For example, C10 spectra with a base peak of approximately 100,000 counts
(corresponding to a concentration of 1.0 mM) contained 56 ions, while C10 spectra with base
peaks of 1500 and 4000 counts (corresponding to 0.05 mM and 0.1 mM) contained only 14 and
25 ions, respectively. In addition, the molecular ion, which is generally responsible for
discrimination, is not observed in spectra with base peaks of 1500 counts and is just above the
instrumental threshold (~300 counts) in spectra with base peaks of 4000 counts. The loss in
association and discrimination is understandable, as ions that are uniquely characteristic of the
compound are missing from the spectra with base peaks below 5000 counts. As noted
previously, these low-abundance ions account for more than 50% of the discriminating ions. The
remaining ions are found at similar abundance ratios in the other alkanes and, therefore, do not
55

Table 2.8. Effect of concentration and base peak abundance on the number of discriminating ions for the comparison of C10 in Set 1
to all alkanes in Set 2 (t-test, 99.9% CL). Zero discriminating ions indicate complete association and the corresponding random-match
probability is shown in parentheses. Entries in red highlight unexpected association or discrimination.
Set 1 C10
Concentration
Base Peak
a
Abundance
Set 2
(mM)
48,955 ± 3,406 97,632 ± 2,054 711,381 ± 21,691
0.5

49,261 ± 3,126

1.0

96,971 ± 11,127

5.0

758,485 ± 52,032

3

C11

0.5
1.0
5.0

49,752 ± 1,881
99,757 ± 4,069
768,555 ± 33,173

C12

0.5
1.0
5.0

C13

-39

3

)

3

1
-40
0 (1.4 x 10 )

3
1
6

6
3
9

9
6
5

66,851 ± 4,524
132,051 ± 11,330
1,125,547 ± 9,800

5
4
11

7
8
15

8
8
22

0.5
1.0
5.0

78,760 ± 2,440
154,944 ± 3,294
1,282,901 ± 28,747

3
7
10

5
15
22

6
15
27

C14

0.5
1.0
5.0

94,112 ± 7,132
205,333 ± 7,039
1,480,021 ± 91,292

3
13
16

2
18
24

3
19
32

C16

0.5
1.0
5.0

80,040± 8,993
170,709 ± 3,568
1,348,779 ± 10,447

8
10
26

12
18
33

11
20
44

a

0 (1.7 x 10
0 (9.1 x 10

-39

)
)

0 (1.8 x 10

-39

)

C10

0 (2.0 x 10

± one standard deviation, n = 3

56

-39

Table 2.9. Effect of lower concentration and base peak abundance on the number of discriminating ions for the comparison of C10 in
Set 1 to all alkanes in Set 2 (t-test, 99.9% CL). Zero discriminating ions indicate complete association and the corresponding randommatch probability is shown in parentheses. Entries in red highlight unexpected association or discrimination.
Set 1 C10
Concentration
Base Peak
a
Abundance
Set 2
(mM)
1,499 ± 187
3,913 ± 301 48,955 ± 3,406 97,632 ± 2,054 711,381 ± 21,691
-26

1,939 ± 276
5,171 ± 292

0.5

49,261 ± 3,126

1.0

96,971 ± 11,127

1

758,485 ± 52,032

11

5

0.05

1,955 ± 455

0.1
0.5

5,368 ± 642
49,752 ± 1,881
99,757 ± 4,069

0 (2.0 x 10

0 (8.9 x 10

2

132,051 ± 11,330
1,125,547 ± 9,800

5

)

1
-39
0 (1.7 x 10 )

2
-39
0 (1.8 x 10 )

2

)

0 (9.1 x 10

-39

)

0 (2.0 x 10

-39

)

3

3
-31

)

1

4

6

2

3

6

9

1
6

-26

3

1
-40
0 (1.4 x 10 )

3
9

6
5

2

2

3

2

3

5

) 0 (8.2 x 10

6

7

8

4
11

8
15

8
22

)

4

1

1.0
5.0

4

2

4,017 ± 79

66,851 ± 4,524

2

2

-24

) 0 (9.6 x 10

4

0.05

0.5

-25

)

3

0 (5.6 x 10

-24

14

9,054 ± 291

-31

2

0 (1.6 x 10

768,555 ± 33,173

0.1

a

) 0 (1.9 x 10
0 (2.7 x 10

1

1.0
5.0
C12

-29

1

5.0
C11

0.05
0.1

C10

1

6
0 (9.3 x 10
0 (8.2 x 10

8

-31
-31

)
)

4

7

4

22

13

± one standard deviation, n = 3
57

Table 2.9 (cont’d)
Set 1 C10
Concentration
Set 2

(mM)

Base Peak
a
Abundance

C13

0.05

3,791 ± 360

0.1
0.5
1.0
5.0
C14

0.05
0.1
1.0

11,120 ± 507
78,760 ± 2,440
154,944 ± 3,294
1,282,901 ± 28,747
5,878 ± 415
15,578 ± 1,288
94,112 ± 7,132
205,333 ± 7,039

1.0
5.0
C16

1,480,021 ± 91,292

0.05

2,993 ± 328

0.1
0.5
1.0
5.0
a

7,143 ± 896
80,040± 8,993
170,709 ± 3,568
1,348,779 ± 10,447

1,499 ± 187

3,913 ± 301
0 (1.1 x 10
1

1
2

-32

48,955 ± 3,406 97,632 ± 2,054 711,381 ± 21,691
)

2

3

5

3

5

6

7
10

15
22

15
27

2

2

3

3

3

3

3

2

3

13
16

18
24

19
32

3

4

4

3

4

2

8

12

11

10
26

18
33

20
44

2

13

1

4
5

1

6

23
0 (5.8 x 10
2

12
-24

) 0 (6.8 x 10
2
0 (1.3 x 10

1
12

0 (5.7 x 10

-22

)

)

5

31
0 (5.2 x 10

-31

17
-24
-24

)

1
-31
) 0 (5.4 x 10 )

5

5

8

5

34

23

± one standard deviation, n = 3

58

allow discrimination. Thus, at very low abundances (base peak < 5000 counts), the spectrum is
no longer representative of the compound.
The effect of concentration on the alkane mass spectra can effectively be demonstrated
using PPMC coefficients. Therefore, PPMC coefficients were calculated for three replicates at
five concentrations (0.05, 0.1, 0.5, 1.0, 5.0 mM) for the alkane spectra in Set 1 (630
comparisons). A table summarizing the results is given in Table 2.10 and the full tables are in the
Appendix D, Table A6. For all the alkanes, the coefficients for pair-wise comparisons of the
same concentration increased as the concentration increased. For example, the coefficient for the
comparison of 0.05 mM C10 to 0.05 mM C10 was 0.9605, while the coefficient for the
comparison of 5.0 mM C10 to 5.0 mM C10 was 0.9998. In every case, the comparisons involving
0.05 and 0.1 mM had the lowest coefficients, indicating the lower concentration spectra were not
as reproducible as the higher concentrations. In addition, for all the alkanes, the coefficients for
pair-wise comparisons of different concentrations decreased as the difference in concentration
increased. For example, the coefficient for the comparison of 5.0 mM C10 to 5.0 mM C10 was
0.9998, while the coefficient for the comparison of 5.0 mM C10 to 0.5 mM C10 was 0.9598. As
noted in Section 2.4.1 the coefficients for pair-wise comparisons of different alkanes ranged from
0.9189 to 0.9973. Therefore, changes in concentration in many cases caused more differences in
the mass spectra of the alkanes than changes in the alkane compound. Specifically, the lower
concentrations, 0.05 and 0.1 mM, have the lowest coefficients and most variation, indicating that
they may not be as representative of the respective compound as the higher concentration
spectra. Therefore, increasing the abundance, either by increasing the injection volume or

59

Table 2.10. Average Pearson product moment correlation (PPMC) coefficients summarizing the effect of concentration on Set 1
alkane mass spectra at five concentrations (0.05, 0.1, 0.5, 1.0, 5.0 mM). Each comparison of the same concentration is an average of 3
PPMC coefficients, while each comparison of different concentration is an average of 9 PPMC coefficients (630 total comparisons).
The full tables are in Appendix D, Table A6.
0.05

C10
0.05
0.1
0.5
1.0
5.0

0.9605
0.9681
0.9655
0.9645
0.9598

C12
0.05
0.1
0.5
1.0
5.0

0.05
0.9724
0.9785
0.9697
0.9679
0.9638

C14
0.05
0.1
0.5
1.0
5.0

0.05
0.9862
0.9855
0.9811
0.9800
0.9789

0.1

0.5

1.0

5.0

0.9871
0.9847
0.9822
0.9777

0.9988
0.9988
0.9977

0.9996
0.9991

0.5

1.0

0.9894
0.9867
0.9850
0.9815

0.9993
0.9992
0.9989

0.9994
0.9993

0.9999

0.1

0.5

1.0

5.0

0.9964
0.9920
0.9911
0.9890

0.9996
0.9996
0.9993

0.9998
0.9996

0.9999

60

0.1

0.5

1.0

5.0

0.9738
0.9657
0.9568
0.9548
0.9525

0.9878
0.9835
0.9822
0.9792

0.9983
0.9987
0.9982

0.9995
0.9995

0.9999

0.05
0.9778
0.9707
0.9715
0.9706
0.9700

0.1

0.5

1.0

5.0

0.9909
0.9897
0.9873
0.9852

0.9993
0.9993
0.9988

0.9996
0.9996

1.0000

C16
0.05
0.1
0.5
1.0
5.0

5.0

0.05

C13
0.05
0.1
0.5
1.0
5.0

0.9998

0.1

C11
0.05
0.1
0.5
1.0
5.0

0.05
0.9757
0.9738
0.9666
0.9654
0.9650

0.1

0.5

1.0

5.0

0.9865
0.9881
0.9864
0.9846

0.9990
0.9991
0.9981

0.9998
0.9995

0.9998

concentration or by decreasing the split ratio, is necessary for accurate association or
discrimination.

As noted above, rigorous discrimination of C10 from the other alkanes was possible at the
three higher concentrations (0.5, 1.0, and 5.0 mM). However, spectra of C10 in Set 1 were not
statistically associated to spectra of C10 in Set 2 at the 5 mM concentration. Similar results were
observed with the comparison of the alkylbenzenes at varying concentrations. In these cases,
statistical association of corresponding compounds is most likely to incur Type II error if the
inherent instrumental variation is not represented adequately. For example, when data were
collected on the same day, the mean and standard deviation of the base peak in replicate C10
spectra were 97632 ± 2054 in Set 1 and 96971 ± 11127 in Set 2. When data were collected one
and three weeks later, the cumulative mean and standard deviation were 79168 ± 39032 and
68040 ± 54770, respectively. Thus, standard deviations for replicate spectra calculated using the
traditional method are not representative of the short-term and long-term instrumental variations
encountered in routine use. Moreover, even greater instrumental variations could occur when
replacing the injector septum or liner, retuning the mass spectrometer, or performing any other
maintenance that requires venting the mass spectrometer [5].
2.4.7 Effect of Predicted Standard Deviation on Association and Discrimination
To address this problem, it is possible to create a mathematical model to predict standard
deviations. The electron multiplier response is based on simple counting statistics and is
statistically predictable. The variations in response are proportional to the square root of the
abundance under shot-noise limited conditions [6]. Standard deviations predicted in this manner
61

only require knowledge of the ion abundance and are independent of the compound being
analyzed as well as its concentration, injection volume, split ratio, etc.
To model the electron multiplier response, a logarithmic graph of mean abundance versus
standard deviation for each ion in the spectra of the six alkanes at all five concentrations was
generated (90 spectra, 1237 ions, Figure 2.1). The equation used to fit the data will then predict
a standard deviation for any given ion abundance in any spectrum acquired with this mass
spectrometer.
An initial examination of the graph indicates that there are potentially two areas of the
graph with distinct slopes. The first is where the standard deviation is proportional to abundance
in a manner similar to that expected for shot-noise limits (slope = 0.5) and the second to that
expected for signal-to-noise scaling directly with signal (slope = 1.0). The data were manually
fit to two linear equations with a slope of 0.5525 and intercept of 0.9211 for the data with lower
standard deviations and a slope of 0.8405 and an intercept of -0.2311 for the data with higher
standard deviations (Figure 2.2). Variations of these equations, with manual fits at either the
upper or lower bounds were also investigated. However, none of the equations adequately
allowed for association of known replicates. In addition, applying two functions to the data
introduces a set value at which the data must be fit differently: this inherently abrupt value then
introduces variability. Lastly, the level of knowledge required to manually fit two regions of
data may not be practical for regulatory applications, such as implementation in a forensic
laboratory.
Due to these limitations, fitting to one linear equation using the automatic fitting in Excel
was investigated. A least-squares linear regression was performed and the resulting best-fit line
had a slope of 0.6900 ± 0.0332 and an intercept of 0.0440 ± 0.0093 (Figure 2.3). Using this
62

6

10
10 6

5 5

Standard Deviation

10
10

4 4

10
10

3 3

10
10

2

10
10 2

1 1

10
10
0

10 0
10
2

10
10 2

3

10
10 3

4

10
10 4
Mean Abundance

5
105

6
106
10

Figure 2.1 Logarithmic graph of standard deviation versus abundance for all ions in replicate mass spectra of alkanes (90 spectra, 1237
ions). Solutes C10, C11, C12, C13, C14, and C16; concentrations 0.05, 0.1, 0.5, 1.0, 5.0 mM; ionizing voltage 70 eV.
63

6

10
10 6

55

Standard Deviation

10
10

4

10
10 4

33

10
10

2

10
10 2

11

10
10
0

10 0
10
2
102
10

3
103
10

104
104

5
105
10

6
106
10

Mean Abundance
Figure 2.2. Logarithmic graph of standard deviation versus abundance for all ions in replicate mass spectra of alkanes (90 spectra,
1237 ions). Solutes C10, C11, C12, C13, C14, and C16; concentrations 0.05, 0.1, 0.5, 1.0, 5.0 mM; ionizing voltage 70 eV. Manual fit
of two linear equations with a slope of 0.5525 and intercept of 0.9211 for the data with lower standard deviations and a slope of
0.8405 and an intercept of and -0.2311 for the data with higher standard deviations.
64

6

10
10 6

55

Standard Deviation

10
10

4

10
10 4

33

10
10

2

10
10 2

11

10
10
0

10 0
10
2
2

10
10

3
3

4
4

10
10

5
5

6
6

10
10
10
10
10
10
Mean Abundance
Figure 2.3. Logarithmic graph of standard deviation versus abundance for all ions in replicate mass spectra of alkanes (90 spectra,
1237 ions). Solutes C10, C11, C12, C13, C14, and C16; concentrations 0.05, 0.1, 0.5, 1.0, 5.0 mM; ionizing voltage 70 eV. Linear best
fit line of slope 0.6900 ± 0.0332 and intercept 0.0440 ± 0.0093.

65

regression equation, predicted standard deviations were determined for each m/z value in the
spectra.
These predicted standard deviations were then used for the pair-wise comparisons (324
total) of all alkane spectra at 0.5, 1.0, and 5mM concentrations using the t-test at the 99.9%
confidence level. As a representative example, the C10 spectra in Set 1 are compared to all
alkane spectra in Set 2 as summarized in Table 2.11. The full tables are in Appendix D, Table
A7. In contrast to the results obtained using traditional standard deviations in Section 2.4.6,
spectra of corresponding alkanes were associated and spectra of different alkanes were
discriminated in nearly all cases.
For example, using traditional standard deviations in Section 2.4.6, C13 spectra in Set 1
could not be associated to C13 spectra in Set 2. This discrimination was due to one ion (m/z 85)
with unnormalized mean ± standard deviations of 67640 ± 160 and 66011 ± 117, respectively for
Sets 1 and 2. These are extremely small standard deviations relative to the mean and lie below
the mean population in Figure 2.3. The intrinsic standard deviations for this ion may not properly
represent all instrumental sources of variance. The spectra are unable to be associated at any
confidence level using this traditional method for calculating standard deviation. In contrast,
using the predicted standard deviation, the corresponding ion (m/z 85) had unnormalized mean ±
standard deviations of 67640 ± 2381 and 66011 ± 2341, respectively for Sets 1 and 2. These
standard deviations are comparable to the rest of the population observed in Figure 2.3. As
shown in Appendix D, Table A7, C13 alkanes associated at the 99.9% confidence level with a

66

43

RMP of 6.8 x 10- . Thus, standard deviations for replicate spectra calculated using the
predicted method appear to be more representative of the instrumental variations.
While discrimination at the most rigorous confidence level of 99.9% was possible in
nearly all cases, for alkanes with sequential carbon numbers, in which at least one was at the
lower concentration (0.5 mM), the spectra were discriminated at the 99.0% confidence level, as
illustrated in Table 2.11 for C10 and C11. In these cases, the molecular ion in the spectra at the
lower concentration was not statistically distinguishable above the instrumental threshold and,
hence, could not provide discrimination. If this were to occur in a practical application, the
compound should be re-analyzed using higher concentration, larger injection volume, or lower
split ratio to allow for differentiation from compounds with similar fragmentation patterns. In
general, however, it appears that the predicted standard deviation method is more reliable than
the traditional method for spectral association and discrimination, provided that the spectra are
representative of the compound.
As can be observed in Table 2.11, the spectra of alkanes at higher concentrations have
many discriminating ions, indicating that the spectra are readily differentiated. As concentration
of the alkanes decreases for either of the spectra being compared, the number of discriminating
ions also decreases. The same general trend can be observed in regard to carbon number; i.e., as
the carbon number decreases, the number of discriminating ions also decreases. Given the
similarity of the fragmentation pattern for the alkanes, it is noteworthy that the developed
statistical method can still identify up to 45 discriminating ions at the highest confidence level of
99.9%. At lower confidence levels, the number of discriminating ions is even greater; i.e., up to
69 and 475 ions at the 99% and 98% confidence levels, respectively.
67

Table 2.11. Effect of concentration and base peak abundance on the number of discriminating ions for comparison of C10 in Set 1
compared to all alkanes in Set 2 (t-test, 99.9% CL) using predicted standard deviation. Zero discriminating ions indicate complete
association and the corresponding random-match probability is shown in parentheses. The full tables are in Appendix D, Table A7.
Set 1 C10
Concentration
Set 2

(mM)

Base Peak
a
Abundance

C10

0.5

49,261 ± 3,126

0 (1.7 x 10- )

1.0

96,971 ± 11,127

0 (9.1 x 10- )

5.0

758,485 ± 52,032

C11

0.5
1.0
5.0

C12

48,955 ± 3,406 97,632 ± 2,054 711,381 ± 21,691
39

0 (1.8 x 10- )

39

39

0 (2.0 x 10- )

39

0 (1.8 x 10- )

38

0 (8.3 x 10- )

49,752 ± 1,881
99,757 ± 4,069
768,555 ± 33,173

1
2
4

11
2
4

2
3
8

0.5
1.0
5.0

66,851 ± 4,524
132,051 ± 11,330
1,125,547 ± 9,800

4
7
6

2
6
10

2
5
22

C13

0.5
1.0
5.0

78,760 ± 2,440
154,944 ± 3,294
1,282,901 ± 28,747

6
10
11

5
12
17

4
10
32

C14

0.5
1.0
5.0

94,112 ± 7,132
205,333 ± 7,039
1,480,021 ± 91,292

10
15
13

6
16
21

5
13
37

C16

0.5
1.0
5.0

80,040 ± 8,993
170,709 ± 3,568
1,348,779 ± 10,447

15
22
22

13
25
30

9
21
45

a

± one standard deviation, n = 3, 99.0% confidence level

68

0 (1.6 x 10- )

40

a

0 (1.3 x 10- )

39

0 (1.4 x 10- )

39
40

A representative example of the effect of confidence level on the number of
discriminating ions is given for the comparison of, 1 mM C10 (Set 1) to 1 mM C11 (Set 2) in
Table 2.12. With decreasing confidence level, the number of discriminating ions increases from
2 to 44. The number of even m/z value ions remains close to 50%, with an average of 52%.
However, the number of low abundance ions dramatically increases (50% to 91%) with the slight
decrease in confidence level from 99.9 to 99.0% and then decreases over the range of 95.0 to
50.0% for an overall average of 76% of the discriminating ions.
It is interesting to note the reasons for the greater success of the predicted standard
deviation method. As observed in Figure 2.1, a number of individual ions have standard
deviations that are much lower than others of the same abundance. As noted previously, this
underestimation of the standard deviation can occur when replicates do not adequately represent
the intrinsic instrumental variation. Most of these outliers occur for ions at abundances less than
100,000. Since discrimination relies heavily on low abundance ions, these ions fail the t-test
when using the traditional method of calculating standard deviations. In contrast, the predicted
standard deviations represent the instrumental variation in a consistent and uniform manner.
Moreover, once the model has been developed and validated, few or no replicates of standards
and samples are required to determine the standard deviation and perform the statistical
comparison. Because this method is more reliable, robust, and practical than the traditional
method, it is recommended for use in the developed statistical procedure.

69

Table 2.12. Effect of confidence level (CL) on the number of discriminating ions (# Ions) in the comparison of 1 mM C10 (Set 1) to 1
mM C11 (Set 2).
CL
99.9%
99.0%

# Ions
2
11

98.0%

14

95.0%

25

90.0%

32

80.0%

36

50.0%

44

Average
a

Low abundance ions (defined as ≤ 5% of base peak) are underlined

70

% Low
a
Abundance

50%
45%

50%
91%

50%

93%

52%

80%

59%

72%

58%

72%

50%

77%

52%

m/z
71, 126
71, 83, 97, 126, 127, 140, 142, 143, 154, 156,
157
59, 71, 82, 83, 97, 126, 127, 128, 140, 142, 143,
154, 156, 157
42, 43, 50, 51, 52, 59, 63, 71, 81, 82, 83, 84, 97,
99, 100, 112, 126, 127, 128, 140, 142, 143, 154,
156, 157
40, 42, 43, 50, 51, 52, 56, 59, 63, 70, 71, 72, 81,
82, 83, 84, 95, 97, 98, 99, 100, 112, 114, 126,
127, 128, 140, 142, 143, 154, 156, 157
40, 41, 42, 43, 44, 50, 51, 52, 56, 59, 63, 65, 70,
71, 72, 81, 82, 83, 84, 95, 97, 98, 99, 100, 109,
112, 114, 126, 127, 128, 140, 142, 143, 154,
156, 157
40, 41, 42, 43, 44, 50, 51, 52, 56, 59, 63, 65, 66,
68, 70, 71, 72, 77, 79, 81, 82, 83, 84, 86, 91, 95,
97, 98, 99, 100, 109, 111, 112, 113, 114, 126,
127, 128, 140, 142, 143, 154, 156, 157

% Even
m/z

76%

2.4.8

Retention Time Differentiation
Identification of compounds is generally based on a combination of retention time

comparison as well as mass spectral comparisons. Therefore, to add additional specificity to the
SAEEUMS method, an optional retention time tolerance was investigated to compare mass
spectra (Appendix E). The retention time comparison was found to be a powerful addition to
SAEEUMS; however it was not crucial for the determination of statistical association or
discrimination.
2.4.9 Comparison to NIST Standard n-Alkanes
As a further test and validation of the proposed method, the spectra acquired in this study
were compared with those in the NIST database [8]. As only one spectrum of each alkane was
available in the NIST database, this was compared to the replicate spectra in Set 1 using a onesample, two-tailed t-test at confidence levels of 98.0, 99.0, and 99.9% (Table 2.13). For each
pair-wise comparison (108 total), alkane spectra in Set 1 were statistically indistinguishable from
spectra of corresponding alkanes in the NIST database at the 99.9% confidence level. There
were three exceptions (5.0 mM concentrations of C13, C14, and C16), in which ions in the NIST
spectra with abundances near the threshold were statistically different from those in Set 1 with
abundances below the threshold. For all spectra that were statistically associated to those in the
NIST database, the random-match probabilities were calculated. As an example, the RMP for
38

C10 alkanes was 2.8 x 10- , indicating that the occurrence of this ion pattern by random chance

71

Table 2.13. The number of discriminating ions for the pair-wise comparison of Set 1 alkanes to the National Institute of Standards and
Technology (NIST) database alkanes (one sample t-test, 99.9% CL unless otherwise specified). Zero discriminating ions indicate
complete association and the corresponding random match probability is shown in parentheses. Entries in red highlight unexpected
association or discrimination.
Concentration
NIST
Set 1
(mM)
C10
C11
C12
C13
C14
C16
C10

0.5
1.0
5.0

37

0 (1.3 x 10- )
0 (2.8 x 10
0 (9.1 x 10

-38

)

-38

)

2

3

1

5

6

3

4

3

6

9

6

10

11

20

31

3

4

38

1

14

38

2

2

5

6

0 (8.6 x 10- )

39

6

6

14

25

1

0 (1.8 x 10- )

1

3

4

)

1

5

6

)

5

8

26

2

3

3
7

5
18

1

0 (4.0 x 10- )

2

0 (2.8 x 10- )

5.0
C12

0.5
1.0

C11

4

0.5

1

1.0

2

1

5.0
C13

10

5

0.5

1

1

38

0 (1.8 x 10
0 (9.5 x 10
1

1.0
5.0
C14

3
14

2
10

2
4

0.5

2

1

1

-38
-40

a

38

0 (2.0 x 10- )
0 (1.2 x 10
7
1

-38

)

41

0 (6.6 x 10- )
-41

2

1.0
5.0

a

2
17

2
6

1
13

0.5

1

1

1

1

1

0 (7.9 x 10- )

1.0
5.0

C16

4
21
3
25

2
20

2
12

1
21

2
5

0 (3.3 x 10- )
6

99.0 % confidence level
72

0 (4.1 x 10
1

)

4
14
42
42

is infinitesimally small. Moreover, this RMP value is comparable to that calculated previously
39

for the C10 alkanes in Set 1 and Set 2 (2.0 x 10- ).

The alkane spectra in Set 1 were statistically distinguishable from spectra of different
alkanes in the NIST database at the 99.9% confidence level, which is the most rigorous level for
discrimination (Table 2.13). There was one exception (0.5 mM C11 in Set 1 compared to C13 in
the NIST database), where discrimination was not possible at the 99.9% confidence level but was
achieved at the 99.0% confidence level. For all alkanes, the number of discriminatory ions
ranged from 1 to 31 and, in nearly all cases, the molecular ion was the sole fragment or among
the fragments leading to discrimination.
The successful association and discrimination of the alkanes in Set 1 to those in the NIST
database further demonstrates the power of this method, since these spectra were analyzed with
different GC-MS instruments, as well as different experimental conditions, concentrations, and
time periods.
2.4.10 Comparison to NIST Standard Branched Alkanes
While differentiation of normal alkane mass spectra can be challenging, the mass spectra
of large chain normal alkane and their respective branched isomers are reported to be
indistinguishable in most cases [9]. Therefore, mass spectra of Set 1 alkanes at 1 mM
concentration were compared to 30 branched alkanes in the NIST database at confidence levels
of 99.0 and 99.9% for a total of 180 comparisons (Table 2.14) [8]. Five isomers of each alkane,
consisting of 1 to 7 branches, were investigated and a representative example of the mass spectra
and corresponding chemical structures is shown for C10 isomers (Figure 2.4).
73

Table 2.14. The number of discriminating ions for the pair-wise comparison of 1 mM Set 1
normal (n) alkanes to the National Institute of Standards and Technology database branched
alkanes (one sample t-test, 99.9% CL unless otherwise specified, 180 total comparisons).
C10 Branched Isomers

n-C10

n-C11

n-C12

n-C13

n-C14

n-C16

2-methylnonane
3-methylnonane
2,3-dimethyloctane
2,4,6-trimethylheptane
2,2,5,5-tetramethylhexane
4-ethyloctane
C11 Branched Isomers

2
2
2
3
4
2

1
4
2
3
2
3

2
3
3
4
3
4

3
3
3
5
3
5

4
4
3
4
4
5

4
4
3
4
4
6

3-methyldecane,
2,3-dimethylnonane,

6
4

4
3

2
3

1
3
3

4
2
a
25
4
2

4
2

2,4,6-trimethyloctane,
2,2,6,6-tetramethylheptane
5-ethyl-2-methyloctane
C12 Branched Isomers

3
3
a
19
2
2

1
4
1

1
6
2

1
5
1

3-methylundecane,

2

3

3

4

4

3,8-dimethyldecane,
2,2,3-trimethylnonane
2,2,7,7-tetramethyloctane
5-ethyldecane

3
4
2
3

5
4
3
3

3
4
3
2

3
4
3
3

2
5
4
3

4
a
41
6
3
2

a

99.0% confidence level

74

Table 2.14 (cont’d)

C13 Isomers

n-C10

n-C11

n-C12

n-C13

n-C14

n-C16

3-methyldodecane
3,9-dimethylundecane,
2,3,4-trimethyldecane

3
5
5

2
2
6

3
4
5

3-methyl-5-propylnonane
4-ethylundecane
C14 Isomers

7
7

3
5

3
3

3
3
4
a
21
3

3
3
4
a
32
2

1
2
2
a
34
1

2-methyltridecane
2,3-dimethyldodecane
4,6-dimethyldodecane
6-methyltridecane

7
12
4
6

3
6
1
3

4
7
2
1

5
7
1
1

3
4
2
2

3,5-dimethyldodecane
C16 Isomers

4

3

1

2

1

2
3
1
1
a
35

3-methylpentadecane
4,11-dimethyltetradecane
4-ethyltetradecane
5-ethyl-5-propylundecane
2,2,4,4,6,8,8-heptamethylnonane

17
11
11
16
2

13
8
9
13
2

10
9
8
12
3

9
7
7
12
4

10
10
9
10
4

6
6
7
8
4

a

99.0% confidence level

75

100

0

B

A

40

240

100

40

C

240

Relative Abundance

D

0
40
100

240 40

E

0
40

240
F

240 40

240

m/z

Figure 2.4. Relative abundance mass spectra of C10 isomers (A) n-decane, (B) 3-methylnonane,
(C) 2,3-dimethyloctane, (D) 2,4,6-trimethylheptane, (E) 2,2,5,5-tetramethylhexane, and (F) 4ethyloctane. Chemical structures shown as inserts.

76

Among all comparisons, 173 were statistically distinguished at a 99.9% confidence level, with 1
to 17 discriminating ions. The other 7 comparisons were statistically distinguished at a 99.0%
confidence level, with 19 to 41 discriminating ions.

