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This is to certify that the
thesis entitled
Differences Between Learning Disabled and

Low Achieving Students
on Standardized Test Performance

presented by

William W. Wiseman

has been accepted towards fulfillment
of the requirements for

 

 

 

Ph_D' degree in Special Education
Que/a.
Major professor
‘Zy/b-94

 

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MSU is an Affirmative Action/Equal Opportunity Institution

 

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RETURNING MATERIQL§:
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LJBRARJES remove this checkout from
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be charged if book is
returned after the date
stamped below.
”Weft“:

 

 

DIFFERENCES BETWEEN LEARNING DISABLED AND LOW ACHIEVING

STUDENTS 0N STANDARD TEST PERFORMANCE

By

William W. Wiseman

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Counseling. Educational Psychology,
and Special Education

1984

ABSTRACT
DIFFERENCES BETWEEN LEARNING DISABLED AND Low ACHIEVING
STUDENTS 0N STANDARDIzED TEST PERFORMANCE
By

William W. Wiseman

The ability and achievement test performance of 404 students
selected from a sample of l.552 students from 45 school districts
throughout Michigan was analyzed to determine if methods proposed in
the literature could assist in formulating useful decision-making rules
for classification purposes. Two hundred thirty students classified as
learning disabled were compared with l74 low achieving students
selected on the basis of their achievement scores on a test of word
recognition. The methods investigated in this study for diagnostic-
utility purposes have been proposed in the literature as criteria for
differentiating between handicapped (learning disabled) and
nonhandicapped students. Methods of z—score discrepancy levels.
ability-test subtest scatter. verbal-performance ability differences.
and general ability and achievement Characteristics have been proposed
as differentiating between classifications. Previous studies comparing
learning disabled with low achieving students have been limited in
sample size and have suffered from inadequate controls.

In the present study. the question of diagnostic utility was of

primary concern. Any method used to compare students that failed to

 

William W. Wiseman

differentiate at an 85% success rate was rejected as not useful. None
of the methods investigated met this criterion for diagnostic utility
and useful decision-making rules. 'The methods used to calculate
discrepancy levels and ability-test subtest scatter indicated
statistically significant differences at the .05 level of confidence.
However. these methods were found not to be useful for practical
diagnostic purposes in differentiating between learning disabled and
low achieving students. Conclusions and recommendations were discussed
in terms of public policy. clinical practice. directions for

educational research. and limitations of the study.

ACKNOWLEDGMENTS

Each of the members of my guidance committee has contributed from
his separate area of expertise to the completion of this work. I
greatly appreciate their efforts.

Harvey Clarizio. my dissertation chairman. has for a long time
been able to understand my strengths and weaknesses and appeared
always. at the right moment. to provide direction. criticism. and
encouragement. His patience and expertise in the completion of this
research are without equal.

Donald Melcer. in his objective and direct communication style.
has assisted me with editorial comments and always responded to ques-
tions with direct and practical answers.

Lawrence Lezotte is appreciated for his efforts in helping me
understand statistical aspects of this research and practical
applications.

Eugene Pernell served as my program advisor and with openness and
sincerity affected my completion of program requirements.

Two very special people are my daughter and my wife. My daughter.
Lydia Wiseman. has been patient and understanding when circumstances
dictated efforts on this work. Her interest. enthusiasm. and
excitement have made it worthwhile. More than anyone else. my wife.

Judith Wiseman. has made this work possible. Her positive attitude.

support. love. and understanding are always present. Her questions.
support. assistance. and belief in my abilities have enabled me to

finish this work and. more important. affect all areas of my life.

TABLE OF CONTENTS

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

Chapter
1 0 INTRODUCTION 0 O O O O O O O O O O O O O O O O O 0

Classification of Students . . . . . . . . . . .
Identification of the Handicapped .
Defining the Learning Disabled . . .
Theoretical Basis for Diagnosis .
Magnitude of the Problem . . . . . .
Synopsis of the Present Investigation

2 O L ITERATURE REV I E" O O O O O O O O O O C O O O O 0

Overview . . . . . . . . . . . . . . . . . . . .
Similarities and Differences Between Populations
Characteristics of the Learning Disabled . . . .
General Ability and Achievement Characteristics
Operationalizing the Discrepancy Model . . . . .
Discrepancy-Model Effectiveness . . . . . . .
Discrepancy-Model Reliability . . . . . . . .
Comparisons of Verbal-Performance Ability
Differences . . . . . . . . . . . . . . .
Comparisons of Ability-Test Subtest Scatter
Direction of the Present Study . . . . . . .
Limitations in the Literature . . . . . .
Contributions of the Present Study . . . .

