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This is to certify that the

thesis entitled

A STUDY TO EXAMINE SHOTGUN PELLET
PATTERN OVERLAP BETWEEN TEST

FIRING DISTANCES AS A METHOD FOR

DETERMINING RANGE-OF-FIRE ESTIMATES

presented by

KENT ALDEN GARDNER

has been accepted towards fulfillment
of the requirements for

Master of Science degree in Criminal Justice

 

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Date 5 H 5

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U 9 ‘2;T~

M B. 7 1991

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A STUDY TO EXAMINE SHOTGUN PELLET
PATTERN OVERLAP BETWEEN TEST
FIRING DISTANCES AS A METHOD FOR

DETERMINING RANGE-OF-FIRE ESTIMATES

BY

Kent Alden Gardner

A THESIS
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

School of Criminal Justice

1987

ABSTRACT

A STUDY TO EXAMINE SHOTGUN PELLET
PATTERN OVERLAP BETWEEN TEST
FIRING DISTANCES AS A METHOD FOR
DETERMINING RANGE-OF-FIRE ESTIMATES

BY

Kent Alden Gardner

This study examined shotgun pellet pattern overlap
between test firing distances to determine how narrow
range-of—fire estimates could be made and analyzed the
effect of low barrel and low shell temperature on the spread
of pellet patterns.

A shotgun was fired through a series of 5 in-line
paper targets placed at 15, 20, 25, 30 and 35 feet. From
100 test firings .95, .96, and .97 confidence intervals
were calculated for the mean pattern diameter at each test
distance. The .95 and .96 confidence intervals did not
overlap between the adjacent 5 foot test distances.

Analysis of variance of the mean pellet pattern
diameter at each test distance for low barrel, low shell
and normal air temperature data groups showed a significant

effect on pattern size caused by low shell temperature.

Dedicated to my father, Charles Gardner

ACKNOWLEDGMENTS

The author would like to extend his sincere
gratitude to Dr. Jay Siegel of Michigan State University
for his guidance, as well as both professional expertise
and personal interest he has shown in this project and
throughout my tenure at Michigan State University.

Sincere appreciation is extended to Professor Frank
Horvath of Michigan State University for his expertise he
graciously gave in developing the statistical methods of
analysis in this research.

Appreciation is extended to professor Ralph Turner
Emeritus of Michigan State University who inspired this
research and for his guidance in this project.

Appreciation is also extended to Dr. Gene Packwood,
Head of Research at Delta College for his assistance with
statistical methods used in this research.

A special thanks to Susan Kline for her help and
support throughout the research and preparation of this

study.

ii

TABLE OF CONTENTS

LIST OF TABLES O O O C O O O I O O O 0

LIST OF FIGURES . . . . . . . . . . . .

Chapter
1. INTRODUCTION . . . . . . . . . .
2. REVIEW OF LITERATURE . . . . . .
3. RESEARCH DESIGN AND PROCEDURES .

COLLECTION OF DATA . . . . . .
DATA MANIPULATION . . . . . .

4. ANALYSIS OF THE DATA . . . . . .
5. DISCUSSION . . . . . . . . . . .
6. SUMMARY . . . . . . . . . . . . .
FOOTNOTES . . . . . . . . . . . . . . .

LITERATURE CITED. . . . . . . . . . . .

iii

Page

iv

12

12
16

20
30
37
39

41

LIST OF TABLES

Pattern sizes: Firings with and without
intervening paper target. . . . . . . . .

.95 confidence intervals for mean pattern
diameter at each test distance . . . . .

.96 confidence intervals for mean pattern
diameter at each test distance . . . . .

.97 confidence intervals for mean pattern
diameter at each test distance . . . . .

Test distance pellet pattern means
for each temperature group . . . . . . .