The ions responsible for discrimination of the normal alkanes from the C10 branched
isomers were further examined for general trends (Table 2.15). The most common discriminating
ions were m/z 71, 85, 98, 112, 142. Ions with low abundance represented 47% of the
discriminating ions. Ions with even m/z values represented 59% of the total discriminating ions,
indicating that well over half of the differentiations resulted from multiple-bond cleavages or
rearrangement. These ions are responsible for 15% more of the differentiation than that observed
for the normal alkanes (44%).
The similarity of the branched and normal alkane mass spectra were compared using
PPMC coefficients (Table 2.16, 180 total comparisons). The coefficients for comparison of the
branched and normal alkanes (Set 1) ranged from 0.7056 to 0.9886, indicating a moderate to
strong correlation for all spectra. Interestingly, the higher the level of branching the lower the
PPMC coefficient. For the alkanes investigated in this work, the more branching, the larger the
difference in fragmentation pattern compared to the normal alkanes. This could be due to
preferential cleavage at branch points, thereby leading to different fragmentation than the normal
alkanes [5]. Many comparisons of branched to normal alkane spectra had higher coefficients
than comparisons of corresponding normal to normal alkane spectra (0.9611 to 1.000, Section
2.4.1). Hence, these compounds also provide a rigorous test of the ability of the proposed
method to discriminate mass spectra. Given the high level of similarity it is remarkable that in

77

Table 2.15. Representative examples of m/z values and general trends of ions responsible for
discrimination of 1 mM Set 1 normal alkanes to C10 branched alkane isomers from the National
Institute of Standards and Technology database, using a two-tailed Student’s t-test at the 99.9%
confidence level.

Set 1/NIST
C10

C11

C12

a

2-methylnonane
3-methylnonane
2,3-dimethyloctane
2,4,6-trimethylheptane
2,2,5,5-tetramethylhexane
4-ethyloctane
2-methylnonane
3-methylnonane
2,3-dimethyloctane
2,4,6-trimethylheptane
2,2,5,5-tetramethylhexane
4-ethyloctane
2-methylnonane
3-methylnonane
2,3-dimethyloctane
2,4,6-trimethylheptane
2,2,5,5-tetramethylhexane
4-ethyloctane

Number
of Ions m/z
2
126, 127

% Even
m/z
50%

% Low
a
Abundance
100%

2
2
3
4
2
1

85, 112
85, 98
84, 85, 127
56, 70, 85, 127
98, 112
142

50%
50%
33%
50%
100%
100%

50%
50%
33%
75%
50%
0%

4
2
3
2
3

85, 112, 113, 142
85, 98
84, 85, 142
56, 85
98, 112, 142

50%
50%
67%
50%
100%

75%
50%
33%
50%
75%

2

42, 142

100%

50%

3
3
4
3
4

85, 112, 113
71, 85, 98
71, 84, 85, 142
56, 70, 85
84, 98, 112, 142

33%
33%
50%
67%
100%

75%
33%
25%
67%
50%

≤ 5% of base peak

78

Table 2.15 (cont’d)

Set 1/NIST
C13

C14

C16

2-methylnonane
3-methylnonane
2,3-dimethyloctane
2,4,6-trimethylheptane
2,2,5,5-tetramethylhexane
4-ethyloctane

Number
of Ions m/z
3
42, 71, 142
3
3
5
3
5

85, 112, 113
71, 85, 98
52, 71, 84, 85, 142
56, 70, 85
52, 84, 98, 112,
142
42, 71, 85, 142

33%
33%
60%
67%
100%

33%
33%
40%
67%
40%

50%

25%

2-methylnonane
3-methylnonane
2,3-dimethyloctane
2,4,6-trimethylheptane
2,2,5,5-tetramethylhexane
4-ethyloctane

4
4
3
4
4
5

56, 85, 99, 112
71, 85, 98
71, 84, 85, 142
56, 70, 85, 99
51, 84, 98, 112,
142

50%
33%
50%
50%
80%

25%
33%
25%
75%
40%

2-methylnonane
3-methylnonane
2,3-dimethyloctane
2,4,6-trimethylheptane
2,2,5,5-tetramethylhexane
4-ethyloctane

4
4
3
4
4
6

42, 71, 85, 142
56, 85, 99, 112
71, 85, 98
71, 84, 85, 142
56, 70, 85, 99
51, 52, 84, 98, 112,
142

50%
50%
33%
50%
50%
83%

25%
50%
33%
25%
75%
67%

59%

47%

% Total
a

% Low
% Even
a
Abundance
m/z
67%
33%

≤ 5% of base peak

79

Table 2.16. Pearson product moment correlation (PPMC) coefficients comparing 1 mM Set 1
normal alkanes to branched alkane isomers from the National Institute of Standards and
Technology (NIST) database (180 total comparisons).
NIST/Set 1
C10 Branched Isomers
2-methylnonane
3-methylnonane
2,3-dimethyloctane
2,4,6-trimethylheptane
2,2,5,5-tetramethylhexane
C11 Branched Isomers
3-methyldecane,
2,3-dimethylnonane,
2,4,6-trimethyloctane,
2,2,6,6-tetramethylheptane
5-ethyl-2-methyloctane
C12 Branched Isomers
3-methylundecane,
3,8-dimethyldecane,
2,2,3-trimethylnonane
2,2,7,7-tetramethyloctane
5-ethyldecane
C13 Branched Isomers
3-methyldodecane
3,9-dimethylundecane,
2,3,4-trimethyldecane
3-methyl-5-propylnonane
4-ethylundecane
C14 Branched Isomers
2-methyltridecane
2,3-dimethyldodecane
4,6-dimethyldodecane
6-methyltridecane
3,5-dimethyldodecane
C16 Branched Isomers
2-methylnonane
3-methylnonane
2,3-dimethyloctane
2,4,6-trimethylheptane
2,2,5,5-tetramethylhexane

n-C10

n-C11

n-C12

n-C13

n-C14

n-C16

0.9159
0.9092
0.9244
0.8253
0.9601

0.9385
0.9144
0.9032
0.8446
0.9672

0.9400
0.9016
0.8967
0.8363
0.9633

0.9363
0.8894
0.8956
0.8349
0.9596

0.9313
0.8794
0.8920
0.8290
0.9534

0.9308
0.8741
0.8773
0.8245
0.9463

0.9561
0.9209
0.9600
0.8185
0.9524

0.9713
0.9400
0.9625
0.8265
0.9621

0.9754
0.9479
0.9552
0.8146
0.9672

0.9773
0.9399
0.9469
0.8178
0.9619

0.9748
0.9333
0.9404
0.8144
0.9562

0.9689
0.9311
0.9342
0.8069
0.9520

0.9573
0.9420
0.7412
0.8102
0.9520

0.9682
0.9581
0.7461
0.8187
0.9659

0.9705
0.9619
0.7263
0.8038
0.9671

0.9727
0.9663
0.7217
0.8042
0.9631

0.9729
0.9686
0.7135
0.8006
0.9600

0.9702
0.9691
0.7056
0.7947
0.9585

0.9593
0.9303
0.9069
0.9268
0.9641

0.9687
0.9495
0.9238
0.9542
0.9644

0.9633
0.9505
0.9375
0.9693
0.9654

0.9601
0.9540
0.9357
0.9763
0.9635

0.9558
0.9554
0.9349
0.9807
0.9615

0.9516
0.9566
0.9339
0.9848
0.9565

0.9702
0.9517
0.9400
0.9395
0.9542

0.9752
0.9649
0.9608
0.9562
0.9683

0.9750
0.9717
0.9704
0.9548
0.9691

0.9686
0.9715
0.9675
0.9522
0.9704

0.9836
0.9642
0.9426
0.9235
0.9421

0.9595
0.9699
0.9656
0.9493
0.9705

0.9629
0.9238
0.9711
0.9508
0.7419

0.9721
0.9241
0.9687
0.9608
0.7615

0.9725
0.9304
0.9694
0.9696
0.7528

0.9737
0.9241
0.9650
0.9748
0.7529

0.9236
0.9180
0.9886
0.9440
0.7078

0.9700
0.9104
0.9532
0.9783
0.7590

80

180 comparisons of normal alkanes to branched alkanes, the proposed method was able to
differentiate the mass spectra at the two highest confidence levels.
2.4.11 Comparison of SAEEUMS to NIST Library Search Algorithm
The results of SAEEUMS were compared to the widely used NIST library search
algorithm (Chapter 1.2.1). For these comparisons, alkanes in Set 1 at 1 mM concentration were
searched in the library and the resulting match factor and probability for the corresponding NIST
standard alkane are given in Table 2.17. In each case the NIST library search returned the
correct identity as the first compound on the match list. Match Factors ranged from 904 to 952,
indicating excellent matching [10]. However, the NIST Probabilities ranged from 32.5 to 52.4%,
indicating low probabilities that the matches are correct. Due to the method for calculating the
probabilities (Chapter 1.2.1), low probability values would be expected as the alkanes have many
similar spectra [10]. Using SAEEUMS, the spectra were statistically associated at a confidence
38

level of 99.9% with RMP on the order of 10-

42

to 10- .

While, the NIST identity was correct for each search, the program was unable to establish
whether this tentative identification was objectively correct (Chapter 1). In addition, the
database probabilities of correctness were under 52.4% in each case, which while explainable, is
still an incorrect indication of the accuracy of the match. In contrast, SAEEUMS was able to
determine that the same spectra were statistically associated at a 99.9% confidence level, as well
as returning the probability that the pattern of ions occurs by random chance alone (RMP).
Therefore, SAEEUMS provides an objective confirmation of the mass spectral identification that
addresses the NRC recommendations and is a timely advance, not only for legal and regulatory
applications, but for any application in which objective validation is desired [11].
81

Table 2.17. The SAEEUMS random-match probability (RMP), after the t-test indicated complete
association at the 99.9% confidence level, and the corresponding Match Factor and Probability
from the NIST library search database for the comparison of Set 1 alkanes at 1mM compared to
the NIST n-alkane standards.

NIST Match
Factor

RMP
38

C10

2.8 x 10-

C11

2.8 x 10

C12

1.8 x 10

C13

1.2 x 10

C14

4.1 x 10

C16

3.3 x 10

-38
-38
-38
-41
-42

NIST
Probability

952

52.4%

904

36.9%

939

38.1%

948

44.1%

921

38.1%

915

35.5%

82

2.5

CONCLUSIONS
A statistical method for comparing mass spectra of an unknown compound to a reference

standard was developed using an alkane and alkylbenzene data set. At the same concentration,
statistical association of corresponding compounds and discrimination of different compounds
was possible at the 99.9% confidence level. For compounds that were statistically associated,
39

the RMPs were on the order of 10-

46

to 10- , indicating the low probability that the

characteristic fragmentation patterns occur by random chance alone. At varying concentrations,
discrimination of different alkanes was still possible, but association of corresponding alkanes
was not possible using the traditional method to calculate standard deviations. In contrast,
standard deviations predicted from a statistical model of the detector were more representative of
short-term and long-term instrumental variance and allowed for association and discrimination of
the alkanes at varying concentrations. In addition, using the predicted standard deviations,
spectra of the alkanes were successfully associated to and discriminated from normal and
branched alkane spectra in the NIST database, even though these spectra were collected on
different instruments using different experimental conditions, and over different time periods.
While proof-of-concept in nature, the statistical approach to establish equivalence of
unabbreviated mass spectra, developed and validated herein, provides a simple and rapid method
to assign statistical assessment in the comparison of mass spectra. This method not only
provides the confidence level for association and discrimination, but also the random-match
probability for association. This method can be implemented without expensive software and is
broadly applicable across many fields, including industrial, pharmaceutical, food, environmental,
and forensic chemistries.

83

2.6

SUMMARY OF FINAL METHOD
The SAEEUMS method is, therefore, composed of two major phases. Initially, statistical

hypothesis testing, in the form of an unequal variance t-test, is applied at every m/z value in the
mass range. This test is used to determine if the spectra are statistically indistinguishable at a
given confidence level. Then, if the spectra are indistinguishable, the RMP is calculated based on
the frequency of ion occurrence at each m/z value in a selected database. In the present case, the
RMP assesses the probability that the characteristic fragmentation pattern of the two mass
spectra would occur by random chance alone.
2.6.1 Considerations
Several considerations involving the sample compound and GC-MS instrument are
essential to the accuracy of the statistical association and discrimination of mass spectra. The
sample compound must be both chemically and thermally stable, as well as sufficiently
concentrated to produce a representative mass spectrum. The column and GC temperature
program should be chosen so the sample compounds are baseline resolved. To insure that the
mass spectra are reproducible, the instrument must be clean and well maintained. The septum
and chromatographic column should be low bleed to minimize extraneous background ions.
Constant instrumental parameters, for example the electron ionization energy and tune
conditions, should be used throughout the duration of data collection.
2.6.2 Data Analysis
The mass spectra are exported from ChemStation Software to Microsoft Excel. All
calculations and logical functions are then performed in Microsoft Excel. The exported data from
ChemStation contains only the abundances of the ions present in the spectrum above the
84

instrumental peak threshold. Therefore, to create a complete mass spectrum, the m/z value for
each ion is rounded to its integer value and the corresponding abundance is tabulated for the
entire mass scan range. For any ion not present in the mass spectrum, an abundance of 0 is
entered. Therefore, to create a complete mass spectrum, an abundance of zero must be entered
for any ion below the threshold. Each m/z value was rounded to its integer value and the
corresponding abundance was tabulated for the entire mass scan range.
Prior to performing the t-test, a predicted standard deviation associated with the
abundance of each ion in the scan range is calculated. The mean abundance and standard
deviation of instrumental replicates (n = 3 recommended) for every ion in the mass scan range
where the abundances are greater than the instrumental threshold for all replicates are then
calculated. A logarithmic graph of the mean abundances versus standard deviation for several
samples (n ≥ 5 recommended) is generated. A separate graph is needed for each instrument on
which data is analyzed; however, one graph is sufficient for all data analyzed on that instrument,
regardless of the identities of the compounds, until spectrometer maintenance (primarily
involving venting) is performed.
A least-squares linear regression is performed and the resulting regression equations are
used to predict standard deviations for each m/z value in the spectra and used in all t-test
comparisons. For any ion at or below the instrumental threshold, the standard deviation is
predicted at the threshold abundance. The mean abundances and standard deviations are then
normalized to the base peak.
The number of instrumental replicates used to calculate the standard deviations on the
logarithmic graph are used as the sample size (n) in the Student’s t-test calculation. An unequal

85

variance student t-test is performed in which the Welch t-statistic, tcalc, and the associated
degrees of freedom are calculated at each m/z value [1]. These are compared to the critical
values, tcrit, at various confidence levels using a two-tailed table. Using an IF function in Excel,
a value of 1 is returned if the mean abundance for each m/z value is statistically indistinguishable
(tcalc ≤ tcrit), and a value of 0 is returned if statistically different (tcalc > tcrit) at the specified
confidence level. The two spectra are considered statistically associated if the product of these
values is 1 (i.e., if values of 1 were returned for every m/z value) and are considered statistically
different if the product is 0 (i.e., if a value of 0 was returned for any m/z value).
To calculate the random-match probability, a binary consolidated array, C, of the two
spectra is created, in which a value of 1 is returned at that m/z value if an ion is present in both
spectra. Conversely, a value of 0 is returned if the ion is absent in both spectra. Although the
spectra are statistically equivalent, it is still possible for an ion to be present in one spectrum (i.e.,
near the threshold) but not in the other (i.e., below the threshold). In such cases, to be
conservative, a value of 0 is returned to eliminate that ion from the RMP calculation.
The NIST Mass Spectral Search Program (version 2.0, Gaithersburg, MD), which
contains 147,198 mass spectra, is used as a representative database to determine the frequency of
fragment ions. The number of spectra in the database containing each ion in the mass scan range
above 1% threshold (the lowest threshold allowed) is tabulated using the search function in the
NIST program. The probability of each ion in C with a value of 1 is calculated as the number of
spectra containing that ion divided by the total number of spectra in the NIST database. The
probability of an ion in C with a value of 0 is calculated as the number of spectra not containing
that ion divided by the total number of spectra in the NIST database. The RMP is then
86

calculated as the product of the probabilities at each m/z value. This represents the probability
that the pattern of ions occurs by random chance alone.
Ions that are known to be chemically irrelevant are removed from the RMP calculations
in two ways. The mass scan range should be chosen to avoid common atmospheric compounds
(such as H2O, N2, etc.) that are not removed completely by the vacuum pump. In addition,
common contaminant ions from column or septum degradation (e.g., m/z 73, 147, 207, 221, 281,
295, 355, 429) or fluorinated hydrocarbons used for mass tuning (e.g., m/z 69, 219, 502) are
ignored in the RMP calculations if below a user-defined value (e.g., 5% of the base peak). If
above this value, the ions are assumed to be chemically relevant to the compound and are
included in the calculation. The options to keep include all ions in the calculation (regardless of
known containment ions) or remove other ions is also possible.
2.6.3 Output
All calculations for this statistical procedure have been automated in a Microsoft Excel
template, thereby minimizing any additional work needed. After the initial preparation of the
predicting standard deviation logarithmic graph, analysts can export spectra of the case sample
and the reference standard into the template, enter in the linear regression slope and intercept,
and specify the desired confidence level. If, at the desired confidence the two spectra are
statistically associated the template automatically returns the random match probability.
Conversely, if not statistically associated at the desired confidence, the number of discriminating
ions is returned in the template.

87

REFERENCES

88

REFERENCES
[1]

Devore JL. Probability and statistics for engineering and the sciences. Belmont, CA:
Duxbury Press, 1990.

[2]

McLafferty FW, Hertel RH, Villwock RD (1974) Probability based matching of mass
spectra, rapid identification of specific compounds in mixtures. Org Mass Spectrom 9:
690-702.

[3]

Bafna V, Edwards N (2001) SCOPE: A probabilistic model for scoring tandem mass
spectra against a peptide database. Bioinformatics 17, Suppl 1: 13–21.

[4]

Fu Y, Yang Q, Sun R, Ling C, Li D, Zhou H, He S, Gao W (2004) Exploiting the kernel
trick to correlate fragment ions for peptide identification via tandem mass spectrometry.
Bioinformatics 20: 1948-1954.

[5]

Smith RM (2004) Understanding mass spectra: a basic approach. Hoboken, New Jersey:
John Wiley and Sons.

[6]

Stein SE, Scott DR (1994) Optimization and testing of mass spectral library search
algorithms for compound identification. J Am Soc Mass Spectrom 5: 859-866.

[8]

Linstrom P, Mallard W, NIST Chemistry WebBook, NIST Standard Reference Database
Number 69, National Institute of Standards and Technology, Gaithersburg, MD,
http://webbook.nist.gov, (retrieved April 25, 2012).

[9]

Issacman G, Wilson KR, Chan AWH, Worton DR, Kimmel JR, Nah T, Hohaus T, Gonin
M, Kroll J, Worsnop DR, Goldstein AH (2012) Improved resolution of hydrocarbon
structures and constitutional isomers in complex mixtures using gas chromatographymass spectrometry. Anal Chem 84: 2335−2342.

89

[10]

Stein SE (2008) NIST standard reference database 1A. Users guide. National Institute of
Standards and Technology, Gaithersburg, MD

[11]

Strengthening Forensic Science in the United States: A Path Forward. National Research
Council of the National Academies. The National Academies Press, Washington D.C.
2009.

[12]

Crawford JD, Morrison JD (1968) Computer methods in analytical mass spectrometry
identification of an unknown compound in a catalog. Anal Chem 40: 1464-1469.

[13]

Forensic chemistry section quality manual. Document DRG‐DOC‐01. Little Rock, AR:
Arkansas State Crime Laboratory, 2009.

90

CHAPTER 3
STATISTICAL COMPARISON OF MASS SPECTRA FOR FORENSIC
IDENTIFICATION OF AMPHETAMINE-TYPE STIMULANTS
3.1

INTRODUCTION
The illegal use of amphetamine-type stimulants (ATS) has increased and, as of 2011,

these stimulants were the second most widely abused controlled substances worldwide [1]. In
North America, between 2005 and 2009, seizures of amphetamine increased by 220%, while
seizures of methamphetamine and 3,4-methylenedioxymethamphetamine (MDMA) increased by
116% and 71%, respectively [1]. Due to this widespread abuse, these compounds constitute a
significant proportion of the controlled substance cases submitted to forensic laboratories around
the world.
Gas chromatography-mass spectrometry (GC-MS) is the most common technique for the
analysis and identification of controlled substances [2]. However, identification of
amphetamine-type stimulants by mass spectrometry can be particularly challenging. Firstly,
many of these compounds readily fragment under the electron ionization conditions typically
used. As a result, the molecular ion is not always present in the spectrum and, hence, no
information on the molecular mass of the compound is obtained [3]. Secondly, since many of
these stimulants have the phenethylamine base structure, the mass spectral fragmentation
patterns are very similar, particularly at low m/z values. To overcome some of these problems in
identification, the stimulants can be derivatized prior to analysis or an alternative, ‘softer’
ionization technique, such as chemical ionization, can be used [2,4]. However, derivatization
increases the total analysis time. In the case of a different ionization technique, modification to
91

the analytical methods or additional instrumentation may be required. Therefore, in many
forensic laboratories, amphetamine-type stimulants are routinely analyzed without derivatization
and by GC-MS with electron ionization [5]. To identify the controlled substance in the case
sample, the resulting mass spectrum is visually compared either to the mass spectrum of a
suitable reference standard or to a reference database.
Unfortunately, with this visual assessment, the comparison of spectra can be subjective in
nature, which could result in rejection of scientific testimony in court [6]. Since the publication
of the National Academy of Sciences National Research Council (NRC) report of the current
state of forensic science in the United States, there has been a growing need for a statistical
assessment of forensic evidence [7]. Currently, when the mass spectrum of a case sample is
compared to spectra in a reference database, a similarity index (SI) is often reported to indicate
the closeness of the match. However, in forensic science, caution is advised against using a SI
for evaluation of the match [8]. As described in Chapter 1.2.1, such indices give only a measure
of the similarity of spectra, not an error rate or associated confidence level in the identification.
Neither the SI nor the visual examination provides a statistical confidence in the identification of
the compound, as required by the Daubert standard for the admissibility of evidence [9].
Therefore, a confidence level associated with the identification of any controlled substance
would be beneficial and further meet the requirements of the Daubert standard and address the
recommendation set forth by the NRC.
In forensic laboratories, the case sample is often not analyzed in replicate and may not
necessarily be analyzed on the same day as the reference standard [10]. In addition, submitted
samples of controlled substances are often not high purity, containing cutting agents and
synthesis by-products. The presence of these additional compounds can increase the complexity
92

of both the chromatogram and the mass spectrum due to co-elution and increased background
noise. In turn, this increases the difficulty in comparing the spectrum of the case sample to that
of the reference standard.
In this chapter, the utility of the statistical approach to establish equivalence of
unabbreviated mass spectra (SAEEUMS) is investigated for practical applications in forensic
laboratories. Mass spectra of appropriate reference standards and submitted case samples
containing amphetamine, methamphetamine, 3,4-methylenedioxyamphetamine (MDA), MDMA,
phentermine, and psilocin were used for this investigation. While not classified as an
amphetamine-type stimulant, psilocin has a similar fragmentation pattern to methamphetamine,
MDMA, and phentermine, and, therefore, was included in this investigation. All spectra were
collected by an accredited forensic laboratory and no modifications were made to the
laboratory’s standard operating procedures for the analysis of these reference standards and case
samples.
3.2

MATERIALS AND METHODS

3.2.1 Sample Preparation
The mass spectra of all reference standards and case samples used in this work were
provided by Garth Glassburg and associates (Northern Illinois Regional Crime Laboratory,
NIRCL, Vernon Hills, IL). Reference standards of amphetamine, MDA, MDMA, and psilocin
(Alltech-Applied Science Labs, State College, PA) were standard solutions in 1 mL methanol
and methamphetamine and phentermine (Sigma-Aldrich, St. Louis, MO) were standard solutions
in 1 mL methanol. All case samples were prepared according to the standard protocols of the
NIRCL. That is, case samples were prepared in methanol (HPLC grade, ThermoFisher
93

Scientific, Waltham, MA) without consideration to concentration. Prior to this work, the NIRCL
had identified the controlled substance in the case samples as follows: Cases 1 - 7 contained
amphetamine, Cases 8 - 13 contained methamphetamine, Cases 14 - 20 contained MDA, Cases
21 - 30 contained MDMA, Case 31 contained phentermine, and Cases 32 - 36 contained psilocin
(Table 3.1).
3.2.2 GC-MS Analysis
All reference standards and case samples were analyzed using an Agilent 6890N gas
chromatograph (Agilent Technologies, Santa Clara, CA) equipped with a HP-1MS column (25 m
x 0.20 mm i.d. x 0.33 µm film thickness, Agilent Technologies, Palo Alto, CA) and an Agilent
7683B automatic liquid sampler (Agilent Technologies). Ultra-high purity helium (Airgas Great
Lakes, Independence, OH) was used as the carrier gas with a nominal flow rate of 1.2 mL/min.
The inlet was maintained at 250 °C and 1 μL of the sample was injected. Various split modes
(splitless, 5:1, 20:1, 50:1, 100:1) were used depending on the sample and apparent concentration.
All reference standards and case samples were analyzed using the following oven temperature
program: 130 °C for 0 min, then 12 °C/min to 190 °C, followed by a 25 °C/min ramp to 290 °C,
with a final hold of 8 min. The two exceptions were one methamphetamine and one MDA
reference standard that were analyzed using an oven temperature program of 100 °C for 0 min,
15 °C/min to 180 °C, followed by a 25 °C/min ramp to 290 °C with a final hold of 7 min. The
transfer line to the Agilent 5975C mass selective detector (Agilent Technologies) was maintained
at 250 °C in all cases. Electron ionization (70 eV) was used and the quadrupole mass analyzer
was operated in the full scan mode (m/z 43 - 400) with a scan rate of 3.66 scans/s and an
instrumental peak threshold of 200.

94

Table 3.1. Date of analysis and retention time (tR) of reference standards and case samples of
amphetamine, methamphetamine, MDMA, MDA, phentermine, and psilocin mass spectra

Sample
Date of Analysis tR (min) Sample
Amphetamine
MDMA
Standard 1
4/28/2011, 21:24
1.919
Standard 7
Standard 2
4/2/2011, 1:24
1.964
Standard 8
Case 1
5/21/2011, 12:17
1.925
Case 21
Case 2
5/12/2011, 13:41
1.909
Case 22
Case 3
7/5/2011, 11:26
1.906
Case 23
Case 4
7/6/2011, 15:46
1.904
Case 24
Case 5
8/11/2011, 15:03
1.529
Case 25
Case 6
6/9/2011, 17:50
1.905
Case 26
Case 7
5/22/2011, 16:42
1.918
Case 27
Case 28
Methamphetamine
Standard 3
7/29/2011, 11:46
2.174
Case 29
Standard 4*
6/8/2009, 20:07
2.713
Case 30
Case 8
3/9/2011, 12:52
2.179
Case 31
Case 9
3/9/2011, 15:24
2.179
Phentermine
Case 10
7/29/2011, 12:40
2.164
Standard 9
Case 11
3/11/2011, 21:21
2.164
Standard 10
Case 12
3/11/2011, 22:02
2.169
Case 31
Case 13
7/28/2011, 14:49
2.180
Psilocin
Standard 11
MDA
Standard 5
2/28/2011, 14:22
4.019
Standard 12
Standard 6*
6/8/2006, 20:29
5.469
Case 32
Case 14
4/2/2011, 15:48
4.076
Case 33
Case 15
4/2/2011, 14:26
4.079
Case 34
Case 16
4/2/2011, 14:47
4.074
Case 35
Case 17
4/2/2011, 15:07
4.080
Case 36
Case 18
4/2/2011, 16:08
4.077
Case 19
4/2/2011, 16:28
4.076
Case 20
4/2/2011, 16:49
4.080
*alternative temperature program used, Section 3.2.2

95

Date of Analysis

tR ( min)

4/2/2011, 4:37
2/19/2011, 15:59
5/27/2011, 11:13
5/12/2011, 15:28
8/5/2011, 8:14
8/5/2011, 18:23
8/8/2011, 9:21
4/2/2011, 13:12
4/1/2011, 15:11
4/1/2011, 15:31
4/2/2011, 11:49
4/2/2011, 12:19
5/2/2011, 13:25

4.533
4.468
4.499
4.507
3.864
3.905
3.869
4.559
4.533
4.530
4.563
4.562
4.583

3/10/2011, 10:25
4/18/2012, 7:51
5/12/2011, 19:01

2.071
1.005
2.087

8/5/2011, 14:46
8/5/2011, 18:56
5/27/2011, 12:44
6/12/2011, 17:11
6/15/2011, 15:56
1/6/2011, 16:42
1/7/2011, 12:40

1.799
6.969
7.501
7.474
7.477
7.559
7.588

3.2.3 Data Analysis
All mass spectra were exported from ChemStation Software (version E01.02.16, Agilent
Technologies, Santa Clara, CA) to Microsoft Excel (version 2007, Microsoft Corp., Redmond,
WA), and analyzed using the SAEEUMS method described in Chapter 2.6.
To predict standard deviations in this work, logarithmic graphs of mean abundance
versus standard deviation were generated using spectra of five case samples containing MDMA.
Three replicates from a total of 15 spectra (502 ions) were used to generate the first graph for
comparison of case samples to reference standards collected on the same instrument and two
replicates from a total of 16 spectra (855 ions) were used to generate the second graph for
comparison of case samples to standards from the NIST database collected on different
instruments. The mean abundance and standard deviation were calculated for every ion in the
mass scan range with abundances greater than the instrumental threshold for all replicates. The
two graphs showed similar trends and the standard deviation is proportional to abundance in a
manner similar to that expected for shot-noise limits (slope = 0.5). A least-squares linear
regression was performed and, for spectra collected on the same instrument, the resulting best-fit
line had a slope of 0.6922 ± 0.0156 with an intercept of 0.3238 ± 0.0632 (Figure 3.1). For
comparison of case samples to NIST standards (collected on different instruments), the best-fit
line had a slope of 0.7139 ± 0.0210 and an intercept of 0.1086 ± 0.0839 (Figure 3.2). Using
these regression equations, standard deviations were predicted for each m/z value in the spectra
and used in all t-test comparisons. For any ion at or below the instrumental threshold (200
counts), the standard deviation was predicted at an abundance of 200. The number of
instrumental replicates used to calculate the standard deviations on the logarithmic graph
discussed above was used as the sample size (n) in the Student’s t-test calculation (n = 3 for
96

6.0
6 6

10
10

5.0
5 5

4 4
4.0

10
10
Log (Standard deviation)

Standard Deviation

10
10

3
3.0

10
10 3

2

10 2.0
102

1

101
10 1.0
0

10 0.0
0

10

2
2

2.0
10
10

2.5

3
3

3.0
10
10

3.5

4
4.0
104
10

4.5
5.0 5
105
10
Log (Abundance)

5.5

6.06
106
10

6.5

7.07
107
10

Mean Abundance

Figure 3.1. Logarithmic graph of mean abundance versus standard deviation for mass spectra of MDMA (15 spectra, 502 ions). Linear
best fit line with slope 0.6922 ± 0.0156 and intercept 0.3238 ± 0.0632.
97

6
6.0

10
10 6
5

105
10 5.0

3

10 3.0
103
Title

Standard Deviation

4

10 4.0
104

2

10 2.0
102

1

10 1.0
101
0

10

0.0
100

-1

10 -1.0
10-1

2
102

2.0

2.5

3.0
3

10
10 3

3.5

4.0
4

4.5

5.0
5

10
10
10 4
10 5
Title
Mean Abundance

5.5

6.0
6

10
10 6

6.5

7.0
7

10 107

Figure 3.2. Logarithmic graph of mean abundance versus standard deviation for mass spectra of MDMA (16 spectra, 855 ions). Linear
best fit line with slope 0.7139 ± 0.0210 and intercept 0.1086 ± 0.0839.
98

spectra collected on the same instrument and n = 2 for spectra collected on different
instruments). Ideally, replicates of both the reference standard and the case samples would be
used to be more representative of the variance. In this work, however, spectra of two reference
standards were compared to the spectrum of the case sample, as no replicates were available for
the case samples. The reference standards were chosen as the two most recently analyzed by the
forensic laboratory for each stimulant from those with acceptable chromatography (e.g. baseline
resolved without excessive fronting). The reference standards were analyzed over a time period
from the same day to two years apart and the case samples were analyzed over a time period of
the same day to two years after the reference standards (Table 3.1).
3.3

RESULTS AND DISCUSSION

3.3.1 Similarity of Amphetamine-type Stimulants
The amphetamine-type stimulants have chemically similar structures due to a common
phenethylamine base (Figure 3.3). Both methamphetamine and phentermine differ structurally
from amphetamine by a methyl group and, hence, these two compounds are structural isomers.
MDA and MDMA differ structurally from amphetamine and methamphetamine, respectively, by
a 3,4-methylenedioxy ring attached to the phenyl ring. Due to the similarity in structures, the
mass spectral fragmentation pattern is similar among these compounds (Figure 3.3).
Amphetamine and MDA have the same base peak (m/z 44) and some similar low abundance ions
(e.g., m/z 51, 65, 77, etc.). Methamphetamine, MDMA, phentermine, and psilocin have the same
base peak (m/z 58) and similar low abundance ions (e.g., m/z 51, 65, 91, etc.). Although psilocin
has a considerably different structure from the other compounds, its fragmentation pattern is
similar to methamphetamine, MDMA, and phentermine.