3 0 METHOD I O O O O O O O O O C O O O O O O O O O O O

Source of Data . . . . . . .
The Sample . . . . . . . . .
Procedures . . . . . . . . .
Dependent Variables . . . .
The Utility of Diagnostic Decisio Rules
Statistical Treatment . . . . . . . . .
Hypotheses . . . . . . . . . . . . . . . .

n

Page
vi

viii

u—nl

mOhNN-J

ll

ll
ll
l3
l5
19
22
23

27
29
3T
32
34

36

36
37
38
40
4T
42
43

4. RESULTS 0 O O O O O O O O O O O O O O O C O O 0

Overview . . . . . . . . . . . . . . . . . . .

Comparisons of Ability and Achievement Test
Performance . . . . . . . . . . . . . . . .
Ability Test Performance Comparisons . . . .

Achievement Test Performance Comparisons . . . .

Ability Achievement Discrepancy Model Comparisons

Absolute z-Score Discrepancy-Level Differences .

Directional z-Score Discrepancy-Level Differences

Discrepancy-Level Variance Between Groups . . . .

erCore Discrepancy-Level Diagnostic Utility
Ability-Test Subtest Scatter Comparisons . . .
Subtest Scatter Variance Between Groups . .
Subtest Scatter Diagnostic Utility . . . . .

Comparisons of Verbal-Performance Ability Differences.
Actual Group Differences . . . . . . . . . . . . . .
Variance of Verbal-Performance Ability Differences

Between Groups . . . . . . . . . . . . . . . . .

Diagnostic Utility of Verbal-Performance
Differences . . . . . . . . . . . . . .
General Findings . . . . . . . . . . . . . .
Achievement Test Performance Correlations
Dependent Variable Correlation . . . . . .
Covariate Correlations . . . . . . . . . .
Covariate Analyses . . . . . . . . . . . .

5. DISCUSSION 0 O O O O O O O O O O O O O O O O O O

summary 0 O O O O I I I O I O O O O O O O O 0
Conclusions and Recommendations for Clinical

PraCtIce O O I I O O I O O O C O O O C O O O O 0

Conclusions and Recommendations Concerning Public

PO] 1cy O I O O O O O l O I O I O O O O I O O O O 0
Conclusions and Recommendations for Further Research

Limitations . . . . . . . . .
Sample Selection
Methodology . .
Results . . . .

APPENDIX C O O O O I O O O O O O O O O O O O O O O O O 0

REFERENCES 0 O O O O O O O O O O O O O O O O O O O O O O

Page
45
45

46
46
49
ST
ST
53
55
59
61
62
64
66
67

67

69
69
7T
7T
72
72

76

76
77

79
81
84
84
85
85

86

94

10.

11.
12.

13I

14.

15.

LIST OF TABLES

Sample Characteristics . . . . . . . . . . . . . . . .

IyTest eratios and Probability Levels for Significant
Differences Between Subsamples' Ability and
ACh1eve'nent scores I I I I I I I I I I I I I I I I I

Summary of Use of Ability and Achievement Characteris-
tics to Classify Students . . . . . . . . . . . . .

Percentages and Numbers of Students Scoring at gyScore
Discrepancy Levels . . . . . . . . . . . . . . . . .

Percentages and Numbers of Students Scoring at gfscore
Discrepancy Levels With Negative Directionality . .

Analysis of Variance--Discrepancy Levels at Grade
Ranges: LD and LA<26th Groups . . . . . . . . . . .

Analysis of Variance--Discrepancy Levels at Grade
Ranges: LA<26th Group . . . . . . . . . . . . . . .

Analysis of Variance--Discrepancy Levels at Grade
Ranges: LD Group . . . . . . . . . . . . . . . . .

Analysis of Variance--Discrepancy Levels at Grade
Ranges: LD and LA<l7th Groups . . . . . . . . . . .

Summary of the Use of grscore Discrepancy Levels to
C1ass1fy StUdents I I I I I I I I I I I I I I I I I

Group Means for Three Measures of IQ Scatter . . . . .

Analysis of Variance--IQ Scatter (NDEV): LD and LA<26th

Groups I I I I I I I I I I I I I I I I I I I I I I I

Analysis of Variance--IQ Scatter (NDEV) at Grade
Ranges: LD Group . . . . . . . . . . . . . . . . .

Analysis of Variance--IQ Scatter (NDEV) at Grade
Ranges: LA<26th Group . . . . . . . . . . . . . . .

Summary of Use of Scatter Methods to Classify Students

vi

Page

39

47

48

52

54

56

56

57

58

60
61

62

63

63
65

16.

17I

A4.
”I

A6.

A7.

I

Percentages and Numbers of Students Scoring at Mean
Deviated and Actual Differences Between Verbal-
Performance 105 . . . . . . . . . . . . . . . . .