Confidence intervals for test data . . .

iv

Page

21

25

26

27

28

34

LIST OF FIGURES

Figure Page
1. In—Line Target Support Structure . . . . . . . . l3
2. Firearm Support Structure . . . . . . . . . . . . 15

3. Circle on Clear Plastic Overlay Positioned
Over Pellet Pattern . . . . . . . . . . . . . . . l7

4. Approximate Sampling Distribution of
Difference Between 2 Means Showing
the Critical Region R and Test
Statistic t . . . . . . . . . . . . . . . . . . . 22

5. Standard deviation bars for the
means of each test firing distance . . . . . . . 23

6. Pellet pattern frequency distributions
for each test distance . . . . . . . . . . . . . 32

CHAPTER 1

INTRODUCTION

The purpose of this research was to develop a
method for determining the degree of shotgun pellet pattern
overlap between test firing distances for range-of—fire
estimation. The variable nature of shotgun pellet
dispersion can result in the same size pellet pattern
appearing at different test firing distances. Determining
the degree that pellet patterns at one test distance
overlap at other test distances will indicate how narrow a
range-of-fire estimate can be determined. This study
examined the amount of pellet pattern overlap between
targets placed at 5 foot test distance intervals. Also of
concern is the effect temperature of the barrel and of the
ammunition has on the spread pellet patterns. To test this
effect two groups of test firings, one with a low barrel
temperature and the other with a low shell temperature,
were compared to a group where temperatures were not
controlled.

This research was inspired by conflicting testimony

I The main issue at that

given in an inquest hearing.
inquest was whether either of two shotguns had been
discharged at a distance greater or less than 30 feet from a

wall inside a house. The wall supported two shotgun

pellet patterns allegedly caused by pellets originating from
the shotguns.

The defense expert witness conducted testing which
led him to the conclusion that the shotguns were fired at a
distance of approximately 25 feet, but less than 30 feet.
The prosecution's expert witness also tested the shotguns
and formed an opinion that the weapons were discharged at a
distance greater than 30 feet but less than 35 feet.

Both experts used the same distance determination
method, one currently practiced by firearms examiners.
Their conclusions were based on a method of visually
comparing the evidence pattern to a few test patterns fired
at each of several test distances. However, the test
patterns of the defense expert were larger than those of
the prosecution, which gave rise to the different
opinions. The only notable difference in the testing was
that the prosecution's testing was conducted with ambient
temperature near 50 degrees F and the defense testing was
done with temperature near 70 degrees F.

Currently, firearms examiners determine the
distance a particular shotgun was fired by visually
comparing the size of an evidence pellet pattern to the
size of test patterns. A test pattern is made by shooting
the firearm at a target placed at a measured distance.
Different test distances are selected and the firearm is
fired at targets placed at those distances. Normally, only

3 or 4 targets are fired at each selected test distance.

The test distance with targets who's pellet patterns are
closest in size to the evidence pattern indicate the
approximate distance-of—fire.

The testing is done with the same weapon and with
shells from the same box of ammunition that produced the
evidence pattern. If the same box of ammunition is not
available from the crime scene then it is substituted with
the same brand and shell components.2

Shotgun pellet patterns vary in size from one
firing to the next. This variable nature results in
patterns of the same size at different test distances.
Consequently, any one test distance cannot be selected as a
distance-of—fire without the possibility of excluding
another test distance with the same pattern size. To avoid
this error, distance determinations are presented as an
estimated range-of—fire with upper and lower boundaries. The
upper boundary is determined by selecting a test distance
with pellet patterns larger in size from that of the
evidence pattern. The lower boundary is selected from a
test distance with pellet patterns smaller than the evidence
pattern. The difference in size of the patterns selected is
determined by the examiner's experience and his observations
in testing.

Previous papers appearing in the forensic science
literature have discussed the application of regression
analysis to the distance estimation problem. The

statistical methods for obtaining range-of-fire estimates

and confidence intervals for those estimates were reported
and tested as an objective approach. This study was
conducted to shed more light on the variable nature of
shotgun pellet dispersion data and the application of those

methods.

CHAPTER 2
REVIEW OF LITERATURE

A review of the current forensic science literature
reporting methods of shotgun distance-of—fire determination
revealed four studies on statistical analysis of pellet
dispersion data and two indirectly related articles.

In 1972 M. Jauhari, M. Chatterjee and P. K. Gosh of
the Central Forensic Science Laboratory, Calcutta, India
showed the use of in-line targets which had the effect of
increasing the amount of data gained per test firing and
presented two methods for estimating distance-of—fire.3
Their study investigated the feasibility of shooting
through several paper targets with one firing. To obtain
test data for statistical analysis a .410 shotgun was fired
10 times through a series of 0.013 cm thick paper targets
placed at 6, 9, 15, and 18 feet. To obtain questioned
pellet patterns for a blind comparison the test shotgun was
fired twice at 3.05 m with the same ammunition as the 10
data test firings. Another questioned pellet pattern was
fired at 2.13 m with ammunition from a different lot
number. This was done to test predictions of a
distance-of—fire with different ammunition than was used at

the crime scene.