99

100

A

B

NH2

H
N

0

210 40

40

100
Relative Abundance

C

210
H

D
O

NH2

O

N

O
O
0
40
100

210 40

E

210

F
NH

NH2

N
OH
0
40

210 40

210

m/z
Figure 3.3. Relative abundance mass spectra of (A) amphetamine, (B) methamphetamine, (C)
MDA, (D) MDMA, (E) phentermine, and (F) psilocin. Chemical structures shown as inserts.

100

The similarity of these mass spectra of the can be effectively demonstrated by their
PPMC coefficients. PPMC coefficients were calculated for all pair-wise comparisons (1128
total) of the amphetamine-type stimulants mass spectra. The results are summarized in Table 3.2
and the full tables are given in Appendix F, Table A9. Pair-wise comparisons of the same
reference standards and case samples spectra had high correlations, ranging from 0.9584 to
1.000. However, pair-wise comparisons of different reference standards and case samples spectra
also had high correlations, ranging from 0.9040 to 0.9689 for compounds with base peaks of m/z
44 and 0.9491 to 0.9981 for compounds with base peaks of m/z 58. Thus, some mass spectra of
different reference standards and case samples were more similar than the mass spectra of the
corresponding reference standards or case samples. The high similarity of the fragmentation
pattern of these mass spectra further highlights the difficulty of identifying the ATS compounds
based on visual comparison of the mass spectra of a case sample and a reference standard or
reference database.
3.3.2 Differentiation of Case Samples Based on Retention Time
Forensic identification of controlled substances is generally based on a combination of
retention time comparison as well as mass spectral comparisons. Therefore, to add additional
specificity to SAEEUMS, a retention time tolerance can be applied first to compare mass spectra.
While there is no standard tolerance used in forensic laboratories to indicate a retention time
match, this work applies the standard protocol of the Northern Illinois Police Crime Laboratory.
The retention times of methamphetamine must be within ± 1% of the corresponding reference
standard and all other ATS compounds must be within ± 2% of the corresponding reference
standard to be considered a match. If the retention

101

Table 3.2. A summary of Pearson product moment correlation (PPMC) coefficients for 1128 total comparisons of case samples and
reference standards of amphetamine (Amp), methamphetamine (Meth), MDMA, MDA, phentermine (Phent), and psilocin mass
spectra. The maximum (Max), minimum (Min), average (Avg) ± standard deviation, and number of comparisons (n) are shown.

Amp

Max
Min
Avg
n
Meth
Max
Min
Avg
n
MDA
Max
Min
Avg
n
MDMA Max
Min
Avg
n

Amp
0.9999
0.9741
0.9943 ± 0.0061
36

Meth
0.0939
0.0184
0.0416 ± 0.0150
72
1.000
0.9892
0.9975 ± 0.0035
28

MDA
0.9689
0.9040
0.9345 ± 0.0156
81
0.0152
0.0054
0.0087 ± 0.0029
72
1.000
0.9967
0.9992 ± 0.0010
36

Max
Min
Avg
n
Psilocin Max
Min
Avg
n
102

Phent
0.1261
0.0221
0.0625 ± 0.0294
27
0.9981
0.9779
0.9924 ± 0.0069
24
0.0323
0.0035
0.0131 ± 0.0126
27
0.9863
0.9501
0.9704 ± 0.0129
36

Psilocin
0.1817
0.0129
0.0522 ± 0.0537
63
0.9915
0.9629
0.9821 ± 0.0081
56
0.1666
0.0100
0.0448 ± 0.0514
63
0.9927
0.9643
0.9823 ± 0.0075
84

0.9988
0.9873
0.9931 ± 0.0057
3

Phent

MDMA
0.0248
0.0059
0.0125 ± 0.0039
108
0.9928
0.9649
0.9846 ± 0.0070
96
0.0450
0.0183
0.0299 ± 0.0062
108
1.000
0.9945
0.9988 ± 0.0012
66

0.9874
0.9491
0.9705 ± 0.0132
21
0.9999
0.9584
0.9878 ± 0.0161
21

times of the two spectra were not within the above tolerance limits, the spectra are considered
differentiated based on retention time.

Methamphetamine case samples (6 total) with an average retention time (tR) of 2.173 ±
0.008 min are representative examples (Table 3.1). When compared to the retention times of the
reference standards, only methamphetamine (Standard 3, tR = 2.174 min) was within the
accepted tolerance (± 0.044 min). Even the phentermine reference standard, which elutes at a
similar retention time (Standard 9, tR = 2.071 min) is differentiated based on retention time.

However, in order to make use of retention time discrimination, it is essential that
reference standards are acquired with sufficient frequency to maintain high precision. For
example, the other methamphetamine reference standard (Standard 4, tR = 2.713 min) was
analyzed two years prior to Standard 3 (Table 3.1). Association based on retention time of case
samples 8 - 13 or even the other known methamphetamine standards to Standard 4 is impossible
with such a retention difference. Similar issues of retention time spread exist for the reference
standards of MDA, phentermine, and psilocin in the data used for this work. If precision is
maintained, however, retention time is a powerful means of differentiating compounds.
3.3.3 Statistical Association of Case Samples to Reference Standards
To demonstrate the forensic application of SAEEUMS, mass spectra of each case sample
and their respective reference standards were pair-wise compared using a two-tailed t-test (36
comparisons). All comparisons of the case samples and corresponding reference standards were
statistically indistinguishable at the 99.9% confidence level and, therefore, were considered

103

associated. This successful association demonstrates the ability of SAEEUMS for assigning
confidence levels to forensic controlled substance identifications.
It should be noted that the 99.9% confidence level is the least rigorous in regards to
statistical association, Appendix A [11]. However, difficulty in association is preferable in a
forensic context because the occurrence of false positives is minimized. It is also interesting to
note that statistical association of the spectra was possible even though the actual concentration
of the controlled substance in each case sample was unknown.
The random-match probabilities were calculated for each pair of statistically associated
spectra (Table 3.3) and represent the probability that the specific ion patterns occur by chance
36

alone. The RMPs ranged from 8.5 x 10-

41

to 4.9 x 10- , indicating that the probability of these

specific ion patterns occurring by chance is infinitesimally small. The successful association of
these case samples to their respective reference standards highlights the potential of this
statistical comparison procedure, especially given the challenges inherent in the data set. That is,
each case sample was only analyzed once (no instrument replicates were available) and the
reference standards were analyzed at different times compared to the case samples (ranging from
the same day up to two years before the case sample).
3.3.4 Statistical Discrimination of Reference Standards and Case Samples
To investigate the likelihood of false positive matches, mass spectra of each case sample
and all reference standards were pair-wise compared using a two-tailed t-test (216 comparisons).
For nearly all comparisons, case samples were discriminated from the other reference standards
at the 99.9% confidence level, which is the most rigorous level for discrimination [11]. The

104

Table 3.3. Random-match probability for reference standards of amphetamine,
methamphetamine, MDMA, MDA, phentermine, and psilocin compared to respective case
samples, using a two-tailed Student’s t-test at the 99.9% confidence level. The sample case
identity is that assigned by the forensic laboratory.

Sample
Case

Sample Case
Identity

RMP

Sample
Case

Sample Case
Identity

RMP

1
2

Amphetamine

1.7 x 10-

MDA (cont’d)

3.1 x 10-

39

19
20

39

21

MDMA

39

22

2.6 x 10-

38

23

7.7 x 10-

38

24

1.5 x 10-

39

25

2.5 x 10-

37

26

2.2 x 10-

37

27

2.0 x 10-

39

28

1.2 x 10-

37

29

7.9 x 10-

37

30

1.4 x 10-

38

31

Phentermine

8.5 x 10-

38

32

Psilocin

1.5 x 10-

39

33

5.6 x 10-

38

34

5.3 x 10-

38

35

9.7 x 10-

38

36

4.9 x 10-

39

3.5 x 10-

3

1.7 x 10-

4

1.7 x 10-

5

7.7 x 10-

6

7.7 x 10-

7

3.3 x 10-

8

Methamphetamine

1.2 x 10-

9

1.5 x 10-

10

6.7 x 10-

11

1.5 x 10-

12

1.5 x 10-

13

1.0 x 10-

14

MDA

3.1 x 10-

15

3.7 x 10-

16

1.6 x 10-

17

2.3 x 10-

18

1.7 x 10-

105

38
38

1.6 x 10-

38

9.1 x 10-

37
38
37
37
37
38
38
38
37
36
38
41
40
39
41

number of discriminatory ions ranged from 1 to 26 ions (Table 3.4), depending on the samples
being compared.
The exceptions to discrimination at the 99.9% confidence level were Case Samples 8 10, 12 and 13, which contained methamphetamine, and Case Samples 34 and 35, which
contained psilocin. For these samples, discrimination from the MDMA reference standard was
not possible at the 99.9% confidence level but was achieved at the 99.0% confidence level. In
addition, discrimination of Case Sample 9, containing methamphetamine, from the phentermine
reference standard was achieved at the 99.0% confidence level. As discussed in Section 3.3.1,
many of these stimulants have very similar fragmentation patterns; therefore, the high confidence
level at which discrimination was achieved is remarkable.
The discrimination of the structural isomers, methamphetamine and phentermine
(molecular ion, m/z 149), was of special interest. These compounds elute at similar retention
times on a (5%-Phenyl)-methylpolysiloxane column (average retention time (tR) of 2.173 and
2.071 min, respectively in this work) making differentiation based on retention time more
challenging. In addition, methamphetamine and phentermine yield similar (sometimes reported
to be indistinguishable) mass spectra [12]. As seen in Table 3.2, methamphetamine and
phentermine mass spectra were highly correlated with PPMC coefficients ranging from 0.9779 to
0.9981. Given the similarity of the fragmentation patterns, it is noteworthy that the developed
statistical method can discriminate the stimulants at either of the two most rigorous confidence
levels of 99.0 or 99.9% identifying up to 12 discriminating ions. At lower confidence levels, the
number of discriminating ions is even greater, i.e., up to 43 and 21 ions at the 95% and 98%
confidence levels, respectively.

106

Table 3.4. Number of ions responsible for discrimination of amphetamine, methamphetamine, MDA, MDMA, phentermine, and
psilocin case samples from reference standards (t-test, two tailed) at the highest confidence level (CL) that discrimination was
maintained, 99.9% CL unless otherwise specified.

Standards
Amphetamine
Case 1
Case 2
10
3
Methamphetamine
9
6
MDA
10
5
MDMA
15
2
Phentermine
15
5
Psilocin
Methamphetamine
Case 8
Case 9
9
7
Amphetamine
7
7
MDA
a
a
10
14
MDMA
a
12
1
Phentermine
3
1
Psilocin
MDA
Case 14 Case 15
3
5
Amphetamine
10
8
Methamphetamine
2
4
MDMA
5
4
Phentermine
4
5
Psilocin
a

Case 3
9
11
13
16
18

Case 4
6
6
7
10
13

Case 5
2
3
4
2
5

Case 6
4
4
3
2
4

Case 10
3
8
a
10

Case 11
11
5
1

Case 12
9
4
a
15

Case 13
6
8
a
11

1
1

1
1

1
1

1
1

Case 16
4
8
3
10
4

Case 17
5
7
5
4
5

Case 18
5
7
2
2
4

Case 19
4
7
2
2
3

99.0 % confidence level

107

Case 7
3
6
4
2
5

Case 20
4
9
2
2
4

Table 3.4 (cont’d)
Standards
MDMA
Case 21 Case 22
7
7
Amphetamine
4
5
Methamphetamine
4
3
MDA
1
3
Phentermine
2
3
Psilocin
Phentermine
Case 31
2
Amphetamine
1
Methamphetamine
6
MDA
1
MDMA
2
Psilocin
Psilocin
Case 32 Case 33
7
7
Amphetamine
4
5
Methamphetamine
5
5
MDA
MDMA
Phentermine

2
2

1
2

Case 23
6
4
4
4
4

Case 24
8
6
5
6
7

Case 25
8
6
4
5
4

Case 34
8
4
4
a
26
2

Case 35
8
4
10
a
10
2

Case 36
4
4
7

a

99.0 % confidence level

108

2
2

Case 26
7
6
4
5
6

Case 27
5
4
6
3
1

Case 28
6
3
7
2
1

Case 29
7
5
5
6
6

Case 30
7
7
10
5
7

A representative example is shown (Table 3.5) of the number and m/z value of ions
responsible for discrimination of one case sample to each of the reference standards not
containing the corresponding stimulant. The number of discriminating ions in these comparisons
varied from 1 to 18. Even-numbered m/z ions contributed to 50, 71, 44, 57, 60, and 55% (an
average of 56%) of the total discriminating ions for amphetamine, methamphetamine, MDA,
MDMA, phentermine, and psilocin case samples, respectively, when compared to all reference
standards (Table 3.5). Fragments with an odd number of electrons (even-numbered m/z)
generally result from cleavage involving nitrogen in nitrogen-containing compounds [13].
Therefore, approximately half of the differentiations was based on cleavages that resulted in
nitrogen-containing fragments. Additionally, ions with low abundance represented 71, 86, 57,
52, 53, and 71% (an average of 65%) of the total discriminating ions (Table 3.5). Low
abundance ions were arbitrarily defined as ≤ 5% of the base peak. Although often present at low
abundance, ions with high m/z values are also reported to be highly characteristic of a given
compound [14]. High m/z ions were defined as ≥ 130 u based on previous work by McLafferty
et al., in which the probability of a particular m/z value occurring in a spectrum was reported to
decrease by a factor of two approximately every 130 u [14]. For the ATS spectra, ions with high
m/z values represented 5, 54, 34, 31, 13, and 34% (an average of 28%) of the total discriminating
ions (Table 3.5). Additionally, in any comparison where the base peaks of the compounds were
not equivalent (e.g., amphetamine and methamphetamine) both base peaks were among the
fragments leading

109

Table 3.5. Representative examples of m/z values and general trends of ions responsible for discrimination of amphetamine,
methamphetamine, MDA, MDMA, phentermine, and psilocin case samples from reference standards, using a two-tailed Student’s ttest at the 99.9% confidence level (unless otherwise specified).

Standards

Ions

Methamphetamine
MDA
MDMA

9
10
13

Phentermine

16

Psilocin

18

Amphetamine
MDA

9
4

MDMA
Phentermine
Psilocin

15
1
1

Amphetamine
Methamphetamine
MDMA
Phentermine
Psilocin

5
7
5
4
5

a

b

m/z
Case Sample 3 (Amphetamine)
44, 45, 56, 58, 65, 91, 92, 103, 120
63, 65, 66, 91, 92, 103, 115, 120, 135, 136
44, 45, 58, 60, 61, 63, 65, 66, 89, 90, 91, 92, 120
44, 45, 50, 51, 58, 62, 63, 65, 74, 77, 89, 91, 92, 93,
118, 120
44, 50, 52, 58, 60, 61, 62, 63, 65, 66, 77, 89, 91, 93,
103, 115, 120, 204
Case Sample 12 (Methamphetamine)
44, 50, 51, 58, 62, 63, 65, 89, 91
44, 58, 135, 136
51, 65, 77, 79, 90, 91, 92, 105, 115, 117, 118, 119,
134, 135, 136
134
204
Case Sample 17 (MDA)
63, 65, 91, 135, 136
44, 56, 58, 65, 91, 135, 136
44, 58, 106, 135, 136
44, 57, 58, 117
44, 58, 135, 136, 204

% Even
m/z
50%
56%
40%
54%

% Low
% High
b
c
Abundance
m/z
71%
5%
67%
0%
70%
0%
69%
20%

Base
d
Peak
58, 44
58, 44

50%

69%

0%

58, 44

50%
71%
44%
75%

78%
86%
67%
75%

6%
54%
0%
20%

58, 44

33%
100%
100%
44%
20%
57%
80%
50%
80%

87%
100%
100%
57%
60%
43%
40%
75%
40%

50%
100%
100%
34%
40%
29%
40%
0%
60%

44, 58
44, 58

58, 44
58, 44
58, 44
58, 44

a

99.0% confidence level; Low abundance ions (defined as ≤ 5% of base peak) in case sample are underlined

b

c

High m/z ions are defined as m/z ≥ 130 u [14]; Ions are from the reference standard and the case sample spectra, respectively

d

110

Table 3.5 (cont’d)

Standards
Amphetamine
Methamphetamine
MDA
Phentermine
Psilocin
Amphetamine
Methamphetamine
MDA
MDMA
Psilocin
Amphetamine
Methamphetamine
MDA
MDMA
Phentermine
Total

b

Ions m/z
Case Sample 24 (MDMA)
8
44, 56, 58, 65, 77, 91, 135, 136
6
51, 53, 65, 91, 135, 136
5
44, 56, 58, 59, 136
6
51, 53, 77, 91, 135, 136
7
56, 77, 78, 79, 135, 136, 204
Case Sample 31 (Phentermine)
2
44, 58
1
56
6
44, 51, 58, 77, 91, 136
1
91
2
91, 204
Case Sample 32 (Psilocin)
7
44, 45, 58, 63, 65, 91, 204
4
51, 91, 92, 204
5
44, 58, 135, 136, 204
a
10
50, 51, 52, 56, 77, 78, 79, 105, 135, 136
2
91, 204

% Even
m/z
57%
50%
17%
80%
17%
57%
60%
100%
100%
50%
0%
50%
55%
43%
50%
80%

% Low
b
Abundance
52%
50%
67%
60%
50%
57%
53%
50%
100%
67%
0%
50%
71%
71%
75%
60%

% High
c
m/z
31%
25%
33%
20%
33%
43%
13%
0%
0%
0%
17%
50%
34%
14%
25%
20%

50%
50%
56%

100%
50%
65%

60%
50%
28%

a

99.0% confidence level; Low abundance ions (defined as ≤ 5% of base peak) in case sample are underlined

b

c

High m/z ions are defined as m/z ≥ 130 u [14]; Ions are from the reference standard and the case sample spectra, respectively

d

111

Base
d
Peak
44, 58
44, 58

44, 58
44, 58

44, 58
44, 58

to discrimination. In all comparisons involving psilocin, the molecular ion (m/z 204) was among
the fragments leading to discrimination.
Some forensic laboratories require a minimum 95% confidence level in uncertainty
measurements [5]. It should be noted that the level of confidence at which this study was
performed, 99.0% or 99.9%, is therefore more rigorous and exceed these guidelines in all
comparisons.
Based on these results, this application of SAEEUMS for the spectral comparison of
these case samples to reference standards appears to be extremely rigorous in regards to
association of spectra from the same compound and discrimination of spectra from different
compounds. The data shown here demonstrate the effectiveness of this statistical approach for
comparison of structurally similar compounds, despite the non-sequential analysis of case
samples and reference standards and the lack of replicates for each case sample.
3.3.5 Comparison to NIST Standards
As a further test and validation of SAEEUMS for forensic application, the case samples
were pair-wise compared to standards in the NIST database (216 total comparisons) [15]. Of
these 212 case samples were statistically associated to their corresponding standard in the NIST
database at the 99.9% confidence level (Table 3.6). There were four exceptions (Cases 15 - 17,
and 36), in which ions in the NIST spectra with abundances near the threshold were statistically
different from those in the case samples with abundances below the threshold. For all spectra
that were statistically associated to those in the NIST database, the random-match probabilities
35

were calculated. The RMPs ranged from 2.4 x 10-

probability of these specific ion patterns occurring by chance is
112

39

to 3.3 x 10- , indicating that the

Table 3.6. The number of discriminating ions for the pair-wise comparison of case samples to standards from the National Institute of
Standards and Technology (NIST) database (one sample t-test, 99.9% CL unless otherwise specified). Zero discriminating ions
indicate complete association and the corresponding random-match probability is shown in parentheses. Entries in red highlight
unexpected association or discrimination.
Amphetamine Methamphetamine
35

Case 1

0 (1.2 x 10- )

Case 2

0 (2.4 x 10

Case 3

0 (1.2 x 10

Case 4

0 (1.2 x 10

Case 5

0 (4.5 x 10

Case 6

0 (4.5 x 10

Case 7

0 (5.6 x 10

Case 8

Case 14

7

Case 16

6

Case 17

8

Case 18

5

)

1
a
7

Case 15

)

-36

2

Case 13

)

-37

2

Case 12

)

-37

1

Case 11

)

-35

1

Case 10

)

-35

1

Case 9

-35

a

Phentermine

Psilocin

3

5

3

1

6

1

4

2

1

4

3

7

3

1

7

2

4

2

1

5

1

5

3

1

5

2

3

4

2

5

1
38
0 (2.0 x 10- )

4

3
a
4

1
a
1

5

a

b

0 (2.5 x 10
0 (3.1 x 10
0 (2.5 x 10
0 (2.5 x 10
0 (4.6 x 10

-38
-37
-38
-38
-37

)
)
)
)
)

2

2

2

2

3
7

a

1

7

1

3
37
0 (3.0 x 10- )

2

1
a
2

2
2
1
3
2

b
a
a
b

1
1
1
3
4
1

a
a

1

2

1

2

1

3

1

1

2

3

1

a

1

1

a

99.0% confidence level;

NIST Standards
MDA
MDMA

1
39
0 (6.6 x 10- )

1

2

4

1

1

2

1
b

98.0% confidence level
113

Table 3.6 (cont’d)
Amphetamine Methamphetamine
a

Case 19

6

Case 20

5

Case 21

2

Case 22

1

Case 23

2

Case 24

2

Case 25

2

Case 26

2

Case 27

2

Case 28

1

Case 29

2

Case 30

2

Case 31

1

Case 32

1

Case 33

1

3

Case 34

1
a
1
2

2

Case 35
Case 36
a

37

0 (3.0 x 10- )

1

a

1
a
9
7

a

12
11
10
11
8
8

3

a
a
a

a

10
1

a

a

11

NIST Standards
MDA
MDMA

a
a

a
a
a
a
b

1
2

0 (1.6 x 10

-37

)

2

Phentermine

Psilocin

1

1

2

1
37
0 (8.5 x 10- )

2
a
10

2

0 (9.9 x 10

1

0 (6.4 x 10

2

0 (5.7 x 10

2

0 (9.7 x 10

2

0 (1.1 x 10

2

0 (9.9 x 10

2

0 (2.5 x 10

1

0 (6.6 x 10

2

0 (2.8 x 10

2

a

-36
-37
-36
-36
-37
-39
-38
-37
-37

)
)
)

8

3

a

11
11

2

a

3

a

4

a

)

11

)

1
a
8

)
)
)
)

8

3
3
2

a

12
11

3

a

3

a

2

5

5

2

1

1
39
0 (3.5 x 10- )

5

2
a
3

1

0 (3.3 x 10- )

1
a
2
2

0 (6.5 x 10- )

3
a
3
7

a

1
2

b

99.0% confidence level; 98.0% confidence level

114

0 (3.9 x 10

3
-35

)

39
37
36

0 (2.9 x 10- )
2

infinitesimally small. Moreover, this RMP value is comparable to that calculated previously for
36

the case samples compared to their corresponding reference standards (8.5 x 10-

41

to 4.9 x 10- ,

Table 3.3).
The spectra of the case samples were statistically distinguishable from spectra of different
standards in the NIST database at either the 98.0, 99.0, or 99.9% confidence level, which are the
more rigorous levels for discrimination. Discrimination was achieved at the 99.9 % confidence
level for the majority of comparisons. However, in the comparisons of methamphetamine,
MDMA, and phentermine, and in the comparisons of amphetamine to MDA, discrimination was
only achieved at the 98.0 or 99.0% confidence level. For all comparisons, the number of
discriminatory ions ranged from 1 to 12. Additionally, in any comparison where the base peaks
of the compounds were not equivalent (e.g., amphetamine and methamphetamine), the base peak
of the NIST standard was among the fragments leading to discrimination. In all comparisons
involving psilocin, the molecular ion (m/z 204) was among the fragments leading to
discrimination.
Successful association and discrimination of the majority of the case samples to those in
the NIST database further demonstrates the power of this method, since these spectra were
analyzed with different GC-MS instruments, as well as different experimental conditions,
concentrations, and time periods. However, given this variability in the analysis conditions,
some case samples were unable to be associated to the NIST standards. In contrast, all case
samples were able to be associated to their respective reference standards. This demonstrates the
superiority of comparing case samples to reference standards analyzed on the same instrument
under the same analysis conditions. Nevertheless, if necessary (e.g. no reference standard is

115

available), SAEEUMS can be used to assign a confidence level to the mass spectral
identification of an unknown compound when compared to standards in the NIST database.
3.4

CONCLUSIONS
The statistical approach to establish equivalence of unabbreviated mass spectra was

further investigated for practical applications in a forensic laboratory using case samples and
reference standards of amphetamine-type stimulants. All data were obtained from an accredited
forensic laboratory, with no modifications to the standard procedures used by the laboratory for
these analyses.
For each case sample, association to the appropriate reference standard was possible at
the 99.9% confidence level, despite the similarities in fragmentation pattern and the lack of
instrumental replicates for each case sample. For compounds that were statistically associated,
37

the random-match probabilities were on the order of 10-

41

to 10- , indicating the low probability

that the characteristic fragmentation patterns occur by random chance alone. Furthermore, the
case samples were statistically discriminated from the other reference standards at the 99.9%
confidence level, which is the most rigorous confidence level for discrimination. The exceptions
to this were some case samples containing methamphetamine and psilocin when compared to the
MDMA reference standard, and one case sample of methamphetamine compared to the
phentermine reference standard. For these exceptions, discrimination was possible at the 99.0%
confidence level. This is especially noteworthy in the comparison of methamphetamine and
phentermine, which elute at similar retention times and have such similar fragmentation patterns
that the mass spectra are sometimes reported to be indistinguishable.

116

The implications of these results are profound for any evidentiary application in which
mass spectra are compared. While this research has focused on mass spectra of controlled
substances, the proposed method is equally applicable to mass spectra obtained for other types of
evidence. Using SAEEUMS, forensic analysts have access to a simple statistical method that
assigns a confidence level and calculates the random-match probability for the comparison mass
spectra of questioned samples and reference standards. This statistical approach improves upon
existing methodologies by providing stronger statistical interpretations of controlled substance
evidence for use in court testimonies, meeting Daubert requirements and the recommendations
set forth in the 2009 report published by the National Academy of Sciences.

117

REFERENCES

118

REFERENCES

[1]

United Nations Office on Drugs and Crime Laboratory and Scientific Section.
Amphetamines and ecstasy: 2011 global ATS assessment. New York, NY: United
Nations, 2011.

[2]

United Nations Office on Drugs and Crime Laboratory and Scientific Section.
Recommended methods for the identification and analysis of amphetamine,
methamphetamine and their ring-substituted analogues in seized materials. Document
ST/NAR/34. New York, NY: United Nations, 2006.

[3]

Cole MD. The analysis of controlled substances. Hoboken, NJ: John Wiley and Sons,
2003.

[4]

Steeves JB, Gagné HM, Buel E. Normalization of residual ions after removal of the base
peak in electron impact mass spectrometry. J Forensic Sci 2000; 45: 882-885.

[5]

Controlled substances procedures manual. Document 221-D100. : Richmond, VA:
Virginia Department of Forensic Science, 2010.

[6]

Heller DN (2002) Prescription and process for achieving acceptable methods of
confirmation [abstract]. In: 224th American Chemical Society National Meeting; 2002
Aug 18-22; Boston, MA. Cape Girardeau, MO: American Chemical Society, Division of
Environmental Chemistry; p 637. Abstract nr 30.

[7]

National Research Council. Strengthening forensic science in the United States: a path
forward. Washington, DC: The National Academies Press, 2009.

[8]

Burns M. Medical-legal aspects of drugs. Tucson, AZ: Lawyer and Judges Publishing,
2007.

[9]

Daubert v. Merrell Dow Pharmaceuticals, Inc., 43 f.3d 1311 (9th cir. 1995).

119

[10]

Controlled substances standard operating procedure. San Francisco Police Department
Criminalistics Laboratory, 2005.

[11]

Devore JL. Probability and statistics for engineering and the sciences. Belmont, CA:
Duxbury Press, 1990.

[12]

Levine B. Principles of forensic toxicology. Washington, DC: American Association for
Clinical Chemistry Press, 2003.

[13]

McLafferty FW (1959) Mass spectrometric analysis molecular rearrangements. Anal
Chem 31: 82-87.

[14]

McLafferty FW, Hertel RH, Villwock RD (1974) Probability based matching of mass
spectra, rapid identification of specific compounds in mixtures. Org Mass Spectrom 9:
690-702.

[15]

Linstrom P, Mallard W. NIST Chemistry WebBook, NIST Standard Reference Database
Number 69, National Institute of Standards and Technology, Gaithersburg, MD,
http://webbook.nist.gov, (retrieved November 11, 2012).