Summary of Use of Verbal-Performance Differences to
01a551fy StUdents I I I I I I I I I I I I I I I I

Univariate Analyses for L0 and LA<26th Groups . . .
Univariate Analyses for LD and LA<l7th Groups . . .
Means. Standard Deviations. Correlation Coefficients.
and Significance Levels Between Subtest Scores for
Wide Range Achievement Test Performance . . . . .
Correlations Between Dependent Variables . . . . . .

Correlations Between Covariates . . . . . . . . . .

Univariate Analyses With Covariates: LD and LA<26th
Groups I I I I I I I I I I I I I I I I I I I I I I

Univariate Analyses With Covariates: LD and LA<l7th
Groups I I I I I I I I I I I I I I I I I I I I I I

vii

Page

68

70
87

88

89
90

91

92

93

LIST OF FIGURES

Page

Discrepancy Level Means at Grade Ranges for LD and
LA<26th Groups I I I I I I I I I I I I I I I I I I I I 57

Discrepancy Level Means at Grade Ranges for L0 and
LA<17th Groups I I I I I I I I I I I I I I I I I I I I 58

IO Scatter (NDEV) Means at Grade Ranges: LD and LA<26th
Groups I I I I I I I I I I I I I I I I I I I I I I I I 64

Adjusted Discrepancy Level Means at Grade Ranges:
LD and LA<26th Groups I I I I I I I I I I I I I I I I I 74

Adjusted Discrepancy Level Means at Grade Ranges:
LD and LA<17th Groups I I I I I I I I I I I I I I I I I 75

viii

CHAPTER 1

INTRODUCTION

Wars

A major purpose and concern of school systems and educational
personnel is classifying students. Students are classified on the
basis of chronological age (by grade) in elementary school and by age
and subject matter at the secondary level (Shinn. Ysseldyke. Deno. &
Tindal. l982). Schools also classify students according to a variety
of special needs (ixm. mental impairment. speech and language
disorder. emotional impairment. physical impairment. and learning
disability). Classification by handicap is intended to benefit the
student and is based on premises similar to those used in classifying
regular students. Providing homogeneous disability groupings
theoretically makes it possible to teach compensating techniques. It
enables the teacher to focus on processes that help students acquire
information and allows school administrators to provide equitable and
appropriate programs for the handicapped. Although the practice of
formal classification of handicapped children was originally intended
for exclusion. when Binet was commissioned to "find a way to locate
those who could not learn so that teachers would not be charged with
failure on their account” (Maurer. 1972). the intention of present

diagnostic practice is to benefit all students.

JEEfludJUEEUUUHLJULJflnLlfiuntUHUHEfii

Individuals and professional groups have for some time been
striving to arrive at specific classification schema for the
handicapped. A major focus of this effort has been to identify
essential characteristics that differentiate handicapped student
populations so that specific curricula can be applied to them. This
type of sorting process has resulted in two broad applications:
classification by disability (94}. mental subnormality versus learning
disability) and classification by severity (exy. mild versus severeL
In both cases. diagnosticians have used standardized-test results to
help differentiate disability groups. Identification of some disabili-
ties is a relatively straightforward process. For example. classi-
fying a student as blind depends on the absence of sight. Other
handicapping conditions pose more difficult diagnostic challenges.
Mental retardation can be differentiated from learning disabilities
(Frame. Clarizio. Porter. & Vinsonhaler. 1982); however. differen-
tiating those with specific learning disabilities from low achievers is
more difficult. Indeed. the literature reviewed in the next chapter
suggests that methods used to differentiate a student with a learning
disability from one with other handicaps and particularly from a
student who is found not to be handicapped but who achieves at a low

academic level may not be of diagnostic utility.

.DeI1n1ng_tbe_Leann1ng_Disabled

In the 19405. Strauss and Lehtinen developed procedures to
identify and teach exogenous and endogenous mentally retarded students.

In the 19505 and early 19605. Cruickshank and his colleagues developed

procedures to identify brain-injured students. In the early 19605.
Kephart developed procedures to identify and teach "slow learners." and
Kirk coined the term "learning disabilities" to refer to students of
essential average intelligence who failed to make adequate progress in
school. In the mid-19605. the federal government established the
category "learning disabled" as a handicapping condition.

All along. the presumption has been that a specific group of
students who were failing in school could be readily identified and
that identifying them would lead to the development of appropriate
educational programs. These students were presumed somehow to be
different from other students who were failing because of low
achievement.

The federal government has established rules for determining a
learning disability. in an attempt to develop guidelines for serving
students with this type of handicap. Now. a team of professionals may
determine that a student has a specific learning disability if there is
one or more low areas of achievement. if there is a discrepancy between
ability and achievement. and if the student exhibits an implied
processing disorder (this requirement is no longer mandatory. although
it is included in many school definitions).