Two methods were discussed for estimating

range-of-fire, the distribution-free method and regression
analysis. The distribution-free method is applied
when it is not possible to assume a normal distribution of
the population consisting of the size of pellet patterns at
different test distances for the case at hand. This
situation is present when the same weapon or the same type
of ammunition as used in the crime is not ‘available for
testing. A normal distribution is assumed when the same
gun and type of ammunition are available. Distribution free
range-of-fire estimates are determined by using the largest
and the smallest pattern diameters of each test distance.
The lower end of an estimated interval is obtained from a
linear interpolation between the two smallest adjacent test
distance patterns. The upper end ofthe estimated interval
is obtained from interpolation between the two largest
adjacent test distance patterns.

Regression analysis was applied to the test data to
calculate confidence intervals for range-of-fire estimates.
The confidence intervals were calculated by multiplying the
standard deviation by a numerical factor obtained from a
table of specified proportions of samples of the population
of test firings. When using .95 and higher confidence
levels the confidence intervals may be wide spread, which
may not be of practical interest. Specifying a proportion
of the sampled population results in a narrower
range—of-fire confidence interval without reducing the

percent of the population sampled.

The results of their study showed that the target

material did not significantly alter the pellet pattern at

the .05 level of significance. The calculated distribution
free range-of—fire limits contained the actual
distance-of—fire for both types of ammunition. Regression

range-of—fire confidence limits calculated for 75, 90, 95,
and 99 percent of the sampled population were found to
contain the actual distance-of-fire.

A report in 1975 by David Brundage adopted the use
of in-line targets to reduce the number of test firings

4 Several test

necessary for distance determinations.
targets were set up, one behind the other, at specific
distances so that one shot fired through the targets would
produce several patterns that could be compared to the
evidence pattern. If different pattern diameters are
required more targets can be made by moving the firearm
closer or further away from the targets. However, no data
obtained by this method was presented.

In 1979 Steve Molnar and Thomas Nicholson conducted
a study indirectly related to firearm distance testing.5
Their study showed that 00 buck pellets tend to hold a
pattern grouping in flight. The pellets formed a
triangular arrangement forming single and double holes in
test targets. However, no information was presented to
show how consistent the pattern formation was or it's value

in distance determinations.

In 1983 Kathleen Heaney and Walter Rowe of The

George Washington University, Washington, D.C. demonstrated
how the number of test firings affects the width of

6 In their

confidence interval range-of-fire estimates.
study a shotgun was fired three times at targets
placed at 10, 30 and 50 feet. Then the gun was fired five
times at targets placed at 10, 20, 30, 40 and 50 feet. The
gun was also fired nine times at 10, 20, 30, 40 and 50 foot
targets. The pellet patterns were measured by the square
root of the area of the smallest rectangle that would
enclose the patterns and also by the radius of the smallest
circle that would enclose the patterns. Data obtained by
both the square root of the area of a rectangle and radius
of a circle measurements were used to determine .95
confidence intervals for the 3, 5 and 9 test firings. The 3
test firings resulted in confidence interval widths of 23.5
ft. for the radius of a circle measurement and 49.9 ft. for
the square root of the area of a rectangle measurement. The
5 test firings resulted in confidence interval width of 5.9
ft. for both measurements and the 9 test firings resulted in
confidence interval widths of 3.5 and 3.0 ft., respectively.

It was determined that increasing the number of
test shots from three to five resulted in a dramatic
decrease in the width of the confidence interval. They
reported no significant difference in the confidence
interval widths by using either method of pattern
measurement. Correlation coefficients greater than .99 were

reported in each test set indicating a linear relationship

between pattern spread and distance of fire.