120

CHAPTER 4
STATISTICAL COMPARISON OF MASS SPECTRA FOR FORENSIC
IDENTIFICATION OF SALVINORIN A
4.1

INTRODUCTION
Mass spectral comparison to a reference standard or library is the predominant means of

compound identification for regulatory applications, such as controlled substance identification
in forensic science. While the specific requirements for identification vary depending on the
standard operating procedures of the individual forensic laboratories, the mass spectrum of the
questioned sample is often visually compared to the mass spectrum of a suitable standard or to
spectra in a reference database. However, more recently, there has been a growing need and
expectation for statistical evaluation of forensic evidence, as indicated by the National Academy
of Sciences (NAS) report on the current state of forensic science in the United States [1].
Currently, in the analysis of controlled substances, no statistical error or confidence level
associated with the mass spectral identification is generally included.
The statistical approach to establish equivalence of unabbreviated mass spectra
(SAEEUMS) was developed using mass spectra of small, straight chain alkanes and
alkylbenzenes (Chapter 2). Although the success of the method was demonstrated, the alkanes
have a relatively simple fragmentation pattern. Hence, to further validate SAEEUMS,
application to more complex spectra and samples is necessary. In this chapter, the effectiveness
of SAEEUMS for association and discrimination of salvinorin A, a compound that is currently of
forensic interest, mass spectra is investigated.

121

Salvinorin A is the active compound in Salvia divinorum, a hallucinogenic perennial herb
from the mint family (Lamiaceae or Labiatae), one of nearly a thousand species of Salvia. S.
divinorum also contains other salvinorins and divinatorins, including salvinorins B, C, and D
(Figure 4.1), which are the most chemically similar to salvinorin A [2,3]. Salvinorin A is
considered to be the most potent known hallucinogen of natural origin [4,5]. As a hallucinogen,
salvinorin A is regulated in many countries, including Australia, Belgium, Canada, Chile,
Croatia, Czech Republic, Denmark, Estonia, Finland, Germany, Iceland, Ireland, Italy, Japan,
Latvia, Lithuania, Norway, Poland, Romania, Russia, South Korea, Spain, Sweden and
Switzerland. Although not federally regulated in the United States, as of 2013, 33 individual
states have regulated either S. divinorum or salvinorin A and several states have pending
legislation [6,7].
In forensic science laboratories, S. divinorum is generally analyzed by gas
chromatography-mass spectrometry (GC-MS) and identified by the detection of salvinorin A
through visual comparison of the mass spectrum to a reference library or reference standard.
However, plant materials, including S. divinorum, have several inherent complications in their
extraction and analysis, which may affect the resulting mass spectrum. Foremost among these is
variation in the concentration of compounds, which occurs due to differences in growing
conditions, such as soil composition and acidity, exposure to sunlight, and availability of water.
Chemical conversion of plant compounds can also occur during extraction, resulting in a
composition that is not representative of the original sample. An example of this has been
reported for the chemical conversion of salvinorin A to salvinorin B by blood esterase [8]. In
addition,

122

O

O

O

R2

O

R

O

R1
O

O

O

O

O

O

Figure 4.1. Chemical structure of salvinorins A, B, C, and D. Salvinorin A (R = OCOCH3),
salvinorin B (R = OH), salvinorin C (R1 = OCOCH3; R2 = OCOCH3), salvinorin D (R1 = OH;
R2 = OCOCH3).
123

co-elution of plant compounds and matrix interferences result in mass spectra that are difficult to
visually compare.
In this chapter, spectra of salvinorin A, extracted from S. divinorum from one geographic
location, were statistically compared to spectra of salvinorin A standards at six concentrations.
Spectra of salvinorin A extracts and standards were then compared to spectra of extracts of
salvinorins B, C, and D to investigate the risk of false positive identifications. Samples analyzed
in a forensic laboratory may have originated from any geographical origin. Therefore, mass
spectra of salvinorin A from different locations analyzed on different instruments over a threeyear period were also statistically compared. Lastly, 441 different Salvia species and varieties
were screened to determine if they contained salvinorin A. Using the developed method, the
mass spectra of compounds eluting with similar retention times to salvinorin A were compared to
the reference standard. These comparisons were used to statistically confirm that, among these
species and varieties, the hallucinogenic compound is found only in S. divinorum [9,10]. As
forensic identification of S. divinorum is generally based on the detection of salvinorin A,
screening in this manner may also allow discrimination of S. divinorum from related Salvia
species [2].
4.2

MATERIALS AND METHODS

4.2.1 Salvinorin A Standards
Reference standards containing 0.5, 2.5, 5.0, 7.5, 10.0, and 12.0 g/L salvinorin A (98.7%
purity, Chromodex, Irvine, CA) were prepared in dichloromethane (99.9% purity, Honeywell
Burdick and Jackson, Morristown, NJ) and spiked with an internal standard of 3.7 g/L

124

progesterone (Sigma, St. Louis, MO) in dichloromethane. All standards were immediately
analyzed in triplicate by GC-MS.
4.2.2 S. divinorum Samples
S. divinorum samples were purchased or collected from eight different geographical
locations and analyzed over an extended period of time (May 2008 to March 2011). As this
work was performed in collaboration with other laboratories, three different extraction
procedures and sets of instrumental parameters were employed. A summary of the geographical
location, extraction method, analysis date, and instrumental parameters for each of the S.
divinorum samples is given in Table 4.1.
In Table 4.1, the term “Extract” indicates one extraction of S. divinorum from one
location, with the following exceptions. Extracts 1 - 3 result from three separate extractions of
one S. divinorum sample and were used to investigate statistical association of extracts from the
same location. Extracts 4 and 5 were commercially purchased, enriched samples of S. divinorum
labeled, respectively, as 5x and 10x the potency of salvinorin A. Extracts 8 and 11 were
collected from the same location, but extracted and analyzed three years apart.
Extracts 6 and 7 were analyzed by Monica Bugeja (Forensic Science Program, School of
Criminal Justice, Michigan State University) and Extracts 8 - 13 were analyzed by Jack E. Hurd
(Alaska Scientific Crime Detection Laboratory, Anchorage, AK).

125

Table 4.1. Sample information for S. divinorum used in this study.
a

Extract

Location

Analysis Date

Extraction Method/Instrument

1

Vancouver, BC

March 2011

A

3

2

Vancouver, BC

March 2011

A

3

3

Vancouver, BC

March 2011

A

3

4

Jackson, MI

March 2011

A

3

5

Jackson, MI

March 2011

A

3

6

E. Lansing, MI

December 2010

B

3

7

Vancouver, BC

December 2010

B

3

8

Santa Clara, CA

April 2011

C

3

9

Anchorage, AK

April 2011

C

9

10

La Honda, CA

May 2008

C

1

11

Santa Clara, CA

August 2008

C

1

Number of Instrument Replicates

12

C

1

13
a

Santa Barbara, CA December 2008
San Francisco, CA

C

1

May 2008

Parameters used for each instrument are given in Table 4.2.

126

4.2.3 Other Salvia Samples
In addition to S. divinorum, 441 other Salvia species and varieties were collected from a
variety of sources (Acknowledgments, Section 4.5) and analyzed by Jack E. Hurd (Alaska
Scientific Crime Detection Laboratory, Anchorage, AK). Each Salvia sample was extracted and
analyzed using the same procedure and instrument over a three-year period. For the purposes of
this study, one instrumental replicate of each sample was acquired.
4.2.4 Extraction Methods
Method A: Extracts 1 - 3 (Ethnosupply, Vancouver, BC, Canada) and Extracts 4 and 5
(Frivolity Kingdom, Jackson, MI) were extracted using this procedure, which was previously
optimized for the extraction of salvinorin A [9]. Briefly, approximately 0.2 g of dried S.
divinorum leaves were extracted in 15.0 mL dichloromethane for 5 min. Extracts were filtered
using a 0.45 μm nylon mesh (Small Parts Inc., Miami Lakes, FL) and rinsed with 5.0 mL
dichloromethane. The filtered solution was evaporated to dryness with nitrogen under gentle
heating at 35 C. Extracts were weighed and then stored at 4 °C until analysis. Prior to GC-MS
analysis, extracts were reconstituted in dichloromethane containing 3.7 g/L progesterone as an
internal standard.
Method B: Extract 6 (Michigan State University Greenhouse, East Lansing, MI) and
Extract 7 (Ethnosupply) were extracted using this procedure, in which approximately 0.04 g of
dried S. divinorum leaves were extracted in 65.0 mL dichloromethane using a rotary agitator
(Rotovapor-R , Büchi Labortechnik, Switzerland) for 16 h at medium speed. Extracts were
filtered using a 0.45 μm nylon mesh and rinsed with a 10.0 mL aliquot, followed by a 2.0 mL
aliquot, of dichloromethane. The filtered solution was evaporated to dryness with nitrogen under
127

gentle heating at 35 C. Extracts were weighed and then stored at 4 °C until analysis. Prior to
GC-MS analysis, extracts were reconstituted in dichloromethane containing 3.7 g/L progesterone
as an internal standard.
Method C: Extracts 8 - 13 and the other 441 Salvia species were extracted using this
procedure. Approximately 100 mg of dried leaves were soaked in 2.0 mL acetone (J. T. Baker,
99.9% purity, Philipsburg, NJ) for 5 min and then ultrasonicated for an additional 1 min.
Extracts were spiked with 1 g/L vanillin (Mallinckrodt, Philipsburg, NJ) in acetone as an internal
standard and immediately analyzed by GC-MS.
4.2.5 GC-MS Analysis
While all extracts were analyzed using the same instrument model (Agilent 6890N gas
chromatograph coupled to an Agilent 5973 mass selective detector, Agilent Technologies, Santa
Clara, CA), three different instruments, with three different analysis methods were used in this
work. The following parameters were consistent for the three instruments and methods: the
column contained a 5%-phenyl-95%-methylpolysiloxane stationary phase (DB-5MS, 30 m x
0.25 mm i.d. x 0.25 µm film thickness, Agilent Technologies, Palo Alto, CA), the carrier gas was
ultra-high purity helium, and the detector was operated in electron ionization mode at 70 eV.
The instrumental parameters that differed among the methods are summarized in Table 4.2 and
the number of replicates for each extract is given in Table 4.1.

128

Table 4.2. Gas chromatography-mass spectrometry parameters used throughout this study.

Parameters

Instrument A

Instrument B

Instrument C

Samples

Extracts 1 - 5 and Standards

Extracts 6 - 7

Extracts 8 - 13,
441 Salvia species and varieties

Inlet

320 °C, 1 μL sample, 50:1 split

320 °C, 1 μL sample, 50:1 split

250 °C, 2 μL sample, splitless

Flow Rate

1 mL/min

1 mL/min

0.8 mL/min

Oven Temperature
Program

200 °C (2 min), 20 °C/min to
340 °C (3 min)

200 °C (2 min), 10 °C/min to
340 °C (6 min)

80 °C (1 min), 20 °C/min to 300 °C
(7 min)

Transfer Line
Temperature

320 °C

320 °C

280 °C

Scan Range

m/z 50 - 550

m/z 50 - 550

m/z 43 - 550

Threshold

150

150

200

Scan Rate

2.91 scans/s

2.91 scans/s

1.85 scans/s

129

4.2.6 Data Analysis
All mass spectra were exported from ChemStation Software (version 01.02.16, Agilent
Technologies, Santa Clara, CA) to Microsoft Excel (version 2007, Microsoft Corp., Redmond,
WA) and analyzed using the SAEEUMS method described in Chapter 2.6.
To predict standard deviations, logarithmic graphs of mean abundance versus standard
deviation were generated using spectra collected from the same instrument (Instrument A, Table
4.2), as well as spectra collected from different instrument (Instruments A – C, Table 4.2). Three
replicates from a total of 36 spectra (5136 ions) were used to generate the first graph and two
replicates from a total of 34 spectra (7084 ions) were used to generate the second graph. The
two graphs showed similar trends and are shown in Figures 4.2 and 4.3. The standard deviation
is proportional to abundance in a manner similar to that expected for shot-noise limits (slope =
0.5). A least-squares linear regression was performed and, for spectra collected on the same
instrument, the resulting best-fit line had a slope 0.5327 ± 0.0045 and an intercept of 0.8107 ±
0.0180, Figure 4.2. For spectra collected on different instruments, the best-fit line had a slope of
0.5123 ± 0.0063 and an intercept of 0.7482 ± 0.0251, Figure 4.3. Using these regression
equations, standard deviations were predicted for each m/z value in the spectra and were used in
all t-test comparisons.
To demonstrate the application of the proposed method, mass spectra of salvinorins A, B,
C, and D in extracts of S. divinorum were compared to those of the reference standard of
salvinorin A at varying concentrations. Next, mass spectra of the

130

1,000,000.06
10
5

10

Standard Deviation

100,000.05
10

4

10
10
10,000.04

3
1,000.03
10
10

2
10
100.02
10

1

10
10.01
10

0

10 0
10
1.0

2

10
100.0
102

3

10 3
1,000.0
10

4

10 4
10,000.0
10

5

10 5
100,000.0
10

6

7

10
10 7
1,000,000.0 10,000,000.0
106
10

Mean Abundance
Figure 4.2. Logarithmic graph of mean abundance versus standard deviation for mass spectra of salvinorin A extracts and reference
standards (36 spectra, 5136 ions). Linear best fit line with slope 0.5327 ± 0.0045 and intercept 0.8107 ± 0.0180.
131

6 6.0
106

10

5

5.0
10 105

4

Log (Standard deviation)

Standard Deviation

4.0
10 104

3

3.0
10 103

2

2.0
10 102

1 1.0

10 101
0

0.0
10 100

-1

-1.0
10 10-1
2
2.0
10
10 2

2.5

3
3.0

10
10 3

3.5

4
4.0

10
10 4

4.5
5.05
105
10
Log (Abundance)

5.5

6.06

106
10

6.5

7.0 7

107
10

Mean Abundance
Figure 4.3. Logarithmic graph of mean abundance versus standard deviation for mass spectra of salvinorin A extracts and reference
standards (34 spectra, 7084 ions). Linear best fit line with slope 0.5123 ± 0.0063 and intercept 0.7482 ± 0.0251.

132

salvinorins in extracts of S. divinorum from different geographic locations and analyzed on
different instruments were compared. Finally, to demonstrate the ability of the proposed method
for screening purposes, 441 different species and varieties of Salvia were examined for
compounds eluting at similar retention times to salvinorin A. To define a peak within this
retention time range, a signal-to-noise (S/N) ratio of 2.5 was used. This S/N ratio is significantly
lower than the value of 31.598 recommended by Winefordner and co-workers [11] for two
replicates at the 99.9% confidence level. It is also lower than the value of 10, which is
recommended by some forensic laboratories [12]. However, this lower S/N ratio was chosen in
this work to be more rigorous and screen more compounds. The developed method was then
used to compare the mass spectrum of salvinorin A to that of any compound in the other Salvia
species with a S/N > 2.5 and a retention time similar to salvinorin A (17.142 ± 0.2 min).
4.3

RESULTS AND DISCUSSION

4.3.1 Statistical Association of Salvinorin A
Mass spectra of salvinorin A in Extracts 1 - 3 and the six salvinorin A standards analyzed
on the same instrument were compared using a two-tailed t-test. All pair-wise comparisons (36
total) of the extracts and standards were statistically indistinguishable and, therefore, were
considered associated at the 99.9% confidence level, Appendix A.
Salvinorin A spectra were successfully associated over the concentration range of 0.5 12.0 g/L, which corresponded to a base peak abundance of 170,000 - 3,500,000 counts. In
Chapters 2.4.6 it was shown that alkanes at low concentrations with base peak abundances ≤
5000 counts could not be statistically associated. At low

133

Table 4.3. Random-match probability (RMP) calculated for pair-wise comparisons of salvinorin A extracted from S. divinorum and
five salvinorin A reference standards (t-test, two tailed, 99.9%).

Base Peak
Abundance
Salvinorin A

6

(x 10 )*

Extract 1

Extract 1

2.54 ± 0.05
2.10 ± 0.04

6.8 x 10-

0.5

2.5

5.0

10.0

9.5 x 10-

Extract 3

Extract 3

0.92 ± 0.03

Extract 2

Extract 2

126
126

5.0 x 10-

133

124

3.3 x 10-

126

1.2 x 10-

126

6.5 x 10-

126

1.7 x 10-

126

2.7 x 10-

Standard Concentrations
(g/L)
0.5

0.17 ± 0.01

1.8 x 10-

2.5

1.04 ± 0.02

2.5 x 10-

5.0

1.79 ± 0.01

6.9 x 10-

10.0

3.23 ± 0.01

2.6 x 10-

12.0

3.47 ± 0.08

1.9 x 10-

128

6.8 x 10-

127

132

9.2 x 10-

129

1.5 x 10-

129

4.4 x 10-

131

7.0 x 10-

129
127

1.8 x 10-

129

134

3.1 x 10-

127

* ± one standard deviation, n = 3

7.9 x 10-

131

1.9 x 10-

125

3.0 x 10-

131

126

3.3 x 10-

127

1.7 x 10-

129

1.4 x 10-

128

132

1.0 x 10-

128

129

2.5 x 10-

concentrations, ions that are uniquely characteristic of the compound may be below the
instrumental threshold or indistinguishable from noise. In the present study, the concentration
range of salvinorin A generated spectra with sufficiently high abundances that association was
possible independent of concentration.
The random-match probabilities (RMPs) were calculated for all extracts and standard
spectra that were statistically associated, and representative values are summarized in Table 4.3.
126

The RMPs range from 7.9 x 10-

134

to 7.1 x 10-

, indicating that the probability of these

specific ion fragmentation patterns occurring by chance is infinitesimally small. The successful
association of the salvinorin A standards and extracts further demonstrates the ability of
SAEEUMS to assign confidence levels to the comparison of complex mass spectra.
4.3.2

Statistical Discrimination of Salvinorin A from Salvinorins B, C, and D
To investigate the likelihood of false positive matches, mass spectra of salvinorin A were

compared to salvinorins B, C, and D. Salvinorin B differs structurally from salvinorin A by a
hydroxyl group, salvinorin C by an acetoxy group, and salvinorin D by a hydroxyl group and the
position of the acetoxy group (Figure 4.1). Representative mass spectra of salvinorins A - D
from extracts of S. divinorum are shown in Figure 4.4. Although the respective fragment ion
abundances differ, all of the salvinorins have four prominent ions in common: m/z 43 (acetyl
cation), m/z 81 (2-methyl furan cation), m/z 94 (phenol cation), and m/z 121 (benzoic acid
cation). Salvinorin D also has m/z 55 and the molecular ion (m/z 432) in common with
salvinorin A. In addition, over the scan range of m/z 50 - 550, the base peak of all four
salvinorins was m/z 94, increasing the apparent similarity of the fragmentation patterns.

135

Relative Abundance

100
100

0
50
50
100
100

100
100

A

C

B

0
0
50
50

550
550

100
100

0
0

550
550

D

0
0
50
50

550
550 m/z

50
50

Figure 4.4. Mass spectra of A) Salvinorin A, B) Salvinorin B, C) Salvinorin C, and D) Salvinorin D

136

550
550

Mass spectra of salvinorin A from Extracts 1 - 3 and the six salvinorin A standards were
compared to spectra of the other salvinorins present in Extracts 1 - 3 using a two-tailed t-test.
The test was performed with n = 3 as this was the number of points used to create the
corresponding logarithmic standard deviation graph (Figure 4.2). For all comparisons (27 total),
spectra of salvinorin A were statistically distinguishable from those of the other salvinorins at the
99.9% confidence level, which is the most rigorous test for statistical discrimination (Appendix
A). Hence, despite the similarity of the chemical structures, the salvinorins were still
distinguishable using the unequal variance t-test.
A representative example of the number and m/z value of ions responsible for
discrimination is reported in Table 4.4. The number of discriminating ions in the comparisons of
salvinorin A to salvinorins B and C was 28 and 44, respectively, whereas only three ions were
discriminatory in the comparison to salvinorin D. Despite the small number of discriminating
ions relative to the total number (300 - 400), statistical discrimination of salvinorins A and D was
still possible.
Ions with even m/z values represented 57, 39, and 67% (average of 54%) of the total
discriminating ions in the comparison of salvinorin A to salvinorins B, C, and D, respectively
(Table 4.4). In non-nitrogen-containing compounds such as the salvinorins, even-numbered
fragments are less common and generally result from multiple bond cleavages, indicating that
rearrangement may have occurred [13]. Therefore, in approximately half of the comparisons,
differentiation was based on rearrangement and other less common cleavage patterns. Given the
relative complexity of the ring structure of salvinorin A, a complex fragmentation pattern with a
significant number of ions resulting from rearrangement is expected.

137

Additionally, ions with low abundance represented 86, 66, and 67% (average of 73%) of
the total discriminating ions in the comparison of salvinorin A to salvinorins B, C, and D,
respectively (Table 4.4). Low abundance ions were arbitrarily defined as ≤ 5% of the base peak.
Although often present at low abundance, ions with high m/z values are also reported to be
highly characteristic of a given compound [14]. This trend was confirmed in this study, where
ions with high m/z value represented 93, 70, and 67% (average of 77%) of the total
discriminating ions in the comparison of salvinorin A to salvinorins B, C, and D, respectively
(Table 4.4). High m/z ions were defined as ≥ 130 u based on previous work by McLafferty et al.,
in which the probability of a particular m/z value occurring in a spectrum was reported to
decrease by a factor of two approximately every 130 u [14]. Of the ions with high m/z values,
the vast majority are also low abundance ions. These values show the comparative difficulty in
discrimination of the ATS spectra in comparison to the salvinorin spectra (Chapter 3.3.4). More
unique ions with high m/z values are present in the salvinorin spectra than the ATS spectra,
hence, ions with higher m/z values are responsible for the majority of the discrimination of the
salvinorins. In addition, the molecular ion of salvinorin A (m/z 432) was among those leading to
discrimination from salvinorins B and C. However, as the molecular ion of salvinorins A and D
have the same m/z value, with statistically similar abundances, this ion was not among the
discriminating ions for the corresponding comparison of these two compounds. The successful
discrimination of salvinorin A from the other salvinorins at the most rigorous confidence level
further demonstrates the power of this method.

138

Table 4.4. Ions responsible for discrimination in the comparison of salvinorin A from Extract 1 to salvinorins B, C, and D from
Extract 1 (t-test, 99.9% confidence level).

Salvinorin A/
Salvinorin B

Salvinorin C

Salvinorin D

Number of
Discriminating
a
m/z
Ions
28

44

3

% Low
% Even
a
Abundance
m/z

m/z

b

96, 107, 153, 179, 191, 199, 206, 208, 209, 216,
220, 234, 245, 252, 266, 273, 274, 276, 291,
294, 328, 356, 359, 360, 361, 372, 432, 433

57%

77, 81, 86, 87, 91, 95, 100, 105, 108, 115, 117,
119, 121, 131, 133, 134, 135, 145, 148, 149,
157, 159, 160, 161, 162, 191, 201, 206, 220,
234, 252, 273, 274, 313, 318, 359, 360, 361,
372, 399, 404, 405, 432, 433

39%

86, 273, 404

67%

67%

67%

54%

73%

77%

Average
a

Low abundance ions (≤ 5% of base peak) are underlined

b

High m/z ions are defined as m/z ≥ 130 u [14]

139

86%

%
High

93%

M+. Ions
Salvinorin
A
(m/z 432)

66%

70%

Salvinorin
A
(m/z 432)

---

4.3.3

Statistical Association of Salvinorin A from Different Geographical Locations
It is generally recommended that compounds whose mass spectra are being compared

should be analyzed sequentially on the same instrument with the same instrumental parameters.
However, in order to investigate the rigorousness of this method, salvinorin A spectra collected
from eight locations and analyzed on different instruments over a three-year period were
compared to Extract 1. All statistical comparisons (12 total) were made using a two-tailed t-test
at confidence levels of 90.0, 95.0, 98.0, 99.0, and 99.9%. The test was performed with n = 2 as
this was the number of points used to create the corresponding logarithmic standard deviation
graph (Figure 4.3). Each of the salvinorin A spectra was statistically indistinguishable from
Extract 1 at the 99.9% confidence level. As noted previously, this confidence level is the least
rigorous with regard to association, whereas the lower confidence levels are more precise
(Appendix A). Accordingly, the lowest confidence level at which association was maintained is
reported in Table 4.5. Extracts 2, 4, 5, 8, and 9 were associated to Extract 1 only at the 99.9%
confidence level, while Extracts 3 and 13 were also associated at the 99.0% confidence level.
Extracts 6, 7, and 11 were associated down to the 98% confidence level, Extract 10 down to the
95% confidence level, and Extract 12 maintained association at all confidence levels. It is
remarkable to note that statistical association was possible in all cases independent of the origin
of S. divinorum, extraction procedure, date of analysis, and GC-MS instrumental parameters.
The RMP calculated for comparisons of the salvinorin A spectra to Extract 1 ranged from 5.1 x
37

10-

126

to 1.9 x 10-

(Table 4.5), indicating that the probability of the ion pattern occurring by

chance is infinitesimally small.

140

Higher RMPs were observed when Extracts 10 - 13 were compared to Extract 1 (Table
4.5). Mass spectra of these extracts had fewer total number of ions (46 - 216) than in spectra
from the other extracts (306 - 414, Table 4.5). There were a number of cases where an ion with a
specific m/z value was present with an abundance near the threshold in one extract but below the
threshold in the other extract (Table 4.5). In such cases, the m/z value was not included in the
RMP calculations (Chapter 2.6), resulting in higher RMPs. For example, Extract 12 contained
only 46 ions and had 123 cases, out of the 500 m/z values scanned, where ions were present
37

above the threshold in only one spectrum. The resulting RMP (5.1 x 10- ), while still an
infinitesimally small number, is the highest RMP of the extracts compared.
The effect of geographical location on the statistical association of mass spectra of
salvinorin A extracts collected on different instruments, was investigated for Extracts 6 - 12 (28
total) in Table 4.6. Extracts 6 and 7 were analyzed on the same instrument and Extracts 8 - 12
were analyzed on the same instrument (Table 4.1). Nearly all the salvinorin A spectra were
statistically indistinguishable and the lowest confidence level at which association was
maintained is also given in Table 4.6. Extracts 6 and 7 compared to all other extracts were
associated only at the 99.9% confidence level. Extracts 8 - 10 compared to each other were also
associated at the 95.0, 98.0 and 99.0% confidence levels. Extracts 11 - 13 compared to each
other were associated down to the 80.0 and 90.0% confidence levels. There were four
exceptions in which association was not possible, and Extract 6 was discriminated from Extracts
8, 10, 11, and 13 with 1 to 3 discriminating ions. Extracts 1 - 7 had increased background due to
the high temperature program used, however Extract 6 was also low abundance (signal-to-noise
= 3). Therefore, association to the Extracts collected on different instruments with low

141

Table 4.5. Random-match probability (RMP) of salvinorin A extracted from S. divinorum
samples at the lowest confidence level (CL) that association was maintained. Average number of
ions in the triplicate spectra and the number of ions present just above the instrumental threshold
in one spectrum and below it in the other (Above/Below Threshold) are also shown. The t-test
was performed at confidence levels of 90.0, 95.0, 98.0, 99.0, and 99.9%. Extract and analysis
information is provided in Tables 4.1 and 4.2.

Comparison of
Extract 1 to

CL

RMP
126

Extract 2

1.9 x 10-

Extract 3

1.8 x 10-

Extract 4

1.7 x 10-

Extract 5

6.1 x 10-

Extract 6

3.5 x 10-

Extract 7

5.5 x 10-

Extract 8

3.2 x 10-

Extract 9

3.7 x 10-

Extract 10

6.6 x 10-

Extract 11

1.9 x 10-

Extract 12

5.1 x 10-

Extract 13

1.9 x 10-

126
122
119
122
121
125
125
99

103
37

102

Average
Number
Ions

Above/Below
Threshold

99.9%

414

7

99.0%

410

5

99.9%

360

10

99.9%

331

35

98.0%

365

70

98.0%

307

56

99.9%

306

33

99.9%

314

26

95.0%

144

45

98.0%

174

41

90.0%

46

123

99.0%

216

36

142

Table 4.6 Number of discriminating ions for pair-wise comparisons of Extracts 6 - 12 at the lowest confidence level that association
was maintained (99.9% confidence level unless otherwise specified). The t-test was performed at confidence levels of 80.0, 90.0, 95.0,
98.0, 99.0, and 99.9%. Zero discriminating ions indicate complete association and the corresponding random-match probability is
shown in parentheses. Extracts 6 and 7 were analyzed on the same instrument and Extracts 8 - 12 were analyzed on the same
instrument (Table 4.2).
Extract 6
Extract 7
Extract 8
Extract 9

Extract 7

Extract 8

Extract 9

Extract 10

Extract 11

Extract 12

162

0 (2.1 x 10-

)
137

1

0 (3.0 x 10143

0 (3.1 x 10-

135

) 0 (1.3 x 10-

)
)

0 (1.8 x 10143 a

)

Extract 10

100

1

0 (2.5 x 10-

)

0 (1.0 x 10-

0 (1.1 x 10-

111 b

103 b

)

Extract 11

107

2

0 (9.4 x 10-

)

116

) 0 (1.5 x 10-

0 (6.8 x 10-

0 (4.4 x 10-

110 a

)

107 d

)

Extract 12

37

0 (4.4 x 10- )

38

0 (5.6 x 10- )

39

0 (2.1 x 10- )

)

38

0 (3.8 x 10- )

42 c

0 (2.4 x 10- )

0 (1.1 x 1040 d

)

Extract 13

102

3

0 (1.4 x 10-

109

) 0 (5.8 x 10-

106

) 0 (6.1 x 10-

107

) 0 (1.9 x 10-

)

0 (2.1 x 10-

0 (3.5 x 10-

106 e

42 e

)

a

b

c

d

e

)

99.0 % confidence level; 98.0 % confidence level; 95.0 % confidence level; 90.0 % confidence level; 80.0 % confidence level

143

background (Extracts 8-13) was more difficult or not possible. Statistical association of
salvinorin A extracts analyzed on the same instrument was possible in all cases and association
of salvinorin A extracts analyzed on different instruments was possible in most cases. This
further emphasizes that association is independent of the origin of S. divinorum, extraction
procedure, date of analysis, and GC-MS instrumental parameters. The RMP calculated for
37

comparisons of the salvinorin A spectra ranged from 4.4 x 10-

162

to 2.1 x 10-

(Table 4.6),

indicating that the probability of the ion pattern occurring by chance is infinitesimally small.
The effect of geographical location on the statistical discrimination of mass spectra of
salvinorin A from salvinorins B, C, and D was also investigated for Extracts 1 - 13 (39 total).
The t-test was performed with n = 2 as this was the number of points used to create the
corresponding logarithmic standard deviation graph (Figure 4.3). Statistical discrimination of
salvinorin A from salvinorins B and C was possible at the 99.9% confidence level, and from
salvinorin D at the 99.0 or 99.9% confidence levels (Table 4.7). The number of discriminating
ions in the comparison of salvinorin A to salvinorin B ranged from 1 to 10. Similar trends were
observed for the comparison of salvinorin A to salvinorin C, with 2 to 48 discriminating ions.
Due to the similarity in fragmentation patterns between salvinorins A and D, discrimination in
some cases was only possible at the lower confidence level of 99.0%, with 1 to 49 discriminating
ions.
This further emphasizes, salvinorin A can be discriminated from salvinorins B, C, and D
at the most rigorous confidence level (99.9%) when extracted using the same procedure and
analyzed sequentially using the same GC-MS conditions. For extracts obtained from different

144

Table 4.7. Number of ions responsible for discrimination in the comparison of salvinorin A from
Extracts 1 - 13 to salvinorins B, C, and D from Extract 1 (t-test, two tailed) at the highest
confidence level (CL) that discrimination was maintained. The t-test was performed at the 99.9%
CL, unless otherwise specified. Extract and analysis information is provided in Tables 4.1 and
4.2.

a

Salvinorin B

Extract 1

10

13

1

Extract 2

3

9

1

Extract 3

4

10

1

Extract 4

3

2

3

Extract 5

1

9

3

Extract 6

3

3

2

Extract 7

5

24

1

Extract 8

2

1

1

Extract 9

6

3

5

Extract 10

9

48

4

Extract 11

10

37

9

Extract 12

1

10

49

Extract 13

2

10

4

a
b

Salvinorin C

a

Salvinorin A in

Salvinorin D

b
b

b
b
b
b

b

In Extract 1
99.0 % confidence level

145

a

locations, extracted using different procedures, and analyzed using different GC-MS instruments
and conditions over a three-year period, discrimination is still possible, at either the same or
slightly lower confidence levels. Some forensic laboratories require a minimum 95.0%
confidence level in uncertainty measurements and, therefore, these data meet or exceed these
guidelines [15].
Extracts 4 and 5 were enriched samples of S. divinorum that, according to the packaging,
were spiked with extracts of S. divinorum to be 5x and 10x the usual potency of salvinorin A.
Both samples were statistically associated to Extract 1 (salvinorin A extracted from S.
divinorum) at a confidence level of 99.9%. Based on the abundance of salvinorin A in the total
ion chromatograms, Extracts 4 and 5 did contain greater masses of salvinorin A than Extract 1,
although less than the claimed 5x and 10x potency. These data confirm that association is
possible independent of concentration.
4.3.4 Statistical Discrimination of Salvinorin A from Compounds Present in Other Salvia
Species
Forensic identification of controlled substances is generally based on a combination of
retention time comparison as well as mass spectral comparison. As S. divinorum is one of nearly
a thousand species of Salvia, it is of forensic interest to statistically determine if the
hallucinogenic compound, salvinorin A, is present in any other Salvia species [2]. Therefore,
chromatograms of 441 different Salvia species and varieties were screened for compounds
eluting at a similar retention time to salvinorin A (defined as ± 0.2 min in this research). The
mass spectra of these compounds were then compared to salvinorin A in Extract 10, collected on
the same instrument, using a t-test at the 99.0 and 99.9% confidence levels (Table 4.8).