To comply with the federal definition of learning disability.
diagnosticians and school personnel continue with predefinition
emphasis on three major factors or characteristics in the assessment of
students. using primarily standardized tests. The existence of a
process disorder. significant nonachievement in one or more academic

areas. and a discrepancy between ability and achievement are purported

to establish the presence of a learning disability. These character-
istics may exist singularly or in combination. as long as the discrep-

ancy criterion is met.

WW
Although both learning disabled and low achieving students may

meet the criterion for low achievement. learning disabled students have
been thought to be unique in how they score on ability and achievement
tests. Researchers have concentrated on identifying behavior patterns
exhibited on tests that could reliably be associated with the learning
disabled student (Sheppard. Smith. & Vojir. 1983). ‘Two focal points
with regard to identification have been prevalent: process disorders
and ability-achievement discrepancy.

.Enggess_disgndens. The concept of process disorders is based on
the assumption that students possessing a learning disability are
deficient in cognitive ability and that standardized intelligence tests
assess accurately the type and functional degree of such ability. For
example. some authorities have argued that. if a student exhibits a
discrepancy between verbal and performance 10 abilities. there is a
likelihood that a learning disability exists (Bateman. 1965). The
student may also exhibit a degree of scatter between subtests in the
verbal and performance ability areas. which. depending on the degree of
variance. implies that the student has a learning disability (Clements.
1966; Matarazzo. 1972). This approach to identification was influenced
by research that emphasized brain—behavior relationships and neurologi-

cal dysfunctions. If different parts of the brain mature at diverse

rates (Bender. 1963; Chusid. 1979; Cowan. 1979; Geschwind. 1964). a
pattern of skills and deficits results. Additional concepts such as
developmental imbalances (Gallagher. 1966) have provided further
impetus for the development of verbal- versus performance-ability
comparisons and subtest scatter analyses.

.Ab111ty:achievemen1_disczepancy. The field of learning disabili-
ties paralleled the remedial-reading field in its attempt to differen-
tiate learning disabled students from "slow learnersJ' In 1932. Monroe
noted that "a child may fail to learn to read and yet be of adequate
intelligence" (p. 1). Bond and Tinker (1957) also highlighted the
concept of underachievement. stating that "the disabled reader is a
child . . . who is not living up to his potential as a learner" (p.
83). Reading specialists emphasized identifying the "disabled reader"
(achievement less than computed expectancy) rather than the "poor
reader" (low achievement but supposedly achieving up to computed expec-
tancy) (Epps. McGue. & Ysseldyke. 1982).

Bateman (1965) and Ysseldyke and Algozzine (1979) emphasized the
use of ability-achievement discrepancy with regard to identifying stu-
dents with learning disabilities. Myklebust (1968) and Algozzine.
Forgnone. Mercer. and Trifiletti (1979) developed formulas to be used
in calculating ability-achievement discrepancies. The current federal
formula was designed to identify those students who were doing poorly
in school but yet were of average intelligence. No consensus exists
among authorities about whether the ability-achievement discrepancy
method is useful in differentiating the learning disabled from the low

achieving student who has not been classified as handicapped. Recent

research (Algozzine & Ysseldyke. 1982b; Epps. Ysseldyke. & Algozzine.

1982a) has indicated that learning disability may be a category of low
achievement. Epps. Ysseldyke. and McGue (1982) focused on the use of

standardized achievement scores without the use of a formula to iden-

tify students who are doing poorly in school. regardless of their

intelligence.

MagnitudefiJbLEmeem
Despite the sizable number of students being declared eligible for

learning disabilities services and the implicit appeal of the term
(Divoky. 1974; Hobbs. 1975). there is little agreement on the
definition of learning disabilities. Vaughan and Hedges (1973)
reported as many as 38 different definitions of learning disability.
and Mercer. Forgnone. and Wolking (1976). in a survey of 42 state
departments of education. found considerable variation in definitions
of the term. Thurlow and Ysseldyke (1979) reported that Child Service
Demonstration centers for learning disabled students varied
considerably in how students within those programs had been identified
as handicapped. This variance of definitions has been accompanied by
a wide range of estimates as to the prevalence of the handicap in the
school population. National estimates range from 1 to 30% (Lerner.
1976). to as much as 70% (Tucker. Stevens. & Ysseldyke. 1982).

The actual number of students served in learning disabilities
programs has increased dramatically in the past decade. During the
1969-70 school year. .02% of the total school population was served in
programs that were analogous to current learning disabilities programs.

By 1977 that figure had risen to stzz (Epps. Ysseldyke. & Algozzine.