In 1984 Alessandro Alfonsi, Sandro Calatri, Emidio
Cerione and Piero Luchi at the University of Cagliari,
Cagliari, Italy, studied the use of partial pellet patterns
to determine distance-of-fire and the effects of barrel
choke on pellet pattern dispersion.7 Ten shots were
fired with a full choke shotgun, ten through a half choke
and ten through a cylindrical barrel gun. Five of the ten
firings were with 00 buck shells and five firings were with
0 buck shells. Test distances of 5, 10, 15, 20, 30 and 40
m were selected. The pellet patterns were measured by the
sum of the distance between one pellet hole and all of the
remaining holes, and also by pattern diameter. The
standard deviation, standard error, r value and a
regression line were determined for each group of five test
patterns.

Analysis of the data showed a high standard
deviation for the mean values of the total distance between
pellet holes and a small standard deviation for the mean
values of the pattern diameters. Plotted regression lines
for the cylindrical barrel gun were significantly separated
from the plots of the nearly superimposed regression lines
for the full and half choke barrels, using both types of
ammunition. Each group tested had a correlation coefficient
of .99 or higher relative to the dispersion of points
pertaining to each regression line.

They concluded that you could not determine

10

distance-of-fire with a partial pellet pattern and that
lack of knowledge about the type of barrel choke can lead
to completely wrong estimates on distance-of-fire.

In 1985, W. F. Rowe and S. R. Hanson of the George
Washington University tested range-of-fire estimates derived

by regression analysis.8

A blind study was conducted with
10 questioned pellet patterns. Five of the patterns were
fired from a 12 gauge Stevens model 77E full choke shotgun.
The other five questioned patterns were fired from a 12
gauge Remington model 870 cylinder bore shotgun.

Test data was obtained by firing six shots from
each gun at distances of 10, 20, 30, 40 and 50 feet. The

resulting pellet patterns were measured by calculating the

area of the smallest rectangle that would enclose the

pattern. The data was analyzed by three methods for
determining distance-of—fire. Confidence intervals were
determined by weighted linear regression. Then both

regression confidence intervals calculated by a factor
based on a proportion of the sampled population and the
distribution-free method was used, as proposed by Jauhari
et a1.

Regression analysis of the data was done with
weighted regression confidence intervals. The standard
deviation at each test distance was found to increase with
range, so a weighted standard error was determined for
computation of the confidence interval range-of—fire

estimates. They reported that with regression analysis,

11

.99 confidence intervals calculated from the test data
contained the actual distance-of-fire for each of the ten
questioned pellet patterns. They found regression analysis
to be a viable method for estimating range-of-fire.
However, they found the last two methods deficient. With
regression confidence intervals calculated with a numerical
factor based on a proportion of the population, the upper
confidence limits could not be calculated for any of the
questioned patterns. The distribution-free method was
applied to the same test data. The confidence limits
contained the actual distance-of—fire for nine of the ten
questioned patterns. However, one of the five questioned
patterns, fired form the Remington gun at 14 feet, was not

contained in it's confidence limit of 10.5 to 12.1 feet.

CHAPTER 3

RESEARCH DESIGN AND PROCEDURES

Collection of data

 

A method was applied in this study which increased
the amount of pellet dispersion data with each test firing.
A series of five paper targets were placed, one after
another, at distances of 15, 20, 25, 30 and 35 feet. The
firearm was test fired 100 times creating 100 targets at
each test distance. A 5 foot interval distance between the
targets was used since this was the range in distance which
was involved in the inquest hearing which inspired this
research and also resulted in an obvious measurable
difference in pellet pattern size from one target distance
to the next.

The target material used was brown wrapping paper
measuring .007 inch thickness. Each target was supported
by a coat hanger which was formed into a circle leaving the
top hook to support the target. The target was centered on
the formed wire circle and was attached to the wire by
several pieces of masking tape on the back side of the
paper. The targets were supported along the span of a 20
foot wooden pole (Figure 1). The narrow side of the plank
was positioned upward to allow the hook end of the hanger

to rest on top of the plank at each test distance.

12

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The firearm used for the test firing was a 12 gauge

Remington, model 870 pump-action shotgun, cylinder bore
measuring .729 inch. The barrel measured 22 inches in
length.

The ammunition used was 12 gauge Winchester-Western,
00 buck, 2 3/4 inch, equivalent to 3 3/4 drams of black
powder. Each shell contained 9 lead pellets, each
measuring approximately .33 inch diameter, approximately 51
grains weight. All shells used in the testing were
produced in the same production run, lot number (AlOlSCS).