146

Table 4.8. Salvia species and number of discriminating ions (# Ions) of compounds eluting within ± 0.2 min of salvinorin A (retention
time, Tr, 17.142 min). The t-test was performed at the 99.9% confidence level, unless otherwise specified.
% Low
% High
% Even
b
c
Abundance
m/z
Tr
Salvia Species
# Ions
m/z
m/z
S. aethiopis
S. aliena
S. areolata
S. africana-lutea
S. azurea
S. bahorucona
S. bella
S. benthamii
S. 'Blue Chiquita'
S. blepharophylla
S. brachyphylla
S. calaminthifolia
S. calolophos
S. cedrosensis
S. claredonensis
a

17.307
17.312
17.298
17.236
17.142
17.047
17.170
16.915
17.132
17.184
17.312
17.165
16.887
17.147
17.298
a
17.132
a

17.250
16.915
17.104
17.156

1
2
2
10
1
2
5
1
8
3
1
1
1
2
2

43
94, 268
43, 94
57, 70, 71, 83, 84, 85, 94, 97, 113, 127
43
43, 94
91, 94, 143, 325, 340
94
97, 162, 174, 187, 191, 202, 205, 220
94, 115, 336
94
94
43
91, 325
268

0%
100%
50%
100%
0%
0%
80%
0%
88%
100%
0%
0%
0%
50%
50%

0%
100%
50%
30%
0%
50%
40%
100%
50%
67%
100%
100%
0%
0%
50%

0%
50%
0%
0%
0%
0%
60%
0%
88%
33%
0%
0%
0%
50%
50%

10

57, 71, 85, 93, 94, 95, 107, 121, 166, 273

100%

20%

20%

8
2
2
6

43, 94, 166, 255, 269, 273, 422, 423
43, 94
43, 94
91, 117, 129, 143, 325, 340

88%
0%
50%
83%

38%
50%
50%
17%

75%
0%
0%
50%

b

c

99.0% confidence level; Low abundance ions (defined as ≤ 5% of base peak are underlined; High m/z ions are defined as m/z ≥
130 u [14]

147

Table 4.8 (cont’d)
Salvia Species
S. columbariae
S. cubensis
S. densiflora
S. dombeyi
S. eriocalyx
S. fallax
S. fruticosa
S. gracilis

Tr
17.241
17.146
17.132
16.901
17.113
17.09
17.236

S. herbacea
S. hirtella
S. 'Hot Lips'
S. 'Jean's Jewel'

17.175
16.915
17.005
17.184
17.326
16.943

4
2
1
1
1
2

17.047

41

17.317

4

S. karwinskii x
pulchella
S. lachnaiocloda

a

# Ions
11
6
2
2
1
1
8
a 11
16.925

% Even
m/z
100%
83%
50%
0%
0%
0%
100%
91%

b

0%
67%
50%
0%
0%
0%
0%
36%

50%
50%
0%
100%
100%
50%

75%
0%
0%
0%
0%
0%

24%

63%

100%
c

36%
17%
50%
50%
100%
0%
25%
45%

88%

53, 63, 65, 77, 78, 79, 91, 95, 103, 105, 115,
117, 120, 123, 128, 131, 132, 143, 145, 148,
149, 157, 163, 165, 169, 173, 176, 197, 199,
200, 211, 215, 217, 229, 243, 247, 249, 263,
264, 272, 340
94, 128, 167, 268

% High
c
m/z

100%
0%
0%
100%
100%
0%

m/z
56, 57, 70, 71, 83, 84, 85, 94, 97, 113, 127
91, 117, 131, 143, 325, 340
94, 325
43, 94
94
43
57, 71, 83, 84, 85, 94, 97, 127
43, 55, 93, 94, 107, 108, 121, 166, 220, 244,
273
94, 180, 181, 329
43, 94
43
94
94
43, 94

% Low
b
Abundance

75%

50%

99.0% confidence level; Low abundance ions (defined as ≤ 5% of base peak are underlined; High m/z ions are defined as m/z ≥
130 u [14]

148

Table 4.8 (cont’d)
Salvia Species
S. lamiifolia
S. lemmonii
S. mexicana
S. meyeri
S. mohavense
S. montecristina

Tr
16.986
17.114
17.189
16.891
17.232
16.976
17.109
16.948
17.076
16.948
17.061
16.896
17.317

S. praeclara

17.189

S. praeterita
S. punicans

17.298
17.123

8
2
a
17.274 4

S. quercetopinorum

16.920

S. paryskii
S. pauciserrata

a

a

20

2

b

c

40%
50%
100%
0%
50%
50%
40%
50%
100%
50%
50%
0%
0%
43%

40%
0%
0%
0%
0%
0%
100%
0%
100%
0%
0%
0%
0%
43%

20%

40%

100%
0%
75%

43, 94

S. parciflora

% High
c
m/z

50%

m/z
79, 91, 95, 272, 340
43, 94
94
43
57, 94
43, 94
162, 187, 191, 205, 220
43, 94
220
43, 94
43, 94
43
105
43, 79, 81, 93, 94, 107, 108, 121, 152, 165, 220,
222, 268, 273
43, 67, 77, 81, 91, 92, 95, 104, 105, 117, 119,
121, 131, 135, 145, 159, 166, 231, 273, 342
94, 141, 167, 178, 194, 239, 250, 268
43, 94
43, 166, 273, 358

% Low
b
Abundance

63%
50%
50%

88%
0%
75%

0%

S. pennellii

# Ions
5
2
1
1
2
2
5
2
1
2
2
1
2
a 14
17.312

% Even
m/z
40%
100%
100%
100%
100%
0%
80%
0%
0%
0%
0%
0%
0%
93%

50%

0%

99.0% confidence level; Low abundance ions (defined as ≤ 5% of base peak are underlined; High m/z ions are defined as m/z ≥
130 u [14]

149

Table 4.8 (cont’d)
Salvia Species
S. reflexa

Tr
# Ions
17.208a 27

S. reptans
S. roscida
S. saccifera
S. similis
S. sprucei

17.293
17.076
17.284
17.180

S. stachydifolia
S. thormannii
S. thymodies

16.901
17.000
17.326
17.080

2
2
1
26

S. tiliaefolia
S. tortuensis

17.326
17.095

2
22

S. tuerckheimii

17.038

18

S. uncinata

17.005

11

a

a

3
2
2
2
a 16
17.180

% Even
m/z
56%

b

33%
50%
100%
50%
31%

67%
0%
50%
0%
50%

0%
50%
100%
54%

50%
50%
100%
19%

0%
50%
100%
23%

100%
91%

100%
27%

50%
77%

94%

28%

72%

91%
c

% High
c
m/z
33%

67%
50%
100%
50%
56%

m/z
43, 67, 77, 78, 79, 81, 91, 92, 95, 96, 104, 105,
115, 117, 118, 119, 121, 129, 131, 133, 135,
145, 159, 166, 231, 273, 342
43, 166, 273
43, 94
94, 268
43, 94
91, 94, 95, 105, 107, 108, 121, 129, 131, 133,
166, 273, 325, 326, 340, 341
43, 94
91, 312
268
53, 55, 57, 67, 68, 77, 79, 81, 91, 92, 93, 97, 98,
105, 107, 109, 111, 119, 120, 123, 133, 145,
171, 173, 174, 201,
94, 268
91, 115, 117, 128, 129, 130, 131, 143, 144, 145,
157, 171, 172, 173, 183, 185, 197, 211, 239,
312, 313, 342
91, 115, 117, 128, 129, 130, 131, 143, 145, 171,
172, 173, 185, 197, 239, 312, 313, 342
91, 115, 117, 128, 129, 131, 145, 171, 173, 239,
312

% Low
b
Abundance
22%

18%

55%

99.0% confidence level; Low abundance ions (defined as ≤ 5% of base peak are underlined; High m/z ions are defined as m/z ≥
130 u [14]

150

Table 4.8 (cont’d)
Salvia Species
S. wagneriana
S. x jamensis
S. x jamensis
'Cherry Queen'
S. x trident

% High
c
m/z

100%
50%

0%
0%

Tr
16.924
16.925

# Ions
1
2

m/z
94
43, 94

16.915

2

43, 94

0%

50%

0%

16.986
17.250

1
13

43
56, 57, 70, 71, 83, 84, 85, 94, 97, 99, 113, 127,
141

0%
100%

0%
31%

0%
8%

51%

47%

26%

Average
a

% Low
b
Abundance

% Even
m/z
0%
0%

b

c

99.0% confidence level; Low abundance ions (defined as ≤ 5% of base peak are underlined; High m/z ions are defined as m/z ≥
130 u [14]

151

Of the 441 Salvia species and varieties, 62 contained a total of 75 compounds within the
designated retention time tolerance of salvinorin A (Table 4.8). Among these compounds, 66
were discriminated at the 99.9% confidence level from salvinorin A, with 1 to 41 discriminating
ions. The other 9 compounds were discriminated at the 99.0% confidence level from salvinorin
A, with 3 to 27 discriminating ions. The salvinorin A base peak (m/z 94) and second highest
abundance ion (m/z 43) were among the discriminating ions in almost all comparisons. For the 9
compounds discriminated at the 99.0% confidence level, the compounds generally had the same
base peak as salvinorin A, removing that ion from among the discriminating ions.
Ions with even m/z values represented, on average, 51% of the total discriminating ions in
the comparison of salvinorin A to the other Salvia species (Table 4.8). Therefore, in
approximately half of the comparisons, differentiation was based on rearrangement and other
less common cleavage patterns. Additionally, ions with low abundance represented 47% of the
total discriminating ions and ions with high m/z value represented 13% of the total discriminating
ions (Table 4.8). Of the ions with high m/z values, the vast majority were also low abundance
ions. The percentages of discriminating ions with even m/z values and low abundance are similar
to those observed in the comparisons of salvinorin A to the other salvinorins (54 and 73%,
respectively, Table 4.3).
In summary, salvinorin A was not present in any of the other Salvia species or varieties
investigated. Therefore, all 441 Salvia species and varieties were discriminated from S.
divinorum based either on comparison of the retention time to salvinorin A (i.e., 379 species
having no compounds within ± 0.2 min) or comparison of the mass spectra to salvinorin A (i.e.,
62 species having no spectral match at 99.0 or 99.9% confidence levels). This application of

152

SAEEUMS appears to be extremely rigorous for the identification S. divinorum as well as for
screening other plant materials for salvinorin A.
4.4

CONCLUSIONS
The statistical approach to establish equivalence of unabbreviated mass spectra was used

to investigate the association and discrimination of salvinorin A. Mass spectra of three extracts
of salvinorin A from S. divinorum were statistically associated to reference standards of
salvinorin A at six different concentrations at the 99.9% confidence level. Mass spectra of
salvinorins B, C, and D in these extracts were statistically distinguishable from salvinorin A at
the 99.9% confidence level. Mass spectra of salvinorin A extracted from S. divinorum from
different geographical locations, extracted using different methods, and analyzed using different
GC-MS instruments and conditions were statistically associated at confidence levels of 90.0 99.9%. Lastly, salvinorin A was not present in any of the other 441 Salvia species and varieties
investigated, such that all other Salvias were discriminated from S. divinorum based either on
retention time of salvinorin A or comparison to the salvinorin A mass spectra. These
applications of SAEEUMS appear to be extremely rigorous in regards to association of spectra
from the same compound and to discrimination of spectra from different compounds.
The implications of these results are profound for any evidentiary application in which
mass spectra are compared, especially for controlled substance identification. Using SAEEUMS,
forensic analysts have access to a simple statistical method that assigns a confidence level and
calculates the random-match probability for the comparison mass spectra of questioned samples
and reference standards. This improves upon existing methodologies by providing stronger
statistical interpretations of controlled substance evidence for use in court testimonies.

153

4.5

ACKNOWLEDGEMENTS
Salvia species and varieties were acquired from the following sources: Richard Dufresne

(Candor, NC), Eric La Fountaine (University of British Columbia Botanical Garden and Centre
for Plant Research, Vancouver, B.C.), Mike Kintgen (Denver Botanic Gardens, Denver, CO),
David Kruse (San Francisco Botanical Garden Society, San Fransisco, CA), Robin Middleton
(Surrey, England), Andrew Salywon (Desert Botanical Garden, Phoenix, AZ), Connie Stegen
(Peckerwood Gardens Conservation Foundation, Hempstead, TX), Kevin Walker (Department of
Chemistry, Michigan State University), Atlanta Botanical Garden (Atlanta, GA), Cabrillo
College (Aptos, CA), Desert Botanical Garden (Phoenix, AZ), Harvard University (Cambridge,
MA), Las Pilitas Nursery (Escondido, CA), New England Unit of the Herb Society of America
(Wayland, MA), Plant Delights Nursery, Inc. (Raleigh, NC), Sandy Mush Herb Nursery
(Leicester, NC), The New York Botanical Garden (Bronx, NY), University of California
Botanical Garden (Berkeley, CA), University of New Mexico Biology Department Herbarium
(Albuquerque, NM).

154

REFERENCES

155

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[1]

Strengthening Forensic Science in the United States: A Path Forward. National Research
Council of the National Academies. The National Academies Press, Washington D.C.
2009.

[2]

Munro TA (2006) The chemistry of Salvia divinorum [Dissertation], Melbourne
(Australia): University of Melbourne.

[3]

Gruber JW, Siebert DJ, Der Marderosian AH, Hock RS (1999) High performance liquid
chromatographic quantification of salvinorin A from tissues of Salvia divinorum Epling
& Jativa-M. Phytochem Anal 10: 22-25.

[4]

Siebert DJ (2004) Localization of salvinorin A and related compounds in glandular
trichomes of the psychoactive sage, Salvia divinorum. Ann Bot London 93: 763-771.

[5]

Epling C, Játiva CD (1962) A new species of Salvia from Mexico. Botanical Museum
Leaflets 20.

[6]

Siebert DJ (2012) The Salvia divinorum research and information center: The legal status
of Salvia divinorum. sagewisdom.org/legalstatus.html. Accessed 15 March 2013

[7]

US Department of Justice (2010) Drug Enforcement Administration drugs and chemicals
of concern: Salvia divinorum and salvinorin A.

[8]

Schmidt MS, Prisinzano TE, Tidgewell K, Harding W, Butelman ER, Kreek MJ, and
Murry DJ (2005) Determination of salvinorin A in body fluids by high performance
liquid chromatography - atmospheric pressure chemical ionization. J Chromatogr B 818:
221-225.

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[9]

Bodnar Willard M, Waddell Smith R, McGuffin VL (2012) Forensic analysis of Salvia
divinorum using multivariate statistical procedures. Part I: discrimination from related
Salvia species. Anal Bioanal Chem 402: 833-842.

[10]

Bodnar Willard M, Waddell Smith R, McGuffin V (2012) Forensic analysis of Salvia
divinorum using multivariate statistical procedures. Part II: association of adulterated
samples to S. divinorum. Anal Bioanal Chem 402: 843-850.

[11]

St. John PA, McCarthy WJ, Winefordner JD (1967) A statistical method for evaluation of
limiting detectable sample concentrations. Anal Chem 39: 1495-1497.

[12]

Forensic chemistry section quality manual (2009) Document DRG‐DOC‐01. Little Rock,
AR: Arkansas State Crime Laboratory.

[13]

McLafferty FW (1959). Mass spectrometric analysis molecular rearrangements. Anal
Chem 31: 82-87.

[14]

McLafferty FW, Hertel RH, Villwock RD (1974) Probability based matching of mass
spectra, rapid identification of specific compounds in mixtures. Org Mass Spectrom 9:
690-702.

[15]

Controlled substances procedures manual (2012) Document 221-D100. Richmond, VA:
Virginia Department of Forensic Science.

157

CHAPTER 5
CONCLUSIONS AND FUTURE WORK
This research involved the development and investigation of statistical approach to
establish equivalence of unabbreviated mass spectra (SAEEUMS) for assigning a confidence
level to the mass spectral identification of unknown compounds. Due to the challenge of
differentiating similar mass spectra, the method was initially developed using alkane and
alkylbenzene standards. The method was then applied to case samples containing amphetaminetype stimulants to investigate the utility of the method for practical applications in forensic
laboratories. Lastly, further investigation of the method was performed using salvinorin A, a
compound with a more complex chemical structure and mass spectral fragmentation pattern than
the alkanes and alkylbenzenes. Each of these goals was successfully accomplished and the
results are summarized in the following sections.
5.1
DEVELOPMENT AND APPLICATION OF A STATISTICAL APPROACH TO
ESTABLISH EQUIVALENCE OF UNABBREVIATED MASS SPECTRA
The statistical method for comparing mass spectra of an unknown compound to a
reference standard was developed using alkane standards of different concentrations (0.05, 0.1,
0.5, 1.0, 5.0 mM). Each standard contained decane (C10), undecane (C11), dodecane (C12),
tridecane (C13), tetradecane (C14), hexadecane (C16), and the alkylbenzenes propylbenzene,
butylbenzene, amylbenzene, and hexylbenzene and was analyzed by gas chromatography-mass
spectrometry (GC-MS). The developed SAEEUMS method included two parts: first an unequal
variance t-test was used to compare mass spectra at every m/z ratio over the entire scan range.
Then, if determined to be statistically indistinguishable at every m/z ratio, the random-match

158

probability (RMP) assesses the probability that the characteristic fragmentation pattern of the
two mass spectra would occur by random chance alone.
Two methods were investigated for obtaining the standard deviations necessary for the ttest. In the first method, standard deviations were calculated in the traditional manner from
replicate measurements. In the second method, the standard deviations were predicted using a
statistical model. The mathematical model is based on statistical variations in the electron
multiplier that fluctuate in a known manner. Standard deviations predicted in this manner
require only knowledge of the ion abundance and are independent of the compound being
analyzed as well as its concentration, injection volume, split ratio, etc. Both methods of
determining the standard deviation were investigated for the alkane and alkylbenzene data.
At the same concentration, statistical association of corresponding alkanes and
39

alkylbenzenes was possible at the 99.9% confidence level, with RMPs ranging from 10-

to 10-

46

, indicating the low probability that the characteristic fragmentation patterns occur by random

chance alone. Discrimination of different compounds was also possible at the 99.9% confidence
level, with the number of discriminatory ions ranging from 1 to 24 ions. Ions with even m/z
values represented 44% of the total discriminating ions, indicating less common fragmentation
that generally resulted from multiple-bond cleavages or rearrangements. Additionally, ions with
low abundance represented 54% of the discriminating ions. This emphasizes the importance of
using the full spectra rather than abbreviated spectra composed of only the most abundant ions,
as over half of the discriminating ions were low abundance. Ions with high m/z value
represented 36% of the total discriminating ions in the comparisons, 38% of which were also low
abundance ions.
159

At different ionizing voltages, statistical association of spectra collected using 90 eV and
70 eV was possible; however, spectra collected using 70 eV could not be associated to those
collected using 50 eV due to changes in abundance ratios. At varying concentrations,
discrimination of different alkanes was still possible, but association of corresponding alkanes
was not possible using the traditional method to calculate standard deviations. In contrast,
standard deviations predicted from the statistical model were more representative of short-term
and long-term instrumental variance and allowed for association and discrimination of the
alkanes at varying concentrations. Because this method of predicting standard deviations is more
reliable, robust, and practical than the traditional method, it is recommended for use in the
developed statistical procedure. In addition, using the predicted standard deviations, spectra of
the alkanes were successfully associated to and discriminated from normal and branched alkane
spectra in the National Institute of Standards and Technology (NIST) Mass Spectral Database
[1], even though these spectra were collected on different instruments using different
experimental conditions, and over different time periods.
5.2

STATISTICAL COMPARISON OF MASS SPECTRA FOR THE FORENSIC

IDENTIFICATION OF AMPHETAMINE-TYPE STIMULANTS
SAEEUMS was further investigated for practical applications in a forensic laboratory
using case samples and reference standards of amphetamine-type stimulants (amphetamine,
methamphetamine, 3,4-methylenedioxyamphetamine (MDA), 3,4methylenedioxymethamphetamine (MDMA), phentermine, and psilocin). All data were obtained
from an accredited forensic laboratory, with no modifications to the standard procedures used by
the laboratory for these analyses.

160

The case samples and corresponding reference standards (36 comparisons) were
statistically indistinguishable at the 99.9% confidence level. Therefore, they were considered
associated, despite the similarities in fragmentation pattern and the lack of instrument replicates
for each case sample. For compounds that were statistically associated, the RMPs were on the
37

order of 10-

41

to 10- , indicating the low probability that the characteristic fragmentation

patterns occur by random chance alone.
To investigate the likelihood of false positive matches, mass spectra of each case sample
and all reference standards were pair-wise compared (216 comparisons). For nearly all
comparisons, case samples were discriminated from the other reference standards at the 99.9%
confidence level, which is the most rigorous level for discrimination. The exceptions to this
were some case samples containing methamphetamine and psilocin when compared to the
MDMA reference standard, and one case sample of methamphetamine compared to the
phentermine reference standard. For these exceptions, discrimination was possible at the 99.0%
confidence level. This is especially noteworthy in the comparison of methamphetamine and
phentermine, which elute at similar retention times and have such similar fragmentation patterns
that the mass spectra are often reported to be indistinguishable.
The number of discriminatory ions ranged from 1 to 26 ions, depending on the samples
being compared. Even-numbered m/z ions contributed to 50, 71, 44, 57, 60, and 55% of the total
discriminating ions (an average of 56%) for case samples of amphetamine, methamphetamine,
MDA, MDMA, phentermine, and psilocin, respectively, when compared to all reference
standards. Therefore, approximately half of the differentiation was based on cleavages that
resulted in nitrogen-containing fragments. Additionally, ions with low abundance represented 71,

161

86, 57, 52, 53, and 71% (an average of 65%) of the total discriminating ions, and ions with high
m/z value represented 5, 54, 34, 31, 13, and 34% (an average of 28%) for case samples of
amphetamine, methamphetamine, MDA, MDMA, phentermine, and psilocin, respectively. The
numbers of ions with low abundance and high m/z values are comparable to the number observed
with the alkane data. Additionally, in any comparison where the base peaks of the compounds
were not equivalent (e.g., amphetamine and methamphetamine), both base peaks were among the
ions leading to discrimination. In all comparisons involving psilocin, the molecular ion (m/z 204)
was among the fragments leading to discrimination. In addition, spectra of the amphetaminetype stimulants were successfully associated to, and discriminated from, mass spectra in the
NIST database in nearly all instances (212 out of 216 comparisons). The four exceptions were
instances in which ions in the NIST spectra with abundances near the threshold were statistically
different from those in the case samples with abundances below the threshold. The successful
association and discrimination of NIST spectra is especially noteworthy as these spectra were
collected on different instruments using different experimental conditions, and over different
time periods.
5.3

STATISTICAL COMPARISON OF SALVINORIN A MASS SPECTRA FOR

FORENSIC IDENTIFICATION
The extraction and analysis of plant materials can be difficult due to variation in the
concentration of compounds that occur due to differences in growing conditions and as a result
of chemical conversion of plant compounds. These variations may result in a composition that is
not representative of the original sample. To investigate the use of the developed statistical
procedure for association of more complex mass spectra, the plant Salvia divinorum was used as
a model. This plant contains the hallucinogen salvinorin A, which not only has a complex
162

chemical structure, but also has as a complex fragmentation pattern. Hence, S. divinorum
provides a challenging plant sample to further investigate SAEEUMS.
Salvinorin A from thirteen samples of S. divinorum from eight different geographical
locations in the US and Canada were extracted and analyzed by GC-MS. These samples were
extracted using three different methods and were analyzed on three different instruments over a
three-year period. Comparisons were made between samples collected from the same location
with mass spectra acquired using the same experimental parameters, as well as between samples
collected from different locations with mass spectra acquired using different experimental
parameters.
Mass spectra of three extracts of salvinorin A from S. divinorum were statistically
associated to reference standards of salvinorin A at six different concentrations (0.5, 2.5, 5.0, 7.5,
10.0, and 12.0 g/L) at the 99.9% confidence level. The RMPs ranged from 10-126 to 10-134,
indicating that the probability of these specific ion fragmentation patterns occurring by chance is
infinitesimally small. S. divinorum also contains other salvinorins and divinatorins, including
salvinorins B, C, and D, which are the most chemically similar to salvinorin A. To investigate
the risk of false positive identifications, mass spectra of salvinorins B, C, and D were compared
to salvinorin A in these extracts and were successfully distinguished from salvinorin A at the
99.9% confidence level. The number of discriminating ions in the comparisons of salvinorin A to
salvinorins B and C was 28 and 44, respectively, whereas only three ions were discriminatory in
the comparison to salvinorin D. Ions with even m/z values represented 57, 39, and 67% (average
of 54%) of the total discriminating ions in the comparison of salvinorin A to salvinorins B, C,
and D, respectively. Therefore, over half of the discriminating ions resulted from multiple-bond
cleavages or rearrangement, similar to the trends observed for the alkanes and the amphetamine163

type stimulants. Additionally, ions with low abundance represented 86, 66, and 67% (average of
73%) of the total discriminating ions in the comparison of salvinorin A to salvinorins B, C, and
D, respectively. This further emphasizes the importance of low abundance ions, as in this case,
they comprise the majority of the discriminating ions. Ions with high m/z value represented 93,
70, and 67% (average of 77%) of the total discriminating ions in the comparison of salvinorin A
to salvinorins B, C, and D, respectively. Of the ions with high m/z values, the vast majority are
also low abundance ions.
Samples analyzed in a forensic laboratory may have originated from any geographical
origin. Therefore, mass spectra of salvinorin A extracted from S. divinorum from different
geographical locations, extracted using different methods, and analyzed using different GC-MS
instruments and conditions were compared and successfully associated at confidence levels of
90.0 - 99.9%. The RMP calculated for comparisons of the salvinorin A spectra from different
geographical locations were comparable to those from the same location and ranged from 10-37 to
10-126, indicating that the probability of the ion pattern occurring by chance is infinitesimally
small.
As S. divinorum is one of nearly a thousand species of Salvia, it was of forensic interest
to statistically determine if the hallucinogenic compound, salvinorin A, was present in any other
Salvia species. Therefore, chromatograms of 441 different Salvia species and varieties were
screened to determine if they contained salvinorin A. Using the developed method, the mass
spectra of compounds eluting with similar retention times to salvinorin A were compared to the
reference standard.

164

Of the 441 Salvia species and varieties, 62 contained a total of 75 compounds within the
designated retention time tolerance of salvinorin A. Among these compounds, 69 were
discriminated at the 99.9% confidence level from salvinorin A, with 1 to 49 discriminating ions.
The other six compounds were discriminated at the 99.0% confidence level from salvinorin A,
with 24 to 96 discriminating ions. Salvinorin A was not present in any of the other 441 Salvia
species and varieties investigated such that all other Salvias were discriminated from S.
divinorum based either on retention time of salvinorin A or comparison to the salvinorin A mass
spectra. This application of SAEEUMS appears to be extremely rigorous for the identification S.
divinorum as well as for screening other plant materials for the presence of salvinorin A.
The implications of these results are profound for any evidentiary application in which
mass spectra are compared. While proof-of-concept in nature, SAEEUMS provides a simple and
rapid method to assign statistical assessment of mass spectral identification. This method not
only provides the confidence level for association and discrimination, but also the random-match
probability for association. Therefore, using SAEEUMS, an objective confirmation of the mass
spectral identification is available and is a timely advance, not only for legal and regulatory
applications, but for any application in which objective validation is desired. This method can be
implemented without expensive software and is broadly applicable across many fields, including
industrial, pharmaceutical, food, environmental, and forensic chemistries.
5.4

FUTURE WORK
While this developed/statistical method is useful and applicable, in theory, to any mass

spectral comparison, this work is preliminary and there are additional studies that should be
conducted to further develop and validate the method. For instance, the random-match

165

probability calculations are based on the assumption that the fragmentation resulting in each of
the m/z values is independent. In any case where a fragment resulted from another fragment, this
is an incorrect assumption. An equation where independence is not assumed would be
challenging to incorporate into the method, as it would require complex knowledge of the
interrelated fragmentation of dependent ions. However, more work needs to be performed to
find a feasible manner of incorporating this equation into the developed method, as it more
accurately reflects the nature of fragmentation.
While the method, in theory, is applicable to any mass spectra, application to different
types of compounds may be necessary to investigate. For example, prior to implementation in a
forensic laboratory, a wide range of controlled substance mass spectra would need to be
investigated. Double blind test to further demonstrate the accuracy of mass spectral
identification would also be beneficial. In addition, investigation of compounds of
environmental and pharmaceutical interest would be useful to demonstrate applicability in other
fields that utilize mass spectral comparisons.
While the application of this method was successfully demonstrated on single-stage mass
spectrometry, in principle this method can also be applied to multistage MS. The investigation
of SAEEUMS using multistage MS data would be an interesting addition to this research, as it
would increase the discriminating power in the mass spectral comparison. In addition, in this
work, Agilent GC-MS instruments with electron ionization and a quadrupole mass spectrometer
were used. To increase applicability it would be beneficial to investigate the modifications to the
method, if any, that would be necessary from differences arising from the use of GC-MS
instruments manufactured by different companies (e.g. Thermo Scientific, Varian, Shimadzu,

166

etc.), as well as different instruments (e.g., LC-MS), ionization methods (e.g. chemical
ionization, electrospray ionization, etc.), and mass analyzers (e.g. ion trap, time-of-flight, etc.).
Lastly, the calculations for this statistical procedure have been automated in a Microsoft
Excel template, thereby minimizing the work required by an analyst. However, further
automation with a more user-friendly interface would increase the applicability of the method to
less knowledgeable analysts. For this purpose, incorporating the method into a program format
would be a beneficial addition to the work.