1982b). Tucker (1980) reported that in one state the percentage of
students identified as learning disabled rose almost 44% from 1970 to
1977. During the 1981-82 school year. the percentage of the total
school population served in learning disabilities programs was 3.01%.
Although the overall percentage of students in learning disabilities
programs has decreased since 1977. 1.455.135 students were served in
1982. which was 34.7% of the total handicapped population (USOE. 1982).

In contrast to the 3.01% incidence figure for students with
learning disabilities. it is believed that there is a large population
of low achieving students who are not identified as handicapped but who
exhibit test characteristics similar to those of learning disabled
students. Up to 33% of the school population may be perceived as low
achievers (Warner. Schumaker. Alley. & Deshler. 1980). A strong
possibility of misdiagnosis exists when these two populations cannot be
specifically differentiated from each other through the use of
currently popular methods.

Of equal importance are considerations of teacher training.
diagnostic and placement costs. and curriculum modifications. which
need to be addressed in providing educational programs for this large
but undiagnosed or misdiagnosed population. School personnel may need
to focus their attention on broader issues than the studentls academic
performance. Situational variables such as the teacher. peer group.
educational content. and method of instruction used in the student's
classes may need to be examined more systematically (Lidz. 1981L. The
system of allocating funds from a categorical basis. along with major

changes in legislation and regulations to allow school districts

flexibility in demonstrating prevention techniques and in solving
problems of the entire school population. may need encouragement

(Reynolds & Wang. 1981).

W
The validity of differentiating the learning disabled from the low

achieving student who has been deemed not handicapped is far from
established. Using general ability and achievement-test performance.
differences between verbal and performance ability levels. degree of
discrepancy between ability and achievement. and analyses of subtest
scatter may not be accurate methods with credible diagnostic utility
(Epps. Ysseldyke. & Algozzine. 1982a). If such is the case. using
these methods to validate the existence of a learning disability apart
from low achievement is counterproductive to the intention of diagnosis
and intervention.

The primary concern of this investigator was to determine whether
there is practical value in using test results in the aforementioned
ways as a diagnostic rationale in identifying students as learning
disabled and not identifying others who share a commom characteristic--
low academic achievement. Current studies that have made efforts in
this direction have defined low achievement as scoring below a specific
point on achievement tests. Epps. Ysseldyke. and Algozzine (1982a)
used scores below the 25th percentile. as did Algozzine and Ysseldyke
(1982a) and Shinn et a1. (1982). In a study involving junior and

senior high school students. Warner et a1. (1980) found sufficient

numbers of students apart from special education programs scoring below
the 33rd percentile and defined them as low achievers.

The present study compared students identified as learning
disabled with those who had been identified as not possessing any
discernible handicap that qualified them for special education
services. The group of students who did not qualify for special
education services scored below the 26th percentile on a test of word
recognition and are designated in this study as low achievers (LAL
The learning disabled and low achieving groups were compared using two
achievement standards: the learning disabled (LD) with the low
achieving (LA) group who scored below the 26th percentile (LA<26th) and
the learning disabled (LD) with the low achieving (LA) group who scored
below the 17th percentile (LA<l7th).

The students included in this study comprised a broad spectrum of
grades and ages. All students were referred for diagnostic evaluation
after experiencing difficulty in school and were judged by a team of
professionals to be either learning disabled or not eligible for
special education services. ‘The sample size was sufficiently large
(flf‘404) to offset statistical errors produced by exceedingly small
samples. ‘The influence of moderator variables on any differences
between groups will be reported. Using different methods to assess
group differences in ability-test performance may indicate which method
is most accurate in affirming classification decisions. The extent to
which the methods used in this study affirm classification decisions
should prove of value to diagnosticians and educational personnel

responsible for making such decisions. ‘This study may also assist in

 

10

delineating test-performance characteristics that would be helpful in
establishing realistic diagnostic criteria for classification

decisions.

CHAPTER 2

LITERATURE REVIEW

mm

The preceding chapter outlined a history of attempts to verify the
existence of learning disabilities apart from other handicaps and the
nonhandicapped students. The general trend of using discrepancy models
to calculate ability-achievement differences. verbal-performance
ability differences. and ability-test subtest scatter analyses was
presented. Of particular note was the fact that the definition of
learning disabilities established by the federal government and used by
school districts contains a strong element of low achievement. This
chapter reviews the literature in the following areas: similarities
and differences between populations. characteristics of the learning
disabled. general ability and achievement characteristics. use of a
discrepancy model. effectiveness and reliability. verbal-performance
ability differences. and ability-test subtest scatter comparisons. The
focus is on studies comparing LA with LD students. 'The final section

of the literature review points to the direction of this study.