The test shotgun was held stationary in a fixture
while it was fired at the in-line targets (Figure 2). The
muzzle of the gun could be moved up and down for target
elevation alignment. Windage alignment was facilitated by
moving the front of the support structure from side to
side. The gun support could be adjusted forward or moved
back along a support rail to vary the muzzle to target
distance. After positioning the shotgun in the support
structure the gun was sighted with the last target at the
35 foot distance. The gun was first test fired at a single
target at the 35 foot distance to ensure proper alignment
and to raise the barrel temperature up to the approximate
temperature at which a particular series of tests would be
conducted. The barrel of the gun was cleaned after each
test firing.

To determine the effect of temperature on pellet

dispersion, 20 shots were fired with a mean barrel

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16

temperature of 0 degrees F, i5 degrees and a mean shell
temperature of 71 degrees F, $17 degrees. Another 20 tests
were fired with a shell temperature of +5 degrees F, and a
mean gun barrel temperature of 87 degrees F, i7 degrees.

The low gun barrel temperatures were achieved by
placing liquid nitrogen into the barrel. Temperatures were
measured by a calibrated secondary nitrogen-above-mercury
thermometer, Fahrenheit scale ranging from -5 degrees to
+125 degrees, in 1 mm increments. The thermometer was
suspended midway into the gun barrel prior to each firing
with the breech closed. The lowered shell temperatures
were measured by the same type of thermometer on a Celsius
scale ranging from -20 degrees to +110 degrees, in 1 mm
increments. The bulb end was suspended in air in the
freezer in which the shell temperature was lowered.

Each test pellet pattern was measured by the
diameter of a circle drawn on a clear plastic overlay
(Figure 3). The pattern diameter measurements were
determined within .25 inch intervals. This level of
discrimination was selected because of the size of the
pellet hole. Measuring with .25 inch increments proved to
be the most accurate in determining pattern diameters. A
particular pellet pattern diameter would be determined by
fitting all nine pellet holes within the closest fitting
overlay circle.

Data manipulation

 

Tests were conducted to determine whether the

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target paper had any significant affect on pellet
dispersion. Ten separate targets were fired at the 35 foot
distance and compared statistically to 10 randomly selected
targets from the total 100 targets at the 35 foot test
distance. A t-test was applied to the means of each group
to determine any significant difference.

To show the variability of the test data pellet
patterns the standard deviation of the pellet patterns at
each test distance was examined.

The data obtained from this research was examined
to determine the degree of pellet pattern size overlap from
one test distance to the next. Confidence intervals were
calculated at .95, .90, .80, .70 and .65 confidence levels
for the mean pellet pattern diameters of targets at the 5
test distances. The amount that each confidence interval
extended in the next adjacent test distance confidence
interval was examined.

To determine if temperature affects pellet pattern
dispersion the mean pattern diameters, at each test
distance, of the 20 low barrel patterns and the mean
pattern diameter of the 20 low shell patterns were compared
to the mean pattern diameter of the remaining 60 ambient
(normal) air temperature group patterns. Analysis of
variance (MANOVA) was applied to the means of each test
distance, for the three temperature groups, to determine
any significant difference between the temperature group

means. A l-way post hoc analysis (ANOVA) using the Scheffe

19

technique was used to uncover the separate effects of the

low temperature groups.

CHAPTER 4

ANALYSIS OF THE DATA

The primary calculations for the statistical
analysis of the research data were performed by computer
using the Statistical Package for the Social Sciences
program (SPSS). Subsequent calculations for confidence
intervals, using the data coefficients obtained by
computer, and the target material t-test were done by hand.

Testing was done to determine if the target paper
had a significant affect on pellet dispersion using in-line
targets. A t-test was applied to the means of 10 randomly
selected test targets from the 35 foot distance and 10
targets fired without intervening targets (Table 1). A
.05 level of significance was chosen and 18 degrees of
freedom were applied to a t-curve probability table. A
value of 2.10 was obtained from the table establishing the
critical region r (Figure 4). A t value of 1.42 was
derived by formula from the test data. The test
statistic t value of 1.42 is less than the critical region
value of 2.10 and falls within the acceptable range on the
t scale. Thus the difference between the two means is
insignificant at the .05 level.