167

REFERENCES

168

REFERENCES
[1]

Stein SE (2008) NIST standard reference database 1A. Users guide. National Institute of
Standards and Technology, Gaithersburg, MD

169

APPENDICES

170

Appendix A
Confidence Level Consideration for the Unequal Variance t-Test

171

A further consideration of the t-test is the confidence level at which the statistical
association or discrimination is determined. Data that are normally distributed can be described
using the Gaussian function

f(x, μ, σ) =

(A1)

where μ and σ are the mean and standard deviation, respectively, of the population [1]. In terms
of mass spectral data, this equation describes the principle that for each compound individual
abundances for a specific m/z value will be spread around the population mean, with the standard
deviation giving a measure of how far the individual value will vary from the mean.
Approximately 68.30% of the abundances fall within 1 standard deviation and 95.45% fall
within 2 standard deviations, 99.70% fall within 3 standard deviations, and 99.99% fall within 4
standard deviations [1].
Figure A1 shows the area under a normal distribution density curve for various
confidence levels for two populations, 1 and 2. At lower confidence levels (95.0%, Figure A1),
the distribution is narrow but becomes broader as confidence level increases (99.9%, Figure A1).
This indicates that a lower confidence interval is actually more rigorous for association, while a
higher confidence interval is more rigorous for discrimination. For example, if 1 and 2 are the
same compound, in Figure A1 they are associated at the 99.9% confidence level. This is the least
rigorous confidence level at which the two could be associated and a confidence level of 95.0%

172

Normalized Amplitude

Confidence Levels
95.0%

Population 2

Population 1

98.0%
99.0%

99.9 %

4

3
3

2
2

1
1

0

1

2
2

4
4 3

3
3 44

2
2

1
1

0
0

1
1

2
2

3
3

4
4

Figure A1. Area under normal distribution density curves for two populations, 1 and 2, at various confidence levels, where Z is the zscore, x is the respective sample value, μ is the sample mean, and σ is the standard deviation.

173

would be a more rigorous demonstration of association. If, for example, 1 and 2 are different
compounds, they are discriminated at 99.0% and lower confidence levels. While these two
samples are not discriminated at a confidence level of 99.9% in the figure, this would be the
most rigorous demonstration of discrimination.
Another way of stating this principle is that the lower the confidence level the narrower
the distribution where similar spectra are considered statistically indistinguishable; while the
higher the confidence interval, the broader the distribution. Therefore, the chosen confidence
level will always be a compromise between rigorous association and rigorous discrimination.
This principle can be related to the length of the confidence interval. For example, the length of
the 99.0 % confidence interval is

2 (2.580) ×

(A2)

at infinite degrees of freedom, where σ is the variance of the population and n is the number of
samples [1]. For the same variance and number of samples, the 99.9% confidence interval is
longer

2 (3.090) ×

(A3)

at infinite degrees of freedom [1]. The length of the interval is directly related to its precision and
inversely related to its reliability [1]. This indicates that a lower confidence interval is more
rigorous for association (i.e., minimizes Type II error), while a higher confidence interval is
more rigorous for discrimination (i.e., minimizes Type I error).

174

Appendix B
Normalization

175

Several methods, such as logarithmic, square root, and base peak, were investigated for
the normalization of mean abundance and standard deviations in order to compare mass spectra
using the t-test. Logarithmic and square root normalizations minimized abundance variations in
the mass spectra. However, for the purpose of this method it was actually desirable to capture the
inherent variance in the data in order to allow for association of spectra of the same compound.
Base peak normalization was determined to account for the largest variations in the mass spectra,
and was therefore, used in this work. In base peak normalization the abundance and standard
deviation at each m/z value in the mass spectrum are divided by the base peak abundance.
Base peak normalization has advantages and disadvantages. Normalizing by a single peak
introduces the possibility of inaccuracy as any error in the base peak will then affect the entire
normalized spectrum. However, by normalizing to the largest peak in the spectrum, the most
variation in the data is then accounted for as this peak is the most likely to be overloaded at high
concentrations or not fully recorded at fast scanning speeds. In addition, base peak normalization
can be applied without knowledge of the compound or the fragment ions present, which would
not be the case if the mass spectrum was scaled to any other peak.

176

Appendix C
Threshold Determination

177

Thresholds from 0 - 100% relative abundance, in 0.5% increments, were investigated for
non-replicate spectra of the alkanes (C10, C11, C12, C13, C14, and C16). Binary arrays for each
spectrum were created using the IF function in Excel. For each m/z value in the spectra a value
of 1 was returned if the relative abundance was greater than the specified threshold, and a value
of 0 was returned if it was less. The total number of ones indicates the number of ions present
above the specified threshold. PPMC coefficients were calculated for comparison of the binary
arrays at each threshold. The number of ions present for each alkane versus the various
thresholds was plotted and evaluated for sufficient peaks (≥ 10). Previous SI from the literature
were calculated based on a minimum of 6 peaks with most algorithms using more than 10 [2,3].
It should be noted that SI calculations use an abbreviated number of peaks to calculate a match
whereas this method uses every peak but insures more than 10 remain above the threshold for
RMP calculations. The PPMC coefficients of pair-wise comparisons of all the alkanes and
replicates were investigated at thresholds from 0 - 100%. The average and lowest PPMC
coefficients for replicates of each alkane were determined. The optimal threshold was chosen
with PPMC coefficients of corresponding alkanes as close to 1 as possible, indicating
association, and different alkanes as close to 0 as possible, indicating discrimination.
Spectra of different alkanes (C10, C11, C12, C13, C14, and C16) were investigated first to
eliminate thresholds at which discrimination was lost. Thresholds from 0 - 100% in 0.5%
increments were investigated for all possible pair-wise comparisons of the 6 alkanes. A
representative table summarizing the results is shown in Table A1. At a threshold of 0% an
average ± standard deviation and maximum PPMC coefficient of 0.7608 ± 0.0646 and 0.9100
respectively, was observed. This is the lowest average, indicating the greatest dissimilarity,
among all the thresholds investigated and is an indication of the inherent variability in the spectra
178

due to chemical differences in the alkanes as well as instrument variation. The other thresholds
can be compared to the 0% threshold to determine the point at which variance due to low
abundance noise is minimized, while maintaining the discrimination provided by lower
abundance ions. In general, for different alkanes, the average PPMC coefficients increase as the
threshold increases from 0.8372 ± 0.0675 to 0.9254 ± 0.0695 for thresholds of 1 - 10%. As the
threshold increases the variance due to noise ions is eliminated making the spectra appear more
similar, with higher PPMC coefficients. The maximum PPMC coefficients observed were 0.8916
to 1.000 for thresholds of 1 - 10%. The 4% threshold had the lowest average PPMC coefficient
of thresholds from 4 - 100% and the lowest maximum and standard deviation of all thresholds
from 0 - 100%. The low average PPMC coefficient at the 4% threshold indicates that variance
due to noise is minimized more than the 0 - 3% thresholds and a greater number of
discriminatory ions are retained than with the 5 - 100% thresholds. The low maximum PPMC
coefficient indicates that sufficient low abundance ions have been retained at the 4% threshold to
allow for discrimination, even among the most similar alkanes (C14, and C16). Thresholds from
5 - 90% have maximum PPMC coefficients of 1.000, indicating that the threshold is too high to
retain the low abundance ions necessary to discriminate different alkanes with such similar
fragmentation patterns.
The 4% threshold was then examined with respect to the similarity of the binary arrays of
corresponding alkane spectra to determine if the minimization of variability due to noise ions

179

Table A1. Average PPMC coefficients (n = 16) for C10, C11, C12, C13, C14, and C16 at 0-5% thresholds. Bolded average, maximum
value (Max) and standard deviation (SD) are representative of all pair-wise comparisons of different alkanes (240 total comparisons).
0%

C10

C11

C12

C13

C10

0.9804

C11

0.7685

0.9649

C12

0.8236

0.7533

0.9896

C13

0.6958

0.8009

0.7390

0.9851

C14

0.7444

0.7316

0.8667

0.7089

C16

0.6865

0.6990

0.8158

0.6878

C10

C11

C12

C13

C14

1%

C16

3%

C10

C11

C12

C13

C14

C16

Average

0.8333

Max

0.9354

SD

0.0600

0.7608 C10
0.9100 C11

0.9860
0.8750

0.9682

0.0646 C12
C13

0.8149

0.8566

1.0000

0.8149

0.8566

0.9354

1.0000

0.9793

C14

0.7559

0.7949

0.8682

0.8682

0.9832

0.8895

0.9812 C16
C16
4%

0.7248

0.7624

0.8327

0.8327

0.9059

C10

C11

C12

C13

0.8372 C10
0.9318 C11

0.9888
0.8694

1.0000

0.0675 C12
C13

0.8341

0.8777

1.0000

0.8262

0.8694

0.8532

0.9888

Average
Max
SD

C14

1.0000

C14

C16

Average

0.8483

Max

0.8916

SD

0.0245

C10

0.9734

C11

0.8394

0.9936

C12

0.7937

0.9101

1.0000

C13

0.7882

0.8968

0.9020

1.0000

C14

0.7292

0.8370

0.8813

0.9031

0.9946

C14

0.8473

0.8151

0.8554

0.8650

1.0000

C16

0.6885

0.7909

0.8331

0.8534

0.9111

0.9904 C16

0.8435

0.8115

0.8135

0.8520

0.8916

C10

C10

C11

C12

C13

C10

C11

C12

C13

C11

0.9808

C12

0.8800

0.9830

C13

0.8442

0.8903

0.9895

C14

0.8255

0.8402

0.8834

0.9836

C16

0.8145

0.8194

0.8584

0.9033

C10

0.7641

0.7685

0.8072

0.8743

Average
Max
SD

C14

C16

C10

0.9597

C14

C16

Average

0.9070

Max

1.0000

SD

0.0349

0.8451 C11
0.9453 C12

1.0000
0.9071

1.0000

0.0488 C13
C14

0.9071

0.9071

1.0000

0.9525

0.9525

0.9525

1.0000

0.9912

C16

0.8886

0.8886

0.8886

0.9333

0.9733

0.9033

0.9797 C10

0.8674

0.8674

0.8674

0.9110

0.9137

Average
Max
SD

180

1.0000

Table A1 (cont’d)

10%

C10

C11

C12

C13

C10

0.9803

C11

0.9097

1.0000

C12

0.9097

1.0000

1.0000

C13

0.9097

1.0000

1.0000

1.0000

C14

0.9097

1.0000

1.0000

1.0000

C16

0.7856

0.8643

0.8643

0.8643

C10

C11

C12

C13

C14

20%

C16

C10

C11

C12

C13

C14

C16

Average

0.9021

Max

1.0000

SD

0.1433

0.9254 C10
1.0000 C11

1.0000
0.7064

1.0000

0.0695 C12
C13

0.7064

1.0000

1.0000

0.7064

1.0000

1.0000

1.0000

1.0000

C14

0.7064

1.0000

1.0000

1.0000

1.0000

0.8643

1.0000 C16

0.7064

1.0000

1.0000

1.0000

1.0000

C10

C11

C12

C13

Average
Max
SD

C14

C10

1.0000

C11

0.7730

1.0000

C12

0.7730

1.0000

1.0000

C13

0.7730

1.0000

1.0000

1.0000

C14

0.8333

0.9326

0.9326

0.9326

C16

0.8935

0.8652

0.8652

0.8652

0.9326

C10

C11

C12

C13

C16

0.9461

30%

50%

Average
Max
SD

C14

70%

1.0000

C14

C16

Average

0.9266

Max

1.0000

SD

0.1074

0.8914 C10
1.0000 C11

1.0000
1.0000

1.0000

0.0864 C12
C13

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

C14

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000 C16
C16
90%

0.7798

0.7798

0.7798

0.7798

0.7798

C10

C11

C12

C13

1.0000 C10
1.0000 C11

1.0000
1.0000

1.0000

0.0000 C12
C13

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9119

C14

C16

Average

1.0000

Max

1.0000

SD

0.0000

C10

1.0000

C11

1.0000

1.0000

C12

1.0000

1.0000

1.0000

C13

1.0000

1.0000

1.0000

1.0000

C14

1.0000

1.0000

1.0000

1.0000

1.0000

C14

1.0000

1.0000

1.0000

1.0000

1.0000

C16

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000 C16

1.0000

1.0000

1.0000

1.0000

1.0000

Average
Max
SD

181

1.0000

was reproducible (Table A2). All replicates for C11, C12, and C14 had average and minimum
PPMC coefficients of 1.000, indicating complete correlation as expected. Replicates of C10, C13,
and C16 varied by 1 to 3 ions among the respective replicates, with average PPMC coefficients
ranging from 1.000 to 0.9597 with C16 having the greatest variability and a minimum PPMC
coefficient of 0.8783.
These results highlight a shortcoming of using a set threshold across a mass range for
minimization of noise ions. Any set threshold is an inherently abrupt value at which ions with a
relative abundance higher than the specified threshold are retained and ions with a relative
abundance lower are excluded. The threshold then introduces variability among ions with a
relative abundance, in this case, within ± 1% of the threshold.
The number of ions above the specified threshold is an additional consideration when
selecting a suitable threshold. As the threshold increases, the number of ions maintained from the
spectra will decrease. At higher thresholds, variability due to noise is reduced or eliminated;
however, the ions that discriminate the spectra may also be eliminated. A count of the number of
ions at various thresholds was therefore investigated for each of the alkanes and a representative
graph of the number of ions versus threshold for the alkanes was constructed (Figure A2). As
anticipated, each of the alkanes exhibited a first order logarithmic decay relationship in the
number of ions with respect to threshold, following a general equation of
y=A

+B

(A4)

where A relates to the number of ions in the spectrum, t is the rate of exponential decay, and B is
the offset (Table A3). Interestingly, t may be proportional to the average threshold at which
discriminatory ions are maintained and noise ions are minimized for a data set. Individual
182

Table A2. Average PPMC coefficients of pair-wise comparisons of the same alkane (n = 10 each) for C10, C11, C12, C13, C14, and
C16 at 4% threshold (60 total comparisons).
Average*
C10

0.9888 ± 0.0180

0.9626

C11

1.0000 ± 0.0000

1.0000

C12

1.0000 ± 0.0000

1.0000

C13

0.9888 ± 0.0180

0.9626

C14
a

Minimum

1.0000 ± 0.0000

1.0000

C16

0.9597 ± 0.0515

0.8783

± one standard deviation

183

Number of Ions

60

0

0

100
Percent Threshold

Figure A2. Decay relationship of number of ions versus threshold for C10, C11, C12, C13, C14,
and C16 spectra.

184

Table A3. The threshold versus the number of ions for each alkane models a first order logarithmic decay relationship (Equation A4).
2
Variable A relates to the number of ions in the spectrum, B is the offset, t-value is the rate of exponential decay, and R is the degree
of fit.
2

Alkane

A

B

t-value

R

C10

32.6

1.19

3.76

0.9515

C11

28.9

1.14

4.67

0.9803

C12

36.5

1.26

3.60

0.9572

C13

30.6

1.16

4.97

0.9850

C14

41.9

1.33

3.57

0.9635

C16
Average

46.9
36.2

1.28
1.23

3.32
3.98

0.9819
0.9699

185

alkanes exhibited t values that ranged from 3.316 to 4.970, with an average t value of 3.980.
Each of the alkanes exhibited variations from the 4% optimal threshold determined using PPMC
coefficient comparisons. However, when considering the data set as a whole, the average t-value
confirms that a 4% threshold was optimal. While further testing of this method is necessary it
may prove to be a simpler method for determining an optimal threshold than that previously
described.
Due to the simple fragmentation pattern of the alkanes, fewer ions are present in the mass
spectrum of an alkane than in more complex compounds. At a 0% threshold alkanes C10, C11,
C12, C13, C14, and C16 had an average of 41, 33, 47, 31, 53, and 54 ions present in the mass
spectrum, respectively. As expected, only 1 ion, the base peak, is present as the threshold
approaches 100%. At a 4% threshold, the alkanes had an average of 12 - 15 ions present. At
thresholds of 5% and greater, the alkanes had fewer than 10 ions present, further confirming the
loss of discriminatory power among the alkanes. Therefore, an optimal threshold of 4% was
chosen due to a low maximum PPMC coefficient of different alkanes and an acceptable number
of ions remaining for discrimination.
The data and conclusions of the threshold investigation are of interest to understanding
the point at which variance due to low abundance noise is minimized, while the discrimination
provided by lower abundance ions is retained. In this work, investigating alkanes, the optimal
point was found to be 4% of the base peak. After the investigation of a threshold, the use of a ttest was investigated to statistically assess every m/z in the mass scan range. The t-test was
determined to be a rigorous measure of statistical association. However, as the t-test was
performed on the full mass spectrum, the use of a threshold was no longer meaningful and,
therefore, was not included in the final method.
186

Appendix D
Supplemental Data Tables for Chapter 2

187

Table A4. Pearson product moment correlation (PPMC) coefficients comparing different alkane mass spectra from Sets 1 and 2 at five
concentrations (0.05, 0.1, 0.5, 1.0, 5.0 mM). Set 1 mass spectra are italicized.
0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

C10

C10

C10

C10

C10

C10

C10

C10

C10

C10

C11

C11

C11

C11

C11

0.05C10
0.1 C10

1.0000

0.5 C10

0.9789 0.9894 1.0000

1.0 C10

0.9777 0.9867 0.9993 1.0000

5.0 C10

0.9727 0.9821 0.9982 0.9993 1.0000

0.05C10
0.1 C10

0.9874 0.9951 0.9839 0.9811 0.9756 1.0000

0.5 C10

0.9779 0.9877 0.9996 0.9998 0.9990 0.9824 0.9923 1.0000

1.0 C10

0.9749 0.9845 0.9989 0.9996 0.9997 0.9787 0.9905 0.9994 1.0000

5.0 C10

0.9732 0.9825 0.9982 0.9994 1.0000 0.9760 0.9883 0.9991 0.9997 1.0000

0.05C11
0.1 C11

0.9792 0.9700 0.9654 0.9619 0.9599 0.9713 0.9715 0.9637 0.9614 0.9597 1.0000

0.5 C11

0.9722 0.9823 0.9937 0.9937 0.9938 0.9787 0.9866 0.9941 0.9942 0.9937 0.9658 0.9882 1.0000

1.0 C11

0.9684 0.9791 0.9926 0.9929 0.9937 0.9750 0.9844 0.9933 0.9936 0.9935 0.9634 0.9865 0.9994 1.0000

5.0 C11

0.9655 0.9757 0.9916 0.9924 0.9937 0.9718 0.9818 0.9926 0.9934 0.9936 0.9611 0.9834 0.9989 0.9997 1.0000

0.05C11
0.1 C11

0.9894 0.9911 0.9831 0.9808 0.9756 0.9928 0.9854 0.9818 0.9777 0.9760 0.9790 0.9878 0.9823 0.9790 0.9759

0.5 C11

0.9681 0.9799 0.9918 0.9920 0.9926 0.9754 0.9842 0.9925 0.9925 0.9924 0.9642 0.9876 0.9993 0.9998 0.9993

1.0 C11

0.9671 0.9792 0.9918 0.9920 0.9925 0.9751 0.9835 0.9925 0.9924 0.9924 0.9630 0.9868 0.9993 0.9998 0.9995

5.0 C11

0.9652 0.9756 0.9914 0.9921 0.9936 0.9713 0.9817 0.9923 0.9931 0.9934 0.9613 0.9836 0.9988 0.9997 1.0000

0.9854 1.0000

0.9841 0.9938 0.9942 0.9912 0.9884 0.9876 1.0000

0.9771 0.9888 0.9844 0.9816 0.9791 0.9831 0.9897 0.9832 0.9808 0.9790 0.9782 1.0000

0.9727 0.9887 0.9875 0.9846 0.9824 0.9847 0.9899 0.9860 0.9846 0.9823 0.9698 0.9947 0.9927 0.9910 0.9886

188

Table A4 (cont’d)
0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

C10

C10

C10

C10

C10

C10

C10

C10

C10

C10

C11

C11

C11

C11

C11

0.05C12
0.1 C12

0.9732 0.9813 0.9727 0.9694 0.9666 0.9814 0.9777 0.9715 0.9684 0.9665 0.9793 0.9883 0.9781 0.9756 0.9729

0.5 C12

0.9584 0.9739 0.9848 0.9851 0.9862 0.9688 0.9759 0.9859 0.9856 0.9861 0.9592 0.9831 0.9931 0.9940 0.9938

1.0 C12

0.9577 0.9724 0.9856 0.9861 0.9878 0.9674 0.9760 0.9868 0.9870 0.9875 0.9586 0.9821 0.9939 0.9952 0.9952

5.0 C12

0.9525 0.9672 0.9825 0.9835 0.9860 0.9616 0.9713 0.9840 0.9848 0.9858 0.9548 0.9782 0.9919 0.9937 0.9942

0.05C12
0.1 C12

0.9695 0.9845 0.9825 0.9800 0.9787 0.9794 0.9837 0.9817 0.9799 0.9786 0.9710 0.9919 0.9880 0.9863 0.9841

0.5 C12

0.9575 0.9723 0.9850 0.9857 0.9873 0.9670 0.9754 0.9863 0.9864 0.9871 0.9579 0.9820 0.9932 0.9945 0.9945

1.0 C12

0.9580 0.9726 0.9860 0.9866 0.9880 0.9679 0.9761 0.9873 0.9872 0.9878 0.9576 0.9816 0.9939 0.9952 0.9953

5.0 C12

0.9533 0.9677 0.9833 0.9844 0.9867 0.9626 0.9720 0.9848 0.9856 0.9865 0.9551 0.9783 0.9924 0.9941 0.9947

0.05C13
0.1 C13

0.9527 0.9571 0.9556 0.9555 0.9563 0.9559 0.9540 0.9574 0.9560 0.9561 0.9737 0.9735 0.9686 0.9683 0.9673

0.5 C13

0.9530 0.9701 0.9806 0.9809 0.9825 0.9643 0.9718 0.9818 0.9817 0.9823 0.9578 0.9818 0.9909 0.9919 0.9917

1.0 C13

0.9493 0.9661 0.9790 0.9799 0.9819 0.9607 0.9684 0.9807 0.9807 0.9817 0.9539 0.9785 0.9899 0.9914 0.9915

5.0 C13

0.9439 0.9609 0.9752 0.9765 0.9793 0.9549 0.9633 0.9772 0.9777 0.9791 0.9502 0.9745 0.9874 0.9894 0.9898

0.05C13
0.1 C13

0.9670 0.9808 0.9767 0.9739 0.9717 0.9784 0.9783 0.9760 0.9732 0.9716 0.9728 0.9906 0.9838 0.9816 0.9790

0.5 C13

0.9503 0.9666 0.9793 0.9801 0.9823 0.9607 0.9690 0.9809 0.9810 0.9820 0.9555 0.9791 0.9900 0.9913 0.9914

1.0 C13

0.9453 0.9632 0.9756 0.9765 0.9787 0.9573 0.9647 0.9773 0.9773 0.9785 0.9517 0.9764 0.9876 0.9893 0.9894

5.0 C13

0.9454 0.9618 0.9765 0.9778 0.9806 0.9560 0.9646 0.9785 0.9790 0.9803 0.9512 0.9751 0.9883 0.9902 0.9907

0.9706 0.9861 0.9830 0.9804 0.9780 0.9826 0.9842 0.9821 0.9794 0.9780 0.9689 0.9920 0.9879 0.9860 0.9835

0.9682 0.9846 0.9844 0.9822 0.9806 0.9790 0.9843 0.9839 0.9814 0.9805 0.9679 0.9921 0.9895 0.9885 0.9860

0.9622 0.9771 0.9787 0.9769 0.9767 0.9704 0.9794 0.9783 0.9772 0.9765 0.9678 0.9908 0.9870 0.9860 0.9841

0.9530 0.9722 0.9745 0.9730 0.9732 0.9653 0.9724 0.9748 0.9732 0.9729 0.9602 0.9855 0.9852 0.9854 0.9838

189

Table A4 (cont’d)
0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

C10

C10

C10

C10

C10

C10

C10

C10

C10

C10

C11

C11

C11

C11

C11

0.05C14
0.1 C14

0.9472 0.9577 0.9572 0.9560 0.9576 0.9522 0.9570 0.9579 0.9570 0.9572 0.9694 0.9775 0.9712 0.9705 0.9691

0.5 C14

0.9426 0.9606 0.9715 0.9724 0.9747 0.9540 0.9611 0.9734 0.9733 0.9745 0.9505 0.9748 0.9847 0.9859 0.9858

1.0 C14

0.9414 0.9595 0.9717 0.9727 0.9752 0.9528 0.9608 0.9736 0.9736 0.9750 0.9500 0.9742 0.9847 0.9862 0.9863

5.0 C14

0.9368 0.9553 0.9694 0.9708 0.9740 0.9487 0.9570 0.9716 0.9721 0.9737 0.9464 0.9708 0.9834 0.9853 0.9858

0.05C14
0.1 C14

0.9514 0.9702 0.9687 0.9667 0.9659 0.9648 0.9668 0.9688 0.9661 0.9657 0.9590 0.9838 0.9795 0.9782 0.9760

0.5 C14

0.9414 0.9605 0.9717 0.9725 0.9746 0.9545 0.9607 0.9736 0.9731 0.9744 0.9496 0.9748 0.9846 0.9860 0.9860

1.0 C14

0.9400 0.9583 0.9707 0.9720 0.9746 0.9519 0.9590 0.9729 0.9729 0.9744 0.9486 0.9729 0.9840 0.9856 0.9858

5.0 C14

0.9378 0.9560 0.9702 0.9716 0.9748 0.9495 0.9579 0.9724 0.9729 0.9745 0.9471 0.9712 0.9839 0.9858 0.9864

0.05C16
0.1 C16

0.9189 0.9268 0.9275 0.9273 0.9301 0.9241 0.9224 0.9298 0.9284 0.9297 0.9572 0.9503 0.9455 0.9463 0.9456

0.5 C16

0.9358 0.9561 0.9655 0.9658 0.9680 0.9488 0.9566 0.9672 0.9666 0.9677 0.9488 0.9733 0.9800 0.9808 0.9804

1.0 C16

0.9299 0.9507 0.9627 0.9635 0.9665 0.9434 0.9516 0.9648 0.9647 0.9662 0.9433 0.9682 0.9782 0.9796 0.9797

5.0 C16

0.9237 0.9445 0.9576 0.9591 0.9627 0.9369 0.9447 0.9602 0.9605 0.9624 0.9379 0.9626 0.9742 0.9760 0.9764

0.05C16
0.1 C16

0.9470 0.9554 0.9565 0.9561 0.9572 0.9523 0.9528 0.9580 0.9566 0.9570 0.9691 0.9745 0.9709 0.9699 0.9688

0.5 C16

0.9356 0.9554 0.9658 0.9664 0.9685 0.9488 0.9554 0.9678 0.9670 0.9683 0.9473 0.9711 0.9800 0.9809 0.9806

1.0 C16

0.9296 0.9503 0.9624 0.9635 0.9664 0.9434 0.9506 0.9647 0.9645 0.9661 0.9422 0.9671 0.9779 0.9792 0.9793

5.0 C16

0.9266 0.9469 0.9603 0.9617 0.9652 0.9395 0.9477 0.9628 0.9631 0.9649 0.9401 0.9646 0.9764 0.9781 0.9785

0.9515 0.9703 0.9705 0.9687 0.9684 0.9639 0.9695 0.9706 0.9686 0.9682 0.9628 0.9850 0.9818 0.9810 0.9791

0.9505 0.9695 0.9755 0.9747 0.9756 0.9628 0.9711 0.9762 0.9754 0.9754 0.9589 0.9838 0.9867 0.9865 0.9855

0.9332 0.9524 0.9540 0.9530 0.9545 0.9467 0.9503 0.9551 0.9540 0.9541 0.9539 0.9726 0.9704 0.9701 0.9689

0.9376 0.9544 0.9570 0.9568 0.9583 0.9467 0.9521 0.9584 0.9573 0.9581 0.9537 0.9736 0.9723 0.9720 0.9708

190

Table A4 (cont’d)
0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

C11

C11

C11

C11

C11

C12

C12

C12

C12

C12

C12

C12

C12

C12

C12

0.05C10
0.1 C10
0.5 C10
1.0 C10
5.0 C10
0.05C10
0.1 C10
0.5 C10
1.0 C10
5.0 C10
0.05C11
0.1 C11
0.5 C11
1.0 C11
5.0 C11
0.05C11
0.1 C11

1.0000

0.5 C11

0.9797 0.9919 1.0000

1.0 C11

0.9796 0.9914 0.9999 1.0000

5.0 C11

0.9757 0.9886 0.9994 0.9995 1.0000

0.9861 1.0000

191

Table A4 (cont’d)
0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

C11

C11

C11

C11

C11

C12

C12

C12

C12

C12

C12

C12

C12

C12

C12

0.05C12
0.1 C12

0.9846 0.9855 0.9770 0.9766 0.9728 1.0000

0.5 C12

0.9710 0.9856 0.9945 0.9944 0.9939 0.9794 0.9904 1.0000

1.0 C12

0.9697 0.9848 0.9954 0.9953 0.9953 0.9775 0.9888 0.9997 1.0000

5.0 C12

0.9641 0.9811 0.9938 0.9937 0.9943 0.9733 0.9851 0.9991 0.9996 1.0000

0.05C12
0.1 C12

0.9810 0.9916 0.9877 0.9869 0.9842 0.9912 0.9968 0.9914 0.9896 0.9867 1.0000

0.5 C12

0.9692 0.9843 0.9948 0.9947 0.9946 0.9767 0.9887 0.9997 0.9998 0.9996 0.9896 0.9920 1.0000

1.0 C12

0.9701 0.9843 0.9954 0.9955 0.9953 0.9769 0.9888 0.9995 0.9999 0.9993 0.9889 0.9916 0.9997 1.0000

5.0 C12

0.9651 0.9815 0.9942 0.9942 0.9947 0.9736 0.9853 0.9991 0.9997 0.9999 0.9866 0.9887 0.9996 0.9995 1.0000