WWW
Diagnostic models designed to differentiate between the LD and the

LA student appear to be predicated on the belief that actual

differences in ability and achievement exist and/or that the LD student

11

12

uses abilities and skills in different ways from other students.
Traditional methods of assessing students for classification purposes
have relied on standardized test results. with the notion that if
differences exist they can best be measured by tests that reflect both
student ability and academic skills learned.

Similarities and differences between LD and LA populations have
been studied in a number of ways. Warner et aL.(1980). in calculating
discrepancy levels between achievement and ability with junior and
senior high school students. reported that no significant differences
were found between LD and LA populations. Others (Algozzine &
Ysseldyke. 1982a; Epps et al.. 1982b; Shinn et al.. 1982) have
indicated a lack of consistent direction for distinguishing between the
two populations in terms of processing information. scoring on ability
subtests. degree of ability-achievement discrepancy. and verbal-
performance IO scores. As Epps et a1. (1982) indicated. "a major
difficulty with studies attempting to identify the salient
characteristics that distinguish the learning disabled from other
students is that they compare with populations that are obviously
different" (p. 209). The L0 population represents a heterogeneous
group characterized by a variety of different behavioral
characteristics (Lerner. 1976; Mercer. 1979). Algozzine and Ysseldyke
(1982b) indicated that the "only common school related characteristic
among many learning disabled children is low achievement of some form"
(p. 117).

A major study that compared such similarities was conducted by

Ysseldyke. Algozzine. Shinn. and McGue (1982). Comparison of 50

13

fourth-grade students who had been identified as LD with 49 LA students
at the same grade level on a number of analyses indicated few
differences. Students were administered a test battery including the
WISC-R. the PIAT. subtests of the Stanford Achievement Test. a
perceptual motor test. and a self-concept scale. Methods for comparing
the two groups included measuring the discrepancy between ability and
achievement. comparing subtest scores in an overlap analysis. and
contrasting performance in the domains of cognition. achievement.
perceptual-motor functioning. and self-concept. The results of the
study indicated that no psychometric differences of practical utility
were observed. The researchers concluded that "there is considerable
misclassification in identification of LD students" (p. 83). They
failed to identify psychometric differences between the two groups on

test performance.

WWW

Analyses of the characteristics of LD students have been con-
ducted. and the results have shown considerable variation among stu-
dents who have been identified as LD. Norman and Zigmond (1980)
analyzed data from the files of 1.966 students. ages 6 to 17 years.

The case studies were selected from populations of LD students from 24
school districts in 22 states. ‘The focus of the study was on examining
characteristics of ability and achievement in terms of variability in
range and level. as well as indications of what percentage of the
sample did not demonstrate empirical evidence of a learning disability.
Two methods were used to support evidence that a student could be

classified as LD: the federal formula used to calculate a severe

 

14

discrepancy and a learning-efficiency model (Zigmond. 1978). The
learning-efficiency model used a formula that yields a percentage score
after actual achievement is divided by expected achievement “IA. x
IQ/lOO-SJD. Students were considered to be correctly classified if
their severe discrepancy level (federal formula) was 50% or greater or
if their learning efficiency was less than 50%.

The authors found that age appeared to be negatively related to ID
level. In a majority of the school districts (54%). there were
students classified as LD who had reading and math scores almost at
grade level. Below-grade-achievement discrepancies of two or more
grades were not evident until a chronological age of 12. Learning
Efficiency Rates (percentage of actual achievement divided by expected
achievement; C.A. x IO/100-5.0) of the total sample were 68.1% in
reading and 74.5% in math. Norman and Zigmond found that less than
half of the populations studied were underachieving.

More recently. Shepard et a1. (1983) studied the test results of
790 L0 students selected from 22 special education administrative units
in Colorado. The students' files were used to obtain IO data. and the
degree of discrepancy between ability and achievement in math and
reading was calculated. The authors used a standard-error-of-
difference correction with both a lenient and a strict criterion to
calculate discrepancy between ability and achievement scores and the
degree of variation between students' verbal-performance 10 scores.
Results of the study indicated variation in IQ levels with 28.5% of the
population having 105 below 90 and 8.3% having 105 below 81. Thirty-

five percent of the students had no significant discrepancies between

15

ability and achievement. However. in 4S~2% of the cases. the files
contained insufficient data for these analyses. Achieving below grade
level as a consistent factor in differentiating LD students from the
rest of the population was not validated in the study. In preschool
and kindergarten. the achievement average was above grade level.
whereas in primary grades fewer than half of the students studied met
the below-grade—level criterion. In summary. Shepard et a1. stated
that less than half of the sample had characteristics consistent with
the definitions of LD students cited in federal statutes and in profes-

sional publications.