Figure 5 shows the standard deviation of the pellet

pattern diameters about the mean of each test firing

20

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distance. The most any test pattern deviates from the
means is .846 inches.

The data obtained by this research was examined to
determine the amount of pellet pattern overlap between 5
foot interval test firing distances. Tables 2 through 4
show .95, .96 and .97 confidence intervals for the mean
pellet pattern diameter at each test firing distance}0
The amount of interval overlap between adjacent test
distances is shown as a positive number and the separation
between adjacent test distance confidence intervals, which
do not overlap, is shown as a negative number in the 4th
column. All of the .95 and .96 confidence intervals did
not overlap between adjacent test distances. The .97
confidence intervals overlapped between 15 and 20, 20 and
25, foot test distances, however, they did not overlap
between 25 and 30, 30 and 35 foot test distances. None of
the confidence intervals overlapped into more than one test
distance.

To determine if temperature affects pellet pattern
dispersion the means of a low barrel temperature group, low
shell temperature group and a normal temperature group were
compared by analysis of variance (MANOVA). Table 5 shows
the pellet pattern means at each test distance for the low
barrel, low shell and normal temperature groups. The
MANOVA revealed a significant difference between the means

of each group at the .05 level of significance. To

determine which test distance means were affected by

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temperature an (ANOVA) was performed on the means which
revealed that temperature had a significant effect at each
test distance, except at the 35 foot test distance. To
uncover the separate effects of low barrel and low shell
temperature, the means at each test distance for each
temperature group were compared independently by a l-way
post hoc analysis of variance using the Scheffe technique.
The results of the Scheffe technique revealed that the
means of the low shell temperature group were significantly
different from the means of the normal temperature group at
the .05 level of significance. The means of the low barrel
temperature group showed no significant difference from the

means of the normal temperature group at the .05 level.

CHAPTER 5
DISCUSSION

At the beginning two problems were introduced,
namely, to develop a method for determining the amount of
shotgun pellet pattern overlap between test firing
distances and to examine the affect temperature has on the
spread of pellet patterns.

The data for this study was obtained by firing
through a series of paper targets placed, one after
another, at equally spaced test distances. The in-line
target arrangement was used to increase the amount of test
data for each test firing. The useof in-line targets can
create a larger amount of test data with limited time and
ammunition. However, the affect of the intervening targets
on pellet pattern dispersion has to be examined. This was
done by shooting 10 targets without any intervening screens
at the furthest test distance and statistically comparing
them to 10 targets from the test data randomly selected at
the furthest test distance. A t-test was applied to the
mean pellet patterns of each group to see if the difference
in pellet dispersion, caused by the intervening targets, is
statistically significant. The results of the t-test
showed no significant difference between the mean pellet

patterns of the two groups at the .05 level of

30

31

significance.

A method was presented for determining the extent
of pattern overlap at adjacent test distances. Pellet
pattern dispersion varies from one firing to the next and
multiple test firings result in pattern size variance at
each test distance. The variance can result in an overlap
of pattern size in adjacent test distances, depending on
the extent of pattern variability and the spacing between
the targets. The extent of pattern overlap at adjacent
test distances shows how narrow a range—of—fire estimate
can be made. If confidence intervals, calculated for the
means of the pattern diameters at each test distance, do
not extend into adjacent test distances, then a
range-of-fire estimate equal to the interval between the
test distance will determine how narrow range-of—fire
estimates can be made. The selected confidence level
reflects the probability that pellet patterns, excluded from
the confidence intervals, are duplicated at adjacent test
distances.

Figure 6 shows frequency distributions for the
pattern diameters at each test distance. The overlapping
of the boundaries of the distributions shows graphically
the total extent of pattern overlap at the 5 foot test
distances. It can be observed that pattern diameters of
7.25, 7.5 and 7.75 were duplicated at the 25, 30 and 35
foot test distances.

To determine the point where pattern overlap can be

32

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eliminated between the test distances, confidence intervals
were calculated at .95, .96 and .97 confidence levels for
the mean pellet pattern diameters at each test distance.
As shown in Tables 2 & 3, .95 and .96 confidence intervals
did not overlap between each test distance. Increasing the
confidence level to 97 percent, as shown in Table 4
resulted in overlap between the 15 and 20, 25 and 30 foot
test distances. The standard deviation of all the pellet
patterns was used to calculate the confidence intervals.
Since one test firing produced targets at each test
distance, the deviation of the pellet patterns at each of
those test distances are necessarily related.