0.05C13
0.1 C13

0.9602 0.9677 0.9700 0.9693 0.9674 0.9818 0.9754 0.9762 0.9753 0.9742 0.9793 0.9746 0.9748 0.9741 0.9739

0.5 C13

0.9672 0.9835 0.9926 0.9924 0.9919 0.9772 0.9870 0.9968 0.9968 0.9963 0.9882 0.9904 0.9964 0.9963 0.9961

1.0 C13

0.9636 0.9804 0.9920 0.9919 0.9917 0.9739 0.9841 0.9964 0.9967 0.9966 0.9852 0.9879 0.9963 0.9964 0.9965

5.0 C13

0.9583 0.9765 0.9899 0.9898 0.9901 0.9702 0.9804 0.9952 0.9957 0.9962 0.9823 0.9847 0.9953 0.9952 0.9959

0.05C13
0.1 C13

0.9786 0.9891 0.9834 0.9827 0.9791 0.9915 0.9944 0.9862 0.9842 0.9806 0.9937 0.9934 0.9840 0.9838 0.9807

0.5 C13

0.9640 0.9806 0.9919 0.9917 0.9916 0.9739 0.9843 0.9963 0.9966 0.9965 0.9857 0.9883 0.9962 0.9961 0.9963

1.0 C13

0.9608 0.9782 0.9901 0.9900 0.9897 0.9727 0.9827 0.9954 0.9956 0.9957 0.9839 0.9867 0.9952 0.9952 0.9955

5.0 C13

0.9594 0.9771 0.9907 0.9906 0.9909 0.9705 0.9809 0.9956 0.9961 0.9965 0.9826 0.9851 0.9957 0.9957 0.9964

0.9834 0.9918 0.9876 0.9868 0.9835 0.9911 1.0000

0.9809 0.9917 0.9900 0.9893 0.9864 0.9876 0.9980 0.9934 0.9918 0.9887 0.9971 1.0000

0.9729 0.9891 0.9875 0.9863 0.9844 0.9849 0.9926 0.9903 0.9892 0.9870 0.9938 0.9942 0.9890 0.9883 0.9867

0.9677 0.9854 0.9871 0.9864 0.9841 0.9826 0.9900 0.9923 0.9913 0.9895 0.9912 0.9927 0.9910 0.9905 0.9892

192

Table A4 (cont’d)
0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

C11

C11

C11

C11

C11

C12

C12

C12

C12

C12

C12

C12

C12

C12

C12

0.05C14
0.1 C14

0.9583 0.9712 0.9725 0.9711 0.9696 0.9824 0.9802 0.9805 0.9788 0.9781 0.9848 0.9815 0.9788 0.9771 0.9772

0.5 C14

0.9577 0.9756 0.9869 0.9866 0.9861 0.9717 0.9815 0.9940 0.9936 0.9938 0.9838 0.9860 0.9934 0.9928 0.9934

1.0 C14

0.9568 0.9748 0.9871 0.9869 0.9867 0.9703 0.9804 0.9941 0.9940 0.9943 0.9827 0.9853 0.9937 0.9933 0.9939

5.0 C14

0.9526 0.9720 0.9861 0.9860 0.9862 0.9674 0.9775 0.9934 0.9936 0.9944 0.9801 0.9824 0.9933 0.9928 0.9940

0.05C14
0.1 C14

0.9682 0.9813 0.9801 0.9797 0.9763 0.9840 0.9891 0.9873 0.9850 0.9827 0.9907 0.9911 0.9850 0.9842 0.9823

0.5 C14

0.9584 0.9754 0.9871 0.9870 0.9862 0.9720 0.9818 0.9942 0.9939 0.9939 0.9832 0.9861 0.9937 0.9934 0.9936

1.0 C14

0.9556 0.9735 0.9865 0.9863 0.9861 0.9691 0.9794 0.9937 0.9936 0.9941 0.9816 0.9843 0.9934 0.9929 0.9937

5.0 C14

0.9534 0.9725 0.9866 0.9865 0.9867 0.9676 0.9779 0.9937 0.9939 0.9947 0.9804 0.9828 0.9936 0.9932 0.9943

0.05C16
0.1 C16

0.9339 0.9429 0.9491 0.9478 0.9462 0.9647 0.9564 0.9610 0.9593 0.9596 0.9632 0.9576 0.9591 0.9574 0.9586

0.5 C16

0.9531 0.9726 0.9823 0.9819 0.9808 0.9706 0.9802 0.9911 0.9903 0.9904 0.9831 0.9850 0.9901 0.9893 0.9898

1.0 C16

0.9475 0.9684 0.9809 0.9806 0.9801 0.9657 0.9759 0.9902 0.9898 0.9904 0.9791 0.9812 0.9895 0.9888 0.9898

5.0 C16

0.9414 0.9627 0.9773 0.9770 0.9769 0.9605 0.9708 0.9876 0.9872 0.9885 0.9745 0.9766 0.9871 0.9861 0.9877

0.05C16
0.1 C16

0.9593 0.9682 0.9719 0.9711 0.9691 0.9816 0.9778 0.9802 0.9786 0.9778 0.9827 0.9793 0.9784 0.9772 0.9772

0.5 C16

0.9531 0.9708 0.9823 0.9820 0.9810 0.9691 0.9792 0.9910 0.9903 0.9902 0.9814 0.9841 0.9900 0.9895 0.9898

1.0 C16

0.9476 0.9673 0.9805 0.9803 0.9797 0.9651 0.9756 0.9900 0.9895 0.9901 0.9783 0.9808 0.9893 0.9886 0.9896

5.0 C16

0.9439 0.9647 0.9793 0.9790 0.9789 0.9620 0.9725 0.9890 0.9887 0.9898 0.9760 0.9783 0.9885 0.9877 0.9891

0.9674 0.9828 0.9829 0.9822 0.9794 0.9831 0.9904 0.9896 0.9880 0.9858 0.9910 0.9923 0.9876 0.9871 0.9855

0.9651 0.9833 0.9879 0.9873 0.9858 0.9797 0.9885 0.9934 0.9927 0.9916 0.9902 0.9913 0.9923 0.9918 0.9912

0.9515 0.9706 0.9725 0.9716 0.9692 0.9762 0.9809 0.9821 0.9805 0.9796 0.9835 0.9818 0.9801 0.9791 0.9789

0.9521 0.9698 0.9743 0.9731 0.9714 0.9736 0.9796 0.9842 0.9822 0.9820 0.9832 0.9830 0.9825 0.9807 0.9810

193

Table A4 (cont’d)
0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

C13

C13

C13

C13

C13

C13

C13

C13

C13

C13

C14

C14

C14

C14

C14

0.05C12
0.1 C12
0.5 C12
1.0 C12
5.0 C12
0.05C12
0.1 C12
0.5 C12
1.0 C12
5.0 C12
0.05C13
0.1 C13

1.0000

0.5 C13

0.9792 0.9930 1.0000

1.0 C13

0.9782 0.9905 0.9996 1.0000

5.0 C13

0.9775 0.9882 0.9990 0.9997 1.0000

0.05C13
0.1 C13

0.9836 0.9943 0.9875 0.9848 0.9815 1.0000

0.5 C13

0.9788 0.9913 0.9997 0.9999 0.9996 0.9850 0.9952 1.0000

1.0 C13

0.9783 0.9895 0.9994 0.9998 0.9998 0.9840 0.9950 0.9996 1.0000

5.0 C13

0.9773 0.9884 0.9991 0.9997 1.0000 0.9817 0.9933 0.9997 0.9997 1.0000

0.9811 1.0000

0.9825 0.9966 0.9965 0.9949 0.9935 0.9932 1.0000

194

Table A4 (cont’d)
0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

C13

C13

C13

C13

C13

C13

C13

C13

C13

C13

C14

C14

C14

C14

C14

0.05C14
0.1 C14

0.9907 0.9887 0.9838 0.9816 0.9813 0.9870 0.9879 0.9828 0.9819 0.9811 1.0000

0.5 C14

0.9781 0.9886 0.9964 0.9963 0.9965 0.9827 0.9927 0.9965 0.9964 0.9964 0.9858 0.9933 1.0000

1.0 C14

0.9773 0.9878 0.9965 0.9966 0.9969 0.9813 0.9922 0.9967 0.9967 0.9968 0.9846 0.9924 0.9998 1.0000

5.0 C14

0.9766 0.9855 0.9959 0.9964 0.9971 0.9785 0.9905 0.9965 0.9966 0.9970 0.9834 0.9902 0.9994 0.9997 1.0000

0.05C14
0.1 C14

0.9797 0.9923 0.9893 0.9871 0.9852 0.9928 0.9934 0.9874 0.9871 0.9851 0.9897 0.9972 0.9913 0.9901 0.9876

0.5 C14

0.9780 0.9877 0.9963 0.9966 0.9966 0.9827 0.9926 0.9965 0.9967 0.9965 0.9844 0.9930 0.9996 0.9997 0.9993

1.0 C14

0.9773 0.9867 0.9961 0.9964 0.9968 0.9805 0.9914 0.9965 0.9965 0.9967 0.9841 0.9917 0.9998 0.9999 0.9998

5.0 C14

0.9765 0.9857 0.9961 0.9966 0.9972 0.9787 0.9906 0.9966 0.9967 0.9972 0.9831 0.9903 0.9994 0.9998 1.0000

0.05C16
0.1 C16

0.9870 0.9658 0.9660 0.9647 0.9659 0.9679 0.9695 0.9660 0.9665 0.9653 0.9894 0.9733 0.9707 0.9697 0.9696

0.5 C16

0.9791 0.9889 0.9947 0.9942 0.9944 0.9830 0.9932 0.9946 0.9946 0.9942 0.9879 0.9936 0.9971 0.9969 0.9964

1.0 C16

0.9766 0.9852 0.9938 0.9940 0.9947 0.9787 0.9908 0.9941 0.9945 0.9944 0.9850 0.9904 0.9969 0.9969 0.9970

5.0 C16

0.9745 0.9814 0.9918 0.9922 0.9936 0.9740 0.9877 0.9925 0.9931 0.9932 0.9831 0.9873 0.9959 0.9959 0.9964

0.05C16
0.1 C16

0.9929 0.9853 0.9835 0.9819 0.9815 0.9866 0.9863 0.9829 0.9823 0.9813 0.9958 0.9891 0.9855 0.9845 0.9834

0.5 C16

0.9773 0.9867 0.9943 0.9941 0.9943 0.9815 0.9918 0.9943 0.9945 0.9941 0.9855 0.9920 0.9969 0.9967 0.9962

1.0 C16

0.9759 0.9843 0.9936 0.9938 0.9946 0.9781 0.9901 0.9940 0.9944 0.9943 0.9842 0.9900 0.9969 0.9968 0.9969

5.0 C16

0.9749 0.9826 0.9929 0.9933 0.9945 0.9753 0.9886 0.9935 0.9940 0.9941 0.9833 0.9881 0.9965 0.9966 0.9970

0.9828 0.9946 0.9920 0.9899 0.9882 0.9930 0.9954 0.9903 0.9897 0.9881 0.9913 1.0000

0.9812 0.9944 0.9956 0.9942 0.9932 0.9897 0.9959 0.9946 0.9938 0.9932 0.9896 0.9975 0.9972 0.9968 0.9954

0.9858 0.9881 0.9862 0.9845 0.9841 0.9865 0.9899 0.9851 0.9852 0.9837 0.9936 0.9934 0.9885 0.9873 0.9864

0.9829 0.9891 0.9885 0.9868 0.9869 0.9853 0.9910 0.9879 0.9875 0.9864 0.9941 0.9936 0.9920 0.9907 0.9895

195

Table A4 (cont’d)
0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

0.05

0.1

0.5

1.0

5.0

C14

C14

C14

C14

C14

C16

C16

C16

C16

C16

C16

C16

C16

C16

C16

0.05C14
0.1 C14
0.5 C14
1.0 C14
5.0 C14
0.05C14
0.1 C14

1.0000

0.5 C14

0.9912 0.9969 1.0000

1.0 C14

0.9895 0.9963 0.9997 1.0000

5.0 C14

0.9875 0.9954 0.9994 0.9998 1.0000

0.05C16
0.1 C16

0.9708 0.9707 0.9699 0.9697 0.9692 1.0000

0.5 C16

0.9909 0.9957 0.9968 0.9967 0.9964 0.9748 0.9929 1.0000

1.0 C16

0.9874 0.9938 0.9967 0.9969 0.9969 0.9736 0.9909 0.9995 1.0000

5.0 C16

0.9845 0.9913 0.9955 0.9962 0.9962 0.9733 0.9891 0.9985 0.9996 1.0000

0.05C16
0.1 C16

0.9881 0.9876 0.9849 0.9843 0.9832 0.9905 0.9927 0.9880 0.9854 0.9838 1.0000

0.5 C16

0.9895 0.9945 0.9968 0.9967 0.9963 0.9734 0.9913 0.9995 0.9995 0.9987 0.9864 0.9940 1.0000

1.0 C16

0.9871 0.9933 0.9967 0.9969 0.9968 0.9731 0.9904 0.9993 0.9999 0.9996 0.9850 0.9931 0.9996 1.0000

5.0 C16

0.9851 0.9921 0.9961 0.9967 0.9969 0.9728 0.9891 0.9988 0.9998 0.9999 0.9840 0.9924 0.9990 0.9998 1.0000

0.9955 1.0000

0.9904 0.9913 0.9879 0.9869 0.9863 0.9861 1.0000

0.9921 0.9928 0.9905 0.9905 0.9893 0.9828 0.9958 0.9955 0.9935 0.9926 0.9926 1.0000

196

Table A5. Pearson product moment correlation (PPMC) coefficients comparing propylbenzene (P), butylbenzene (B), amylbenzene
(A), and hexylbenzene (H) mass spectra from Sets 1 and 2 at five concentrations (0.05, 0.1, 0.5, 1.0, 5.0 mM). Set 1 mass spectra are
italicized.

0.05 P
0.1 P
0.5 P
1.0 P
5.0 P
0.05 P
0.1 P
0.5 P
1.0 P
5.0 P
0.05 B
0.1 B
0.5 B
1.0 B
5.0 B
0.05 B
0.1 B
0.5 B
1.0 B
5.0 B

0.05 P
1.0000
0.9925
0.9927
0.9910
0.9891
0.9946
0.9938
0.9922
0.9899
0.9890
0.8729
0.8933
0.8784
0.8735
0.8735
0.8679
0.8921
0.8768
0.8702
0.8713

0.1 P

0.5 P

1.0 P

5.0 P

0.05 P

0.1 P

0.5 P

1.0 P

5.0 P

0.05 B

0.1 B

0.5 B

1.0 B

5.0 B

1.0000
0.9981
0.9971
0.9952
0.9975
0.9987
0.9978
0.9965
0.9951
0.8615
0.8900
0.8758
0.8712
0.8710
0.8609
0.8890
0.8740
0.8680
0.8689

1.0000
0.9994
0.9981
0.9972
0.9990
0.9998
0.9989
0.9980
0.8563
0.8860
0.8735
0.8693
0.8693
0.8548
0.8853
0.8720
0.8659
0.8670

1.0000
0.9995
0.9957
0.9979
0.9997
0.9999
0.9995
0.8568
0.8854
0.8740
0.8705
0.8708
0.8540
0.8847
0.8728
0.8671
0.8686

1.0000
0.9936
0.9960
0.9988
0.9998
1.0000
0.8558
0.8835
0.8729
0.8702
0.8707
0.8521
0.8826
0.8721
0.8667
0.8685

1.0000
0.9984
0.9966
0.9949
0.9934
0.8573
0.8824
0.8671
0.8621
0.8619
0.8535
0.8810
0.8653
0.8587
0.8597

1.0000
0.9986
0.9971
0.9958
0.8550
0.8833
0.8692
0.8646
0.8644
0.8533
0.8821
0.8675
0.8612
0.8622

1.0000
0.9994
0.9987
0.8591
0.8882
0.8763
0.8724
0.8725
0.8571
0.8875
0.8749
0.8690
0.8703

1.0000
0.9998
0.8573
0.8854
0.8744
0.8713
0.8716
0.8541
0.8847
0.8733
0.8679
0.8695

1.0000
0.8560
0.8835
0.8730
0.8703
0.8709
0.8522
0.8827
0.8722
0.8669
0.8687

1.0000
0.9897
0.9878
0.9873
0.9869
0.9932
0.9885
0.9874
0.9871
0.9871

1.0000
0.9966
0.9945
0.9935
0.9946
0.9989
0.9959
0.9941
0.9932

1.0000
0.9995
0.9990
0.9932
0.9976
0.9999
0.9994
0.9989

1.0000
0.9999
0.9914
0.9956
0.9998
0.9999
0.9998

1.0000
0.9904
0.9946
0.9995
0.9999
1.0000

197

Table A5 (cont’d)

0.05 A
0.1 A
0.5 A
1.0 A
5.0 A
0.05 A
0.1 A
0.5 A
1.0 A
5.0 A
0.05 H
0.1 H
0.5 H
1.0 H
5.0 H
0.05 H
0.1 H
0.5 H
1.0 H
5.0 H

0.05 P
0.8515
0.8835
0.8466
0.8432
0.8354
0.8560
0.8506
0.8450
0.8355
0.8386
0.7904
0.7738
0.7986
0.7883
0.7820
0.8310
0.8180
0.7912
0.7863
0.7835

0.1 P
0.8476
0.8797
0.8449
0.8419
0.8337
0.8532
0.8483
0.8435
0.8339
0.8369
0.7856
0.7722
0.7968
0.7867
0.7804
0.8262
0.8159
0.7900
0.7848
0.7819

0.5 P
0.8422
0.8763
0.8411
0.8385
0.8303
0.8477
0.8432
0.8399
0.8303
0.8337
0.7771
0.7644
0.7914
0.7813
0.7750
0.8202
0.8096
0.7846
0.7795
0.7766

1.0 P
0.8421
0.8760
0.8417
0.8396
0.8317
0.8473
0.8426
0.8409
0.8315
0.8351
0.7774
0.7615
0.7922
0.7825
0.7766
0.8200
0.8094
0.7857
0.7808
0.7782

5.0 P
0.8406
0.8745
0.8409
0.8393
0.8318
0.8456
0.8407
0.8405
0.8314
0.8352
0.7762
0.7580
0.7917
0.7824
0.7768
0.8188
0.8081
0.7854
0.7808
0.7784

0.05 P
0.8391
0.8713
0.8352
0.8321
0.8239
0.8439
0.8390
0.8339
0.8240
0.8271
0.7771
0.7629
0.7862
0.7759
0.7695
0.8181
0.8059
0.7793
0.7740
0.7711

0.1 P
0.8388
0.8722
0.8361
0.8333
0.8250
0.8440
0.8391
0.8348
0.8251
0.8283
0.7746
0.7616
0.7863
0.7761
0.7697
0.8165
0.8055
0.7794
0.7741
0.7713

198

0.5 P
0.8449
0.8789
0.8441
0.8418
0.8338
0.8504
0.8458
0.8432
0.8337
0.8371
0.7803
0.7663
0.7948
0.7850
0.7788
0.8230
0.8125
0.7881
0.7831
0.7804

1.0 P
0.8427
0.8763
0.8427
0.8408
0.8331
0.8479
0.8431
0.8420
0.8328
0.8364
0.7787
0.7620
0.7937
0.7843
0.7785
0.8209
0.8104
0.7874
0.7826
0.7801

5.0 P
0.8408
0.8747
0.8411
0.8396
0.8320
0.8458
0.8408
0.8407
0.8316
0.8354
0.7764
0.7582
0.7920
0.7828
0.7771
0.8190
0.8083
0.7857
0.7811
0.7787

0.05 B
0.9436
0.9474
0.9375
0.9345
0.9311
0.9456
0.9386
0.9356
0.9325
0.9327
0.9331
0.8996
0.9284
0.9243
0.9204
0.9400
0.9322
0.9257
0.9222
0.9216

0.1 B
0.9419
0.9528
0.9385
0.9348
0.9301
0.9464
0.9415
0.9361
0.9316
0.9319
0.9185
0.8995
0.9228
0.9169
0.9122
0.9349
0.9301
0.9188
0.9148
0.9134

0.5 B
0.9388
0.9496
0.9395
0.9365
0.9325
0.9443
0.9402
0.9374
0.9339
0.9343
0.9168
0.8950
0.9271
0.9223
0.9182
0.9321
0.9301
0.9240
0.9204
0.9194

1.0 B
0.9380
0.9483
0.9397
0.9372
0.9336
0.9433
0.9391
0.9379
0.9348
0.9354
0.9172
0.8928
0.9283
0.9241
0.9203
0.9316
0.9298
0.9255
0.9222
0.9215

5.0 B
0.9375
0.9478
0.9397
0.9374
0.9339
0.9428
0.9385
0.9380
0.9351
0.9358
0.9165
0.8905
0.9282
0.9242
0.9206
0.9309
0.9292
0.9256
0.9225
0.9219

Table A5 (cont’d)
0.05 B
0.05 P
0.1 P
0.5 P
1.0 P
5.0 P
0.05 P
0.1 P
0.5 P
1.0 P
5.0 P
0.05 B
0.1 B
0.5 B
1.0 B
5.0 B
0.05 B
0.1 B
0.5 B
1.0 B
5.0 B

0.1 B

0.5 B

1.0 B

5.0 B

1.0000
0.9941
0.9926
0.9916
0.9905

0.05 A

0.1 A

1.0000
0.9969 1.0000
0.9953 0.9997 1.0000
0.9944 0.9994 0.9999 1.0000

199

0.5 A

1.0 A

5.0 A

0.05 A

0.1 A

0.5 A

1.0 A

5.0 A

Table A5 (cont’d)

0.05 A
0.1 A
0.5 A
1.0 A
5.0 A
0.05 A
0.1 A
0.5 A
1.0 A
5.0 A
0.05 H
0.1 H
0.5 H
1.0 H
5.0 H
0.05 H
0.1 H
0.5 H
1.0 H
5.0 H

0.05 B
0.9377
0.9441
0.9333
0.9295
0.9256
0.9421
0.9360
0.9308
0.9274
0.9272
0.9239
0.8992
0.9245
0.9194
0.9150
0.9347
0.9294
0.9210
0.9173
0.9162

0.1 B
0.9427
0.9542
0.9405
0.9368
0.9321
0.9480
0.9437
0.9380
0.9336
0.9339
0.9186
0.9009
0.9256
0.9197
0.9150
0.9356
0.9318
0.9217
0.9176
0.9163

0.5 B
0.9373
0.9482
0.9385
0.9358
0.9319
0.9427
0.9386
0.9366
0.9332
0.9337
0.9155
0.8926
0.9263
0.9217
0.9177
0.9308
0.9288
0.9232
0.9198
0.9190

1.0 B
0.9373
0.9472
0.9391
0.9367
0.9331
0.9426
0.9385
0.9373
0.9344
0.9349
0.9172
0.8927
0.9284
0.9243
0.9206
0.9311
0.9296
0.9257
0.9225
0.9218

5.0 B
0.9384
0.9483
0.9406
0.9384
0.9350
0.9437
0.9395
0.9391
0.9362
0.9369
0.9184
0.8921
0.9299
0.9260
0.9225
0.9322
0.9306
0.9273
0.9243
0.9237

0.05 A
1.0000
0.9961
0.9968
0.9954
0.9941
0.9989
0.9978
0.9960
0.9948
0.9942
0.9415
0.9209
0.9417
0.9374
0.9334
0.9489
0.9453
0.9389
0.9352
0.9344

0.1 A

0.5 A

1.0 A

5.0 A

0.05 A

0.1 A

0.5 A

1.0 A

5.0 A

1.0000
0.9946
0.9927
0.9902
0.9969
0.9961
0.9935
0.9909
0.9909
0.9356
0.9194
0.9407
0.9352
0.9307
0.9501
0.9462
0.9369
0.9329
0.9318

1.0000
0.9996
0.9990
0.9975
0.9983
0.9998
0.9993
0.9991
0.9352
0.9134
0.9436
0.9402
0.9367
0.9440
0.9431
0.9412
0.9382
0.9378

1.0000
0.9998
0.9957
0.9966
0.9999
0.9998
0.9998
0.9315
0.9070
0.9405
0.9376
0.9344
0.9400
0.9391
0.9385
0.9357
0.9355

1.0000
0.9941
0.9953
0.9995
0.9999
1.0000
0.9294
0.9035
0.9389
0.9364
0.9335
0.9370
0.9364
0.9371
0.9346
0.9345

1.0000
0.9988
0.9964
0.9950
0.9944
0.9443
0.9253
0.9475
0.9430
0.9390
0.9529
0.9504
0.9445
0.9408
0.9401

1.0000
0.9972
0.9961
0.9954
0.9378
0.9217
0.9439
0.9395
0.9354
0.9475
0.9463
0.9409
0.9373
0.9365

1.0000
0.9997
0.9996
0.9328
0.9095
0.9415
0.9384
0.9351
0.9418
0.9406
0.9394
0.9365
0.9362

1.0000
0.9999
0.9320
0.9071
0.9411
0.9384
0.9354
0.9394
0.9388
0.9392
0.9366
0.9364

1.0000
0.9303
0.9042
0.9398
0.9373
0.9344
0.9381
0.9375
0.9381
0.9355
0.9354

200

Table A5 (cont’d)
0.05 H
0.05 A
0.1 A
0.5 A
1.0 A
5.0 A
0.05 A
0.1 A
0.5 A
1.0 A
5.0 A
0.05 H
0.1 H
0.5 H
1.0 H
5.0 H
0.05 H
0.1 H
0.5 H
1.0 H
5.0 H

1.0000
0.9753
0.9892
0.9882
0.9867
0.9899
0.9905
0.9887
0.9875
0.9869

0.1 H

1.0000
0.9755
0.9712
0.9679
0.9805
0.9830
0.9727
0.9702
0.9680

0.5 H

1.0000
0.9995
0.9987
0.9916
0.9966
0.9997
0.9992
0.9988

1.0 H

1.0000
0.9998
0.9886
0.9943
0.9999
0.9999
0.9998

5.0 H

1.0000
0.9864
0.9926
0.9995
0.9999
1.0000

0.05 H

1.0000
0.9965
0.9896
0.9880
0.9866

0.1 H

0.5 H

1.0 H

5.0 H

1.0000
0.9951 1.0000
0.9939 0.9998 1.0000
0.9927 0.9996 0.9999 1.0000

201

Table A6. Pearson product moment correlation (PPMC) coefficients comparing the effect of concentration on three replicates (a, b, c)
of C10 mass spectra at five concentrations (0.05, 0.1, 0.5, 1.0, 5.0 mM) from Set 1.