sammummmmmmnmum

Studies comparing the overall general characteristics of the LD
population with those of a LA population appear to have been limited to
students at the elementary-school leveL. The major exception is the
research conducted by Warner et a1. (1980). who compared the test
results of junior and senior high school students in an attempt to
discover if differences existed on tests of ability and achievement.
In reporting the results of their research comparing 234 L0 students
with 220 low achievers. the authors noted several differences between
the two groups. Scores on the reading. mathematics. and written-
1anguage subtests of the Woodcock Johnson Psychoeducational Battery
indicated that the LD group scored significantly lower than the low
achievers at both junior and senior high school levels. Scores from
selected subtests of the Wechsler Battery (used to predict estimated

105) indicated that the LD group scored significantly below the LA

16

group at both junior and senior high school levels. Both the LD group
means (senior high--93.02. junior high-~87.9) and the LA group means
(senior high--99.08. junior high--98.99) were below average. The
authors indicated that "the traditional characteristics of LD students
as having average ability would not characterize a substantial
proportion of the students in our sample" (p. 31). They noted that the
results. particularly in the achievement area. may have been due to
sample selection. The LA group had been selected on the basis of
scoring below the 33rd percentile because it had been difficult to find
a sufficient number of students who scored below the 25th percentile on
achievement tests.

Taylor. Satz. and Friel (1979) compared the test performance of 80
L0 students with 80 students who were not diagnosed as handicapped but
who exhibited poor performance in reading on a locally normed teacher
judgment scale and the IOTA (Monroe. 1928). They used Peabody Picture
Vocabulary Test (Dunn. 1965) results to control for 10 level in a
sample selected from 570 second-grade boys. Taylor et ale results
indicated that the nonlabeled students could not be distinguished from
the students labeled LD.

Ysseldyke et a1. (1982) compared the performance of students
labeled LD with students who scored below the 25th percentile on the
Iowa Test of Basic Skills. Test results from the WISC—R. the Woodcock
Johnson Tests of Cognitive Ability. the Peabody Individual Achievement
Test. the Stanford Achievement Test. and the Woodcock Johnson Tests of
Achievement were compared for 50 L0 and 49 LA fourth graders. Although

there were statistically significant differences between groups on

17

tests of achievement. the authors noted that the real difference
between the means was only 1.26 points. which was the result of
answering one more math problem correctly. When identical scores were
computed. at least one-half the number of both groups compared had the
same scores.

Shinn et al. (1982) compared the performance of 34 L0 students
with that of 37 students who were not identified as handicapped but who
scored below the 26th percentile on the Iowa Test of Basic Skills.
These 71 fifth graders were administered measures of reading (word
lists). spelling (word lists). and written expression (vocabulary
words). which were constructed and used in identical formats with both
groups over a 5-week period. The test results were compared for
overall differences. test-area differences. and learning rates on a
week-by-week basis for each test area. 'The non-LD group significantly
outperformed the LD group in reading words correctly. Reading
differences between the groups ranged from 23.6 to 26.1 words per
minute. However. there was no difference in the groupsfl learning rates
in reading. On an average. the LD group increased at a rate of 1:74
words per week. whereas the non-LD group increased at a rate of 2.35
words per week. In spelling. the non-LD group spelled more words
correctly. with a 6.7 to 8.6 word advantage. Written expression
differed significantly between groups; the non-LD group outperformed
the LD group by an average of approximately seven words per week.
Absolute growth in all academic areas indicated no differences between
the groups. Contrary to all other findings. the LD group excelled in

the learning rate of written expression. They gained an average of one

18

word per week. whereas the non-LD group lost an average of one-half
word per week.

Of particular note in comparing the results of the Shinn et a1.
(1982) and the Ysseldyke et a1. (1979) investigations is that both
studies used the same student samples. Shinn et a1. (1982) found
differences in word-recognition. spelling. and written-expression
skills between the LD and the LA groups (measured by nonstandardized
tests). whereas Ysseldyke et a1. (1979) found no differences between
the groups on standardized test performance. Shinn et a1. suggested
that such differences in findings might have been a result of the
indirect measurement of skills done by standardized tests and that.
indeed. differences between LD and LA students do exist. Given their
findings. the authors seemed to indicate that standardized testing
fails to substantiate differences between LD students and others who
may be doing poorly in academic tasks.

The issue of competency versus performance may arise when
standardized tests are used to measure differences between groups for
the purposes of classification. If differences between LD and LA
students are not found on standardized test scores but are seen by the
classroom teacher in competency-based tasks. the methods used for
diagnostic purposes need clarification. Are students identified as LD
on the basis of performance. or. as discussed elsewhere in this
chapter. are they identified by focusing on the characteristics of the
diagnostic process? If so. focusing on the characteristics of the

diagnostic process may be due. in part. to the belief that what matters

19

is not actual differences in ability and skills but in how students

perform in the classroom.