The results obtained by examining pattern overlap
between the 5 foot test distances, were compared to another
method for determining range-of—fire as outlined by Heaney
and Rowe.ll The Heaney and Rowe method determines
range-of-fire by calculating confidence intervals from
coefficients derived from all the test data. Table 6 shows
.95, .90, .80, .75, .70 and .65 confidence intervals
calculated from coefficients obtained from the 500 test
targets from this study, as shown in Table 6, a .75
confidence level width. In comparison to the results of this
study, as shown in Table 2, a .95 confidence level resulted
in no pellet pattern overlap at the 5 foot test distances.
A .96 confidence level was the highest confidence level
which eliminated the overlap. Selecting a .95 confidence

level with the Heaney and Rowe method results in a

34

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range-of-fire width of 8.48 feet.

The effect of temperature on the size of pellet
pattern dispersion was examined by comparing the test
pattern means of a low barrel temperature group and a low
shell temperature group to the pattern means of a normal
temperature group. The l-way post hoc analysis of variance
using the Scheffe technique revealed that low shell
temperature had a significant affect, at the .05 level, on
the means at each test distance, except at 35 ft. The low
barrel temperature had no significant affect. In Table 5
the means of the low shell temperature group are smaller,
for each test distance, than the means of the low barrel
and normal temperature groups. It is hypothesized that the
low shell temperature caused incomplete burning of the
propellent powder resulting in a smaller pattern size
resulting in a smaller mean at each test distance. At the
35 foot test distance it is suspected that the pattern
variance is so great that the difference in means is less
significant. The variance of the pellet pattern at each
test distance can be observed in Figure 5.

In light of the results of this research it is
suspected that the reason for the different range-of-fire
estimates arrived at in the case which inspire this study
was due, in part, to the method used. With that method
selection of a range-of—fire is a result of the examiners
observations in testing and his experience. A more

objective approach is the statistical treatment of test data

36

for range-of—fire estimation based on the variability
experienced in testing. In this study the overlap of pellet
pattern confidence intervals showed the variability
experienced in the testing to arrive at a range-of—fire
based on the target distance interval. If the data from
the inquest hearing testing had been subjected to this type
of statistical approach, subjective interpretations in
analyzing the data would have been minimized and the
estimated range-of-fire would have reflected the variable
nature of shotgun pellet dispersion in a more objective
approach. Also, analysis of the data supports temperature
as a factor which should be looked at in collecting data
for range-of—fire estimates. The inquest hearing data was
collected at two different temperatures which may have had

a significant affect on the results.

CHAPTER 6

SUMMARY

This study examined a method for determining shotgun
pellet pattern overlap and analyzed the effect of low
barrel and low shell temperature on the spread of pellet
patterns.

The data was obtained by shooting through a series
of in-line targets to increase the amount of data. Tests
were done to determine if the target paper altered the
pellet patterns. A t-test on the mean of a sample data
group and a control group, both at the furthest target
distance, showed no significant difference at the .05
level.

It was shown that the distance between test
targets, where pellet pattern overlap does not occur,
determines how narrow range-of-fire estimates can be made.
To determine the amount of pellet pattern overlap,
confidence intervals were calculated at the .95, .96 and
.97 confidence levels for the mean pellet pattern at each
test distance. The .95 and .96 confidence intervals did
not overlap between adjacent test distances. Two of the
.97 confidence intervals did not overlap between each test
distance.

The results of this method were compared to a

37

38

method outlined by Heaney and Rowe. Using their method
range-of-fire confidence intervals were calculated from the
test data at .95, .90, .80, .75, .70 and .65 confidence
levels. The .75 confidence interval resulted in a 5 foot
range-of—fire. The .95 confidence interval produced a 8.48
foot range—of—fire.

The affects of low barrel and low shell temperature
on pellet pattern dispersion were compared to a normal
temperature group. An analysis of variance determined a
significant difference between the means of the low shell
temperature group and the normal temperature group, except
at the furthest test distance. The low barrel temperature
group means were not significantly different from the means

of the normal temperature group.

10.