C10
0.05_a
0.05_a 1.0000
0.05_b 0.9584
0.05_c 0.9694
0.9642
0.1_a
0.9662
0.1_b
0.9751
0.1_c
0.9567
0.5_a
0.9563
0.5_b
0.9568
0.5_c
0.9571
1.0_a
0.9526
1.0_b
0.9525
1.0_c
0.9468
5.0_a
0.9469
5.0_b
0.9455
5.0_c

0.05_b

0.05_c

0.1_a

0.1_b

0.1_c

0.5_a

0.5_b

0.5_c

1.0_a

1.0_b

1.0_c

5.0_a

5.0_b

1.0000
0.9536
0.9630
0.9631
0.9589
0.9703
0.9717
0.9667
0.9719
0.9710
0.9705
0.9706
0.9712
0.9719

1.0000
0.9749
0.9668
0.9806
0.9692
0.9673
0.9746
0.9706
0.9668
0.9674
0.9633
0.9619
0.9597

1.0000
0.9868
0.9870
0.9877
0.9879
0.9886
0.9871
0.9865
0.9857
0.9820
0.9825
0.9815

1.0000
0.9875
0.9842
0.9827
0.9803
0.9794
0.9807
0.9780
0.9746
0.9761
0.9759

1.0000
0.9840
0.9828
0.9840
0.9821
0.9810
0.9796
0.9756
0.9761
0.9749

1.0000
0.9994
0.9987
0.9987
0.9990
0.9986
0.9979
0.9979
0.9977

1.0000
0.9983
0.9989
0.9990
0.9987
0.9983
0.9983
0.9981

1.0000
0.9991
0.9983
0.9986
0.9975
0.9971
0.9963

1.0000
0.9994
0.9996
0.9989
0.9989
0.9983

1.0000
0.9997
0.9993
0.9995
0.9992

1.0000
0.9995
0.9994
0.9990

1.0000
0.9998
0.9996

1.0000
0.9999

202

Table A6 (cont’d)
C11
0.05_a
0.05_a 1.0000
0.05_b 0.9693
0.05_c 0.9837
0.9646
0.1_a
0.9706
0.1_b
0.9624
0.1_c
0.9626
0.5_a
0.9608
0.5_b
0.9606
0.5_c
0.9602
1.0_a
0.9583
1.0_b
0.9583
1.0_c
0.9577
5.0_a
0.9575
5.0_b
0.9576
5.0_c

0.05_b

0.05_c

0.1_a

0.1_b

0.1_c

0.5_a

0.5_b

0.5_c

1.0_a

1.0_b

1.0_c

5.0_a

5.0_b

1.0000
0.9683
0.9649
0.9676
0.9632
0.9534
0.9462
0.9536
0.9507
0.9490
0.9507
0.9467
0.9481
0.9477

1.0000
0.9603
0.9730
0.9645
0.9603
0.9554
0.9581
0.9558
0.9549
0.9549
0.9520
0.9531
0.9524

1.0000
0.9885
0.9869
0.9851
0.9803
0.9831
0.9819
0.9815
0.9807
0.9780
0.9789
0.9786

1.0000
0.9880
0.9903
0.9861
0.9889
0.9873
0.9860
0.9861
0.9832
0.9837
0.9837

1.0000
0.9817
0.9777
0.9781
0.9792
0.9787
0.9783
0.9753
0.9759
0.9753

1.0000
0.9985
0.9990
0.9990
0.9988
0.9988
0.9979
0.9981
0.9982

1.0000
0.9974
0.9987
0.9987
0.9988
0.9988
0.9985
0.9986

1.0000
0.9988
0.9981
0.9983
0.9977
0.9980
0.9982

1.0000
0.9994
0.9996
0.9994
0.9995
0.9996

1.0000
0.9995
0.9995
0.9996
0.9995

1.0000
0.9995
0.9996
0.9996

1.0000
0.9999
0.9999

1.0000
0.9999

203

Table A6 (cont’d)
C12
0.05_a
0.05_a 1.0000
0.05_b 0.9721
0.05_c 0.9621
0.9709
0.1_a
0.9862
0.1_b
0.9796
0.1_c
0.9804
0.5_a
0.9824
0.5_b
0.9816
0.5_c
0.9789
1.0_a
1.0_b 0.9805
0.9818
1.0_c
0.9794
5.0_a
0.9792
5.0_b
0.9793
5.0_c

0.05_b

0.05_c

0.1_a

0.1_b

0.1_c

0.5_a

0.5_b

0.5_c

1.0_a

1.0_b

1.0_c

5.0_a

5.0_b

1.0000
0.9828
0.9819
0.9786
0.9834
0.9694
0.9702
0.9720
0.9707
0.9682
0.9675
0.9655
0.9642
0.9641

1.0000
0.9763
0.9681
0.9814
0.9550
0.9577
0.9589
0.9572
0.9540
0.9524
0.9490
0.9468
0.9472

1.0000
0.9855
0.9902
0.9832
0.9825
0.9845
0.9853
0.9823
0.9809
0.9794
0.9773
0.9780

1.0000
0.9925
0.9907
0.9908
0.9907
0.9881
0.9891
0.9891
0.9871
0.9863
0.9866

1.0000
0.9849
0.9861
0.9865
0.9842
0.9834
0.9829
0.9802
0.9793
0.9795

1.0000
0.9992
0.9993
0.9988
0.9996
0.9993
0.9991
0.9989
0.9990

1.0000
0.9995
0.9989
0.9995
0.9994
0.9989
0.9987
0.9988

1.0000
0.9990
0.9995
0.9992
0.9990
0.9987
0.9987

1.0000
0.9994
0.9990
0.9990
0.9985
0.9987

1.0000
0.9997
0.9997
0.9995
0.9996

1.0000
0.9997
0.9996
0.9997

1.0000
0.9999
0.9999

1.0000
0.9999

204

Table A6 (cont’d)
C13
0.05_a
0.05_a 1.0000
0.05_b 0.9813
0.05_c 0.9714
0.9719
0.1_a
0.9756
0.1_b
0.9575
0.1_c
0.9710
0.5_a
0.9723
0.5_b
0.9718
0.5_c
0.9705
1.0_a
0.9703
1.0_b
0.9724
1.0_c
0.9712
5.0_a
0.9713
5.0_b
0.9705
5.0_c

0.05_b

0.05_c

0.1_a

0.1_b

0.1_c

0.5_a

0.5_b

0.5_c

1.0_a

1.0_b

1.0_c

5.0_a

5.0_b

1.0000
0.9807
0.9718
0.9769
0.9681
0.9673
0.9693
0.9686
0.9668
0.9663
0.9667
0.9665
0.9665
0.9664

1.0000
0.9727
0.9730
0.9689
0.9747
0.9734
0.9749
0.9748
0.9745
0.9728
0.9726
0.9724
0.9726

1.0000
0.9926
0.9879
0.9911
0.9887
0.9912
0.9893
0.9882
0.9870
0.9857
0.9854
0.9855

1.0000
0.9923
0.9916
0.9910
0.9917
0.9895
0.9894
0.9885
0.9877
0.9873
0.9876

1.0000
0.9879
0.9860
0.9880
0.9856
0.9854
0.9832
0.9827
0.9822
0.9829

1.0000
0.9993
0.9996
0.9995
0.9994
0.9989
0.9987
0.9985
0.9986

1.0000
0.9990
0.9994
0.9993
0.9994
0.9994
0.9994
0.9994

1.0000
0.9994
0.9994
0.9988
0.9985
0.9983
0.9984

1.0000
0.9998
0.9995
0.9994
0.9993
0.9994

1.0000
0.9996
0.9995
0.9994
0.9995

1.0000
0.9998
0.9998
0.9998

1.0000
1.0000
1.0000

1.0000
1.0000

205

Table A6 (cont’d)
C14
0.05_a
0.05_a 1.0000
0.05_b 0.9906
0.05_c 0.9840
0.9873
0.1_a
0.9869
0.1_b
0.9876
0.1_c
0.9812
0.5_a
0.9819
0.5_b
0.9822
0.5_c
0.9802
1.0_a
0.9803
1.0_b
0.9799
1.0_c
0.9786
5.0_a
0.9786
5.0_b
0.9784
5.0_c

0.05_b

0.05_c

0.1_a

0.1_b

0.1_c

0.5_a

0.5_b

0.5_c

1.0_a

1.0_b

1.0_c

5.0_a

5.0_b

1.0000
0.9839
0.9867
0.9860
0.9858
0.9807
0.9813
0.9808
0.9800
0.9799
0.9798
0.9790
0.9788
0.9789

1.0000
0.9811
0.9829
0.9851
0.9806
0.9804
0.9810
0.9802
0.9800
0.9800
0.9796
0.9790
0.9788

1.0000
0.9971
0.9968
0.9912
0.9927
0.9912
0.9908
0.9904
0.9908
0.9885
0.9887
0.9886

1.0000
0.9952
0.9920
0.9940
0.9930
0.9927
0.9918
0.9923
0.9900
0.9903
0.9902

1.0000
0.9910
0.9920
0.9909
0.9909
0.9899
0.9907
0.9882
0.9881
0.9883

1.0000
0.9995
0.9995
0.9996
0.9997
0.9998
0.9996
0.9996
0.9996

1.0000
0.9996
0.9997
0.9995
0.9996
0.9990
0.9992
0.9991

1.0000
0.9996
0.9995
0.9995
0.9991
0.9993
0.9991

1.0000
0.9997
0.9998
0.9994
0.9995
0.9995

1.0000
0.9998
0.9997
0.9998
0.9997

1.0000
0.9996
0.9997
0.9997

1.0000
0.9999
0.9999

1.0000
0.9999

206

Table A6 (cont’d)
C16
0.05_a
0.05_a 1.0000
0.05_b 0.9755
0.05_c 0.9769
0.9693
0.1_a
0.9771
0.1_b
0.9727
0.1_c
0.9698
0.5_a
0.9670
0.5_b
0.9680
0.5_c
0.9674
1.0_a
0.9680
1.0_b
0.9683
1.0_c
0.9680
5.0_a
0.9700
5.0_b
0.9696
5.0_c

0.05_b

0.05_c

0.1_a

0.1_b

0.1_c

0.5_a

0.5_b

0.5_c

1.0_a

1.0_b

1.0_c

5.0_a

5.0_b

1.0000
0.9747
0.9679
0.9763
0.9756
0.9630
0.9624
0.9606
0.9589
0.9584
0.9599
0.9578
0.9573
0.9579

1.0000
0.9741
0.9766
0.9749
0.9703
0.9691
0.9691
0.9693
0.9691
0.9695
0.9676
0.9683
0.9689

1.0000
0.9858
0.9810
0.9877
0.9864
0.9845
0.9848
0.9836
0.9846
0.9807
0.9819
0.9822

1.0000
0.9927
0.9904
0.9900
0.9892
0.9874
0.9877
0.9888
0.9864
0.9862
0.9865

1.0000
0.9885
0.9880
0.9883
0.9862
0.9870
0.9877
0.9862
0.9851
0.9862

1.0000
0.9991
0.9990
0.9987
0.9984
0.9990
0.9975
0.9976
0.9978

1.0000
0.9990
0.9990
0.9987
0.9992
0.9979
0.9975
0.9978

1.0000
0.9994
0.9995
0.9996
0.9991
0.9989
0.9991

1.0000
0.9997
0.9997
0.9994
0.9994
0.9995

1.0000
0.9998
0.9997
0.9995
0.9997

1.0000
0.9994
0.9992
0.9994

1.0000
0.9998
0.9999

1.0000
0.9999

207

Table A7. Effect of concentration on the number of discriminating ions for pair-wise comparison of Set 1 alkanes compared to all
alkanes in Set 2 (t-test, 99.9% CL) using predicted standard deviation. Zero discriminating ions indicate complete association and the
corresponding random-match probability is shown in parentheses. Entries in red highlight unexpected association or discrimination.
Set 1 C10

Set 1 C11

Concentration
Set 2

(mM)

0.5

1.0

C10

0.5

0 (1.7 x 10- )

1.0

0 (9.1 x 10- )

5.0

0 (1.8 x 10- )

0.5

1

11

1.0

2

5.0
C12

5.0

39

0 (1.8 x 10- )

39

0 (2.0 x 10- )

38

0 (8.3 x 10- )

0.5

39

0 (1.6 x 10- )

40

39

0 (1.4 x 10- )

39
40

a

40

0 (2.4 x 10- )

41

0 (1.5 x 10- )

40

0 (2.4 x 10- )

41

0 (1.5 x 10- )

40

0 (1.2 x 10- )

40

0 (1.9 x 10- )

1
2
4

2
2
12

1
9
7

5
9
10

2
5
22

5
13
37

9
14
9

7
12
16

4
11
35

9
21
45

13
23
20

13
17
29

6
17
48

2

0 (1.7 x 10- )

2

3

0 (1.7 x 10- )

4

4

8

0 (8.8 x 10- )

0.5
1.0
5.0

4
7
6

2
6
10

2
5
22

10
4
5

C13

0.5
1.0
5.0

6
10
11

5
12
17

4
10
32

C14

0.5
1.0
5.0

10
15
13

6
16
21

C16

0.5
1.0
5.0

15
22
22

13
25
30

C11

a

5.0

0 (1.3 x 10- )

39

1.0

99.0% confidence level
208

a

40
40
40

Table A7 (cont’d)
Set 1 C12

Set 1 C13

Concentration
Set 2

(mM)

C10

0.5
1.0
5.0

C11

0.5
1.0
5.0

C12

0.5

0 (2.6 x 10- )

1.0

0 (2.6 x 10- )

5.0

0 (5.5 x 10- )

C13

0.5

0.5

1.0

5.0

42
42

a

0 (2.6 x 10- )

42

8

0 (2.6 x 10- )

0.5

1.0

42

0 (5.5 x 10- )

42

0 (5.5 x 10- )

0 (5.5 x 10- )

42

0 (2.9 x 10- )

1

2

0 (4.4 x 10- )

5.0

42
42
42

43

0 (1.1 x 10- )

42

0 (1.1 x 10- )

42

0 (6.8 x 10- )

42

42

43

0 (6.8 x 10- )

0 (6.8 x 10- )

43

0 (6.8 x 10- )

43

1.0

2

2

2

0 (1.1 x 10- )

5.0

4

5

13

0 (1.1 x 10- )

C14

0.5
1.0
5.0

3
6
6

4
11
12

2
4
23

11
4
4

1
5
5

2
2
11

C16

0.5
1.0
5.0

8
16
17

7
15
23

4
9
49

7
11
13

2
11
20

2
4
31

a

99.0% confidence level

209

a

43

Table A7 (cont’d)
Set 1 C14

Set 1 C16

Concentration
Set 2

(mM)

C10

0.5
1.0
5.0

C11

0.5
1.0
5.0

C12

0.5
1.0
5.0

C13

0.5
1.0
5.0

C14

0.5

0 (5.1 x 10- )

1.0

0 (5.1 x 10- )

5.0
C16

0.5

1.0

5.0

44

0 (3.1 x 10- )

44

0 (3.1 x 10- )

0 (5.1 x 10- )

44

0.5

0.5

1.0

44

0 (3.1 x 10- )

44

0 (3.1 x 10- )

0 (3.1 x 10- )

44

0 (3.1 x 10- )

2

1

2

0 (2.5 x 10- )

1.0

7

5

2

0 (2.5 x 10- )

5.0

8

14

19

0 (2.5 x 10- )

5.0

44
44
44

210

45

0 (6.7 x 10- )

45

0 (1.7 x 10- )

45

0 (1.1 x 10- )

45

0 (1.1 x 10- )

44

45

0 (6.4 x 10- )

45

0 (6.4 x 10- )

46
46

Appendix E
Retention Time Differentiation

211

While there is no standard tolerance used to indicate a retention time match, this work
applies the standard protocol of the Arkansas Forensic Laboratory [4]. In this standard, the
retention times (tR) of spectra must be within ± 2% of each other for tR ≤ 3 minutes or ± 1% for
tR > 3 minutes, for the spectra to be considered a match [4]. If the retention times of the two
spectra are not within the above tolerance limits, the spectra are differentiated based on retention
time.
Replicate spectra (n = 21) of each alkane were investigated to insure the retention times
were within the tolerance chosen. Each alkane peak was visually examined and the retention
time of the selected mass spectrum was obtained from the apparent peak maximum. Little to no
retention time drift was observed among the same alkanes, with respective retention times
compared to the allowable tolerance shown in Table A8. Each replicate was easily within the
specified tolerance (± 1% of each other). In addition, each alkane was easily outside the
tolerance window when compared to the other alkanes, indicating the retention time modifier
would be an effective addition against false positive matching. In this work, then, retention time
is a powerful means of differentiating compounds and can be used as an optional addition to the
SAEEUMS method.

212

Table A8. Retention time of replicates (n = 21) of alkanes and the tolerance accepted by the
Arkansas Forensic Laboratory [4]
a
b
tR (min)
Tolerance
C10
C11
C12
C13
C14
C16
a
b

5.931 ± 0.002
7.068 ± 0.001
8.106 ± 0.003
9.065 ± 0.004
9.965 ± 0.003
11.606 ± 0.004

5.931 ± 0.059
7.068 ± 0.071
8.106 ± 0.081
9.065 ± 0.091
9.965 ± 0.100
11.606 ± 0.116

± one standard deviation
± 2% of each otherif tR ≤ 3 minutes or ± 1% of each other if tR > 3 minutes

213

Appendix F
Supplemental Data Tables for Chapter 3

214

Table A9. Pearson product moment correlation (PPMC) for 1128 total pair-wise comparisons of case samples and reference standards
of amphetamine (Amp), methamphetamine (Meth), MDMA, MDA, phentermine (Phent), and psilocin mass spectra.
Amp 1
Amp 2
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
Meth 1
Meth 2
Case 8
Case 9
Case 10
Case 11
Case 12
Case 13
MDA 1
MDA 2
Case 14
Case 15
Case 16
Case 17
Case 18
Case 19
Case 20

Amp 1
1.0000
0.9877
0.9995
0.9974
0.9999
0.9999
0.9939
0.9942
0.9985
0.0777
0.0332
0.0382
0.0400
0.0518
0.0383
0.0389
0.0455
0.9267
0.9396
0.9295
0.9241
0.9268
0.9256
0.9281
0.9281
0.9244

Amp 2

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

Meth 1

Meth 2

Case 8

1.0000
0.9827
0.9741
0.9870
0.9888
0.9989
0.9986
0.9948
0.0411
0.0184
0.0210
0.0245
0.0286
0.0206
0.0207
0.0242
0.9542
0.9689
0.9577
0.9517
0.9547
0.9532
0.9560
0.9565
0.9524

1.0000
0.9989
0.9996
0.9993
0.9902
0.9906
0.9964
0.0847
0.0362
0.0416
0.0431
0.0563
0.0417
0.0424
0.0496
0.9191
0.9316
0.9218
0.9164
0.9191
0.9180
0.9203
0.9203
0.9166

1.0000
0.9976
0.9967
0.9835
0.9842
0.9920
0.0939
0.0399
0.0461
0.0471
0.0621
0.0463
0.0471
0.0552
0.9067
0.9185
0.9093
0.9040
0.9067
0.9056
0.9079
0.9078
0.9041

1.0000
0.9998
0.9934
0.9937
0.9981
0.0785
0.0335
0.0386
0.0404
0.0523
0.0387
0.0393
0.0460
0.9262
0.9388
0.9289
0.9235
0.9263
0.9251
0.9275
0.9275
0.9238

1.0000
0.9946
0.9949
0.9988
0.0768
0.0332
0.0380
0.0399
0.0514
0.0381
0.0386
0.0451
0.9290
0.9419
0.9318
0.9263
0.9291
0.9278
0.9303
0.9304
0.9266

1.0000
0.9999
0.9984
0.0524
0.0230
0.0264
0.0294
0.0358
0.0261
0.0263
0.0308
0.9480
0.9622
0.9513
0.9454
0.9484
0.9469
0.9496
0.9500
0.9461

1.0000
0.9986
0.0602
0.0306
0.0340
0.0369
0.0434
0.0337
0.0340
0.0385
0.9479
0.9620
0.9512
0.9453
0.9483
0.9468
0.9495
0.9499
0.9460

1.0000
0.0656
0.0285
0.0328
0.0352
0.0442
0.0326
0.0331
0.0386
0.9388
0.9523
0.9418
0.9361
0.9390
0.9376
0.9402
0.9404
0.9366

1.0000
0.9892
0.9911
0.9898
0.9956
0.9917
0.9920
0.9943
0.0152
0.0129
0.0132
0.0132
0.0134
0.0137
0.0132
0.0136
0.0149

1.0000
0.9997
0.9998
0.9982
0.9997
0.9997
0.9988
0.0076
0.0065
0.0059
0.0057
0.0062
0.0061
0.0058
0.0066
0.0078

1.0000
0.9998
0.9987
0.9999
0.9999
0.9994
0.0079
0.0068
0.0062
0.0061
0.0065
0.0065
0.0062
0.0069
0.0081

215

Table A9 (cont’d)
MDMA 1
MDMA 2
Case 21
Case 22
Case 23
Case 24
Case 25
Case 26
Case 27
Case 28
Case 29
Case 30
Phent 1
Phent 2
Case 31
Psilocin 1
Psilocin 2
Case 32
Case 33
Case 34
Case 35
Case 36

Amp 1
0.0119
0.0151
0.0119
0.0211
0.0125
0.0126
0.0139
0.0110
0.0087
0.0092
0.0110
0.0104
0.0558
0.0435
0.1071
0.1784
0.0169
0.0355
0.0287
0.0301
0.0606
0.0147

Amp 2
0.0098
0.0103
0.0073
0.0145
0.0076
0.0079
0.0084
0.0071
0.0059
0.0066
0.0070
0.0067
0.0277
0.0221
0.0641
0.1720
0.0144
0.0300
0.0253
0.0262
0.0581
0.0129

Case 1
0.0124
0.0162
0.0129
0.0224
0.0136
0.0137
0.0151
0.0118
0.0093
0.0098
0.0119
0.0113
0.0610
0.0476
0.1149
0.1795
0.0174
0.0365
0.0294
0.0309
0.0611
0.0151

Case 2
0.0131
0.0179
0.0144
0.0248
0.0154
0.0153
0.0169
0.0132
0.0103
0.0107
0.0133
0.0125
0.0682
0.0530
0.1261
0.1804
0.0182
0.0381
0.0304
0.0321
0.0616
0.0157

Case 3
0.0119
0.0152
0.0120
0.0212
0.0127
0.0128
0.0141
0.0111
0.0087
0.0092
0.0111
0.0105
0.0565
0.0441
0.1083
0.1785
0.0170
0.0357
0.0289
0.0303
0.0606
0.0148

Case 4
0.0125
0.0158
0.0126
0.0218
0.0132
0.0133
0.0146
0.0116
0.0093
0.0098
0.0117
0.0111
0.0548
0.0429
0.1054
0.1796
0.0172
0.0358
0.0290
0.0305
0.0611
0.0151

216

Case 5
0.0103
0.0115
0.0084
0.0161
0.0088
0.0090
0.0098
0.0080
0.0066
0.0072
0.0080
0.0076
0.0364
0.0288
0.0773
0.1744
0.0153
0.0317
0.0264
0.0275
0.0591
0.0135

Case 6
0.0179
0.0193
0.0162
0.0240
0.0166
0.0168
0.0176
0.0157
0.0142
0.0149
0.0157
0.0153
0.0440
0.0363
0.0851
0.1817
0.0227
0.0392
0.0339
0.0349
0.0664
0.0209

Case 7
0.0115
0.0137
0.0105
0.0190
0.0110
0.0112
0.0122
0.0099
0.0080
0.0086
0.0099
0.0094
0.0466
0.0366
0.0928
0.1771
0.0164
0.0339
0.0279
0.0291
0.0602
0.0144

Meth 1
0.9697
0.9680
0.9686
0.9649
0.9668
0.9672
0.9657
0.9687
0.9699
0.9698
0.9687
0.9690
0.9960
0.9924
0.9957
0.9629
0.9687
0.9655
0.9629
0.9671
0.9682
0.9678

Meth 2
0.9928
0.9881
0.9893
0.9830
0.9871
0.9876
0.9853
0.9901
0.9926
0.9926
0.9900
0.9907
0.9942
0.9970
0.9779
0.9742
0.9915
0.9846
0.9842
0.9880
0.9893
0.9913

Case 8
0.9910
0.9865
0.9876
0.9813
0.9855
0.9860
0.9837
0.9885
0.9910
0.9909
0.9884
0.9891
0.9960
0.9981
0.9814
0.9730
0.9905
0.9839
0.9833
0.9871
0.9884
0.9902

Table A9 (cont’d)
Case 9
Amp 1
Amp 2
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
Meth 1
Meth 2
Case 8
Case 9
Case 10
Case 11
Case 12
Case 13
MDA 1
MDA 2
Case 14
Case 15
Case 16
Case 17
Case 18
Case 19
Case 20

Case 10

Case 11

Case 12

Case 13

MDA 1

MDA 2

Case 14

Case 15

Case 16

Case 17

Case 18

1.0000
0.9983
0.9998
0.9997
0.9990
0.0131
0.0121
0.0115
0.0113
0.0117
0.0117
0.0114
0.0121
0.0134

1.0000
0.9990
0.9991
0.9996
0.0122
0.0105
0.0104
0.0103
0.0106
0.0107
0.0103
0.0110
0.0122

1.0000
1.0000
0.9995
0.0072
0.0060
0.0055
0.0054
0.0058
0.0058
0.0055
0.0062
0.0074

1.0000
0.9996
0.0072
0.0060
0.0055
0.0054
0.0058
0.0058
0.0055
0.0062
0.0074

1.0000
0.0087
0.0073
0.0069
0.0069
0.0072
0.0073
0.0070
0.0076
0.0088

1.0000
0.9972
0.9992
0.9996
0.9997
0.9997
0.9996
0.9992
0.9995

1.0000
0.9985
0.9967
0.9976
0.9971
0.9978
0.9981
0.9969

1.0000
0.9993
0.9995
0.9995
0.9996
0.9999
0.9993

1.0000
0.9999
1.0000
0.9998
0.9995
0.9999

1.0000
0.9999
0.9999
0.9996
0.9998

1.0000
0.9999
0.9996
0.9999

1.0000
0.9996
0.9998

217

Table A9 (cont’d)
MDMA 1
MDMA 2
Case 21
Case 22
Case 23
Case 24
Case 25
Case 26
Case 27
Case 28
Case 29
Case 30
Phent 1
Phent 2
Case 31
Psilocin 1
Psilocin 2
Case 32
Case 33
Case 34
Case 35
Case 36

Case 9
0.9923
0.9877
0.9888
0.9827
0.9867
0.9873
0.9850
0.9897
0.9921
0.9921
0.9896
0.9903
0.9951
0.9977
0.9797
0.9747
0.9913
0.9846
0.9842
0.9880
0.9894
0.9910

Case 10
0.9864
0.9831
0.9841
0.9789
0.9821
0.9825
0.9805
0.9846
0.9865
0.9865
0.9846
0.9851
0.9973
0.9978
0.9872
0.9721
0.9855
0.9801
0.9788
0.9828
0.9844
0.9850

Case 11
0.9908
0.9863
0.9874
0.9813
0.9853
0.9858
0.9836
0.9883
0.9907
0.9907
0.9882
0.9888
0.9962
0.9981
0.9819
0.9727
0.9901
0.9836
0.9830
0.9867
0.9881
0.9898

Case 12
0.9905
0.9862
0.9872
0.9812
0.9851
0.9857
0.9834
0.9881
0.9905
0.9904
0.9880
0.9886
0.9963
0.9981
0.9824
0.9727
0.9897
0.9832
0.9826
0.9863
0.9877
0.9894

Case 13
0.9881
0.9842
0.9852
0.9796
0.9832
0.9837
0.9816
0.9860
0.9881
0.9881
0.9859
0.9865
0.9972
0.9981
0.9856
0.9722
0.9874
0.9816
0.9806
0.9845
0.9857
0.9870

MDA 1
0.0261
0.0346
0.0305
0.0449
0.0348
0.0355
0.0389
0.0300
0.0231
0.0239
0.0304
0.0288
0.0054
0.0058
0.0323
0.1656
0.0130
0.0272
0.0231
0.0237
0.0556
0.0117

218

MDA 2
0.0217
0.0279
0.0240
0.0362
0.0272
0.0279
0.0305
0.0236
0.0183
0.0191
0.0239
0.0227
0.0040
0.0045
0.0297
0.1666
0.0123
0.0262
0.0224
0.0230
0.0552
0.0111

Case 14
0.0240
0.0322
0.0282
0.0424
0.0323
0.0330
0.0363
0.0275
0.0209
0.0217
0.0279
0.0264
0.0035
0.0039
0.0301
0.1656
0.0113
0.0255
0.0215
0.0221
0.0539
0.0100

Case 15
0.0246
0.0331
0.0290
0.0435
0.0336
0.0344
0.0378
0.0286
0.0217
0.0224
0.0290
0.0274
0.0036
0.0040
0.0303
0.1637
0.0113
0.0254
0.0214
0.0219
0.0537
0.0100

Case 16
0.0246
0.0329
0.0289
0.0431
0.0332
0.0339
0.0372
0.0284
0.0216
0.0224
0.0288
0.0272
0.0039
0.0043
0.0304
0.1646
0.0118
0.0260
0.0219
0.0225
0.0543
0.0105

Case 17
0.0248
0.0332
0.0292
0.0436
0.0336
0.0344
0.0378
0.0287
0.0218
0.0226
0.0291
0.0275
0.0040
0.0043
0.0307
0.1642
0.0115
0.0257
0.0216
0.0222
0.0540
0.0103

Case 18
0.0239
0.0319
0.0279
0.0420
0.0322
0.0329
0.0362
0.0274
0.0208
0.0216
0.0278
0.0263
0.0035
0.0039
0.0301
0.1643
0.0113
0.0255
0.0215
0.0221
0.0539
0.0101

Table A9 (cont’d)
Case 19
Amp 1
Amp 2
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
Meth 1
Meth 2
Case 8
Case 9
Case 10
Case 11
Case 12
Case 13
MDA 1
MDA 2
Case 14
Case 15
Case 16
Case 17
Case 18
Case 19
Case 20

Case 20

1.0000
0.9995

MDMA
1

MDMA
2

Case 21

Case 22

1.0000

219

Case 23

Case 24

Case 25

Case 26

Case 27

Case 28

Table A9 (cont’d)

MDMA 1
MDMA 2
Case 21
Case 22
Case 23
Case 24
Case 25
Case 26
Case 27
Case 28
Case 29
Case 30
Phent 1
Phent 2
Case 31
Psilocin 1
Psilocin 2
Case 32
Case 33
Case 34
Case 35
Case 36

Case 19
0.0248
0.0328
0.0288
0.0430
0.0331
0.0339
0.0372
0.0283
0.0217
0.0225
0.0287
0.0272
0.0042
0.0047
0.0306
0.1657
0.0122
0.0263
0.0223
0.0229
0.0547
0.0109

Case 20
0.0267
0.0347
0.0308
0.0450
0.0352
0.0361
0.0395
0.0303
0.0235
0.0244
0.0307
0.0292
0.0054
0.0059
0.0316
0.1662
0.0133
0.0273
0.0233
0.0239
0.0556
0.0120

MDMA
1
1.0000
0.9978
0.9986
0.9945
0.9977
0.9980
0.9967
0.9992
0.9999
0.9999
0.9991
0.9994
0.9787
0.9859
0.9544
0.9704
0.9927
0.9847
0.9850
0.9884
0.9905
0.9927

MDMA
2

Case 21

Case 22

Case 23

Case 24

Case 25

Case 26

Case 27

Case 28

1.0000
0.9998
0.9989
0.9996
0.9994
0.9991
0.9994
0.9982
0.9982
0.9995
0.9993
0.9743
0.9811
0.9531
0.9673
0.9868
0.9799
0.9795
0.9831
0.9854
0.9866

1.0000
0.9985
0.9997
0.9997
0.9993
0.9998
0.9989
0.9989
0.9999
0.9997
0.9755
0.9825
0.9536
0.9676
0.9881
0.9810
0.9807
0.9842
0.9864
0.9879

1.0000
0.9991
0.9987
0.9992
0.9977
0.9951
0.9951
0.9978
0.9973
0.9694
0.9759
0.9501
0.9647
0.9806
0.9748
0.9737
0.9774
0.9799
0.9803

1.0000
0.9999
0.9998
0.9995
0.9981
0.9981
0.9996
0.9993
0.9738
0.9806
0.9523
0.9654
0.9861
0.9792
0.9788
0.9823
0.9846
0.9859

1.0000
0.9998
0.9996
0.9983
0.9983
0.9997
0.9995
0.9743
0.9811
0.9526
0.9660
0.9865
0.9794
0.9791
0.9826
0.9849
0.9863

1.0000
0.9990
0.9971
0.9971
0.9991
0.9987
0.9721
0.9789
0.9512
0.9643
0.9839
0.9772
0.9767
0.9802
0.9824
0.9837

1.0000
0.9995
0.9994
1.0000
1.0000
0.9767
0.9837
0.9541
0.9674
0.9897
0.9822
0.9821
0.9855
0.9878
0.9896

1.0000
1.0000
0.9994
0.9996
0.9791
0.9863
0.9552
0.9688
0.9927
0.9847
0.9850
0.9883
0.9904
0.9927

1.0000
0.9994
0.9996
0.9790
0.9861
0.9550
0.9691
0.9926
0.9846
0.9849
0.9883
0.9904
0.9926

220

Table A9 (cont’d)
Case 29
MDMA 1
MDMA 2
Case 21
Case 22
Case 23
Case 24
Case 25
Case 26
Case 27
Case 28
Case 29
Case 30
Phent 1
Phent 2
Case 31
Psilocin 1
Psilocin 2
Case 32
Case 33
Case 34
Case 35
Case 36

Case 30

Phent 1

Phent 2

Case 31

Psilocin
1

Psilocin
2

Case 32

Case 33

Case 34

Case 35

Case 36

1.0000
1.0000
0.9765
0.9835
0.9540
0.9675
0.9894
0.9819
0.9818
0.9853
0.9875
0.9893

1.0000
0.9772
0.9842
0.9543
0.9680
0.9902
0.9827
0.9827
0.9861
0.9883
0.9902

1.0000
0.9988
0.9931
0.9625
0.9807
0.9751
0.9741
0.9778
0.9790
0.9801

1.0000
0.9873
0.9665
0.9874
0.9810
0.9804
0.9838
0.9853
0.9870

1.0000
0.9491
0.9566
0.9547
0.9516
0.9558
0.9569
0.9554

1.0000
0.9636
0.9608
0.9584
0.9640
0.9692
0.9631

1.0000
0.9967
0.9975
0.9981
0.9977
0.9999

1.0000
0.9992
0.9987
0.9958
0.9964

1.0000
0.9985
0.9963
0.9974

1.0000
0.9969
0.9979

1.0000
0.9976

1.0000

221

REFERENCES

222

REFERENCES
[1]

Devore JL. Probability and statistics for engineering and the sciences. Belmont, CA:
Duxbury Press, 1990.

[2]

Smith RM (2004) Understanding mass spectra: a basic approach. Hoboken, New Jersey:
John Wiley and Sons.

[3]

Crawford JD, Morrison JD (1968) Computer methods in analytical mass spectrometry
identification of an unknown compound in a catalog. Anal Chem 40: 1464-1469.

[4]

Forensic chemistry section quality manual (2009) Document DRG‐DOC‐01. Little Rock,
AR: Arkansas State Crime Laboratory.

223