LIST OF FOOTNOTES

Inquest hearing, James Osterman, Michael Ellicott and
Oliver B. Moorer, Saginaw County Circuit Ct. 81CR2403
(1981).

Julian J. Hatcher, Frank J. Jury, Jac Weller, Firearms
Investigation, Identification and Evidence
(Pennsylvania: The Stackpole Co., 1977), 338.

 

M. Jauhari, S.M. Chatterjee and P.K. Gosh, "Statistical
Treatment of Pellet Dispersion Data for Estimating
Range-of-Firing," Journal of Forensic Sciences, Vol.
17, No. 1, (Jan., 1972), 141-1495.

 

David J. Brundage, "Range Determination for Shotguns,"
Association of Firearms and Tool Mark Examiners
Journal, Vol. 7,4TDec., 1975), 66-68.

 

Steve Molnar and Thomas V. Nicholson, "Shot Pattern
Phenomena With 00 Buck," Association of Firearms and
Tool Mark Examiners Journal, Vol. 9, (July, 1979),
132-133.

 

 

Kathleen D. Heaney and Walter F. Rowe, "The Application
of Linear Regression to Range-of-Fire Estimates Based
on the Spread of Shotgun Pellet Patterns," Journal of
Forensic Sciences, Vol. 28, No. 2, (April, 1983), 434.

 

 

Alessandro Alfonsi, Sandro Calatri, Emidio Cerioni and
Piero Luchi, "Shooting Distance Estimation for Shots
Fired by a Shotgun Loaded with Buckshot Cartridges,"
Forensic Science International, Vol. 25, (June, 1984),
83-91.

 

W.F. Rowe and S.R. Hanson, "Range-of—Fire Estimates
From Regression Analysis Applied to the Spread of
Shotgun Pellet Patterns: Results of Blind Study,"
Forensic Science International, Vol. 28, No. 3, 4,

 

(Aug., 1985), 240.

Paul J. Blommers and Robert A. Forsyth, Elementary
Statistical Methods in Psychology and Education

 

 

(Boston: Houghton Mifflin Co., 1977), 347.

Blommers and Forsyth, Elementary Statistical Methods,
324.

 

39

40

ll. Heaney and Rowe, Application of Linear Regression, 435.

LIST OF REFERENCES

LI ST OF REFERENCES

Alfonsi, Alessandro "Shooting Distance Estimation for
Shots Fired by a Shotgun Loaded With Buckshot
Cartridges." Journal of Forensic Sciences, Vol. 28, No.
2, (April, 1983).

 

Blommers, Paul J., and Forsyth, Robert A. Elementary
Statistical Methods in Psychology and EducatiOn.
Boston: Houghton Mifflin Co., 1977.

 

 

Brundage, David J., "Range Determination for Shotguns."
Association of Firearms and Tool Mark Examiners Journal,

 

V01. 7, (DeC., 1975), 66-68.

"Gunshot, Residue and Shot Pattern Tests." F.B.I. Law
Enforcement Bulletin, (Sept., 1970, revised Feb., 1979),
5.

 

 

Hatcher, Julian J., Jury, Frank J., Weller, Jac.
Firearms Investigation, Identification and Evidence.
Pennsylvania: The Stackpole Co., 1977.

 

Heaney, Kathleen D., and Rowe; Walter F. "The
Application of Linear Regression to Range-of-Fire
Estimates Based on the Spread of Shotgun Pellet
Patterns," Journal of Forensic Sciences, Vol. 28, No.
1, Jan., 1972), 141-149.

 

Jauhari, M., Chatterjee, S.M. and Gosh, P.K.
"Statistical Treatment of Pellet Dispersion Data for
Estimating Range of Firing," Journal of Forensic
Sciences, Vol. 28, No. 2, (April, 1983), 433-436.

 

Molnar, Steve, and Nicholson, Thomas V. "Shot Pattern
Phenomena With 00 Buck," Association of Firearms and
Tool Mark Examiners Journal, Vol. 9, (July, 1979),
132-133.

 

 

Rowe, W.F., and Hanson, S.R. "Range-of-Fire Estimates
from Regression Analysis Applied to the Spread of
Shotgun Pellet Patterns: Results of Blind Study,"
Forensic Science International, Vol. 28, No. 3, 4,
(Aug., 1985) 239-250.

 

41

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