WW
Although Birch and Belmont (1964). Browning (1967). and Schwartz

and Bryan (1971) were among those who emphasized the importance of the
ID as the major determinant of learning disabilities. a number of
researchers have endorsed the notion of comparing differences between
ability and achievement. As early as 1932. Monroe noted that a child
may fail to learn to read and yet have adequate intelligence. Bond and
Tinker (1957) also highlighted the concept of underachievement. stating
that the "disabled reader is a child . . . who is not living up to his
potential as a learner."

Bateman (1965) expressed the view that a realistic quantifying
method is necessary to clarify the extent of learning disability. and
such authors as Myklebust (1968) and Algozzine et a1. (1979) have
developed formulas similar to those used in calculating reading
expectancies.

Various methods have been used to compare ability and achievement.
Schere. Richardson. and Bialer (1980) proposed a formula that averaged
grade scores from group- and individually administered achievement
tests. Lerner (1981) compared four methods of quantification and
cautioned that different ages give different indications of a
discrepancy.

The present uses of discrepancy models vary greatly. depending on
school districts' policies for establishing special-program cutoff

points. However. all such models attempt to meet the federal

20

requirement that achievement be significantly lower than ability.
regardless of other criteria used in determining whether a learning
disability exists.

At present there is no empirical evidence that a discrepancy model
can differentiate between the LD student and the low achiever. Brenton
and Gilmore (1976) reviewed the discrepancies between ability and
achievement of 60 students and found that 67% were identified as
handicapped. They noted that considerable caution should be exercised
when classifying children. especially females. as LD. A recent
investigation by Epps et a1. (1982) comparing the performance of 48 L0
and 96 nonidentified students on 10 different discrepancy formulas had
varied results. 'The investigators compared student performance using
six ability-achievement methods based on test results and four below-
grade-placement achievement methods. 'The most successful method of
affirming classification decisions was the below-grade—placement
method. which used a standard score cutoff of below 86 points on
achievement tests. including the Woodcock Johnson Test of Achievement
subtests (reading. mathematics. and written expression) and the Peabody
Individual Achievement Test subtests (mathematics. reading recognition.
and reading comprehension). Seventy-eight percent of the LD and 35.2%
of the nonidentified group scored below the cutoff point. Application
of the federal formula to test results indicated that 25% of the LD and
4.4% of the nonidentified group met the criterion of a significant
discrepancy between ability and achievement. ‘The authors concluded
that there is considerable doubt that school personnel can accurately

and reliably identify LD students using the methods included in their

21

study. None of the definitions used was in high agreement with the
schools' classification of students as L0 or non-LD. Approximately 18%
of the schools' identified LD students were not identified by more than
one definition. The authors indicated that: "As it is presently
conceptualized. the category of learning disabilities is an ill-defined
disorder with little consistency among definitions to allow for
reliable prediction of LD classification" (p. 20).

Attempts to validate discrepancies between ability and cognitive
functions. other than those assessed by achievement tests. have yielded
inconsistent results. Burns (1977) studied the relationship between
abilities assessed by the ITPA and found there was a nonlinear
relationship that lends little support to the credibility of this
method.

Other researchers have compared ability with achievement in
various ways to ascertain if previously diagnosed LD children are
different from the LA population and from randomly sampled populations
that are comparable in age. sex. and socioeconomic status. Algozzine
and Ysseldyke (1982a) compared 50 children diagnosed as LD with 49
students who were low achievers. The students'Itest results were
compared on 16 discrepancy models. including the current and
alternative federal formulas. statistical ceiling models. standard score
cutoff models. and learning-quotients models. The findings indicated
that no one model or formula was capable of differentiating the LA
student from the L0. The results indicated a range of differential
classification from 0 to 15%; no child was classified on all

definitions. In addition. Algozzine and Ysseldyke found that 92% of

22

the LA population met the criterion for L0 classification on at least
one definition.

Epps et a1. (1982) used a larger sample that included randomly
selected students who were not referred for evaluation. students who
scored below the 25th percentile on a standardized group achievement
test. and students diagnosed by school districts as L0. The results
offered little support for the usefulness of the federal definition.
Comparison of the populations in grades 3 through 5 focused on six
forms of ability-achievement discrepancy and four forms of grade-
placement discrepancy. The results indicated there is a substantial
lack of agreement and uniformity in applying the federal model. with no
clear direction toward a definition that distinguishes the LD from

other students.

WWW

0f major concern in evaluating the effectiveness of a discrepancy
model are the direction and ceiling at which the majority of the given
population fits the assigned criteria. Algozzine and Ysseldyke (1982b)
compared 40 L0 students and a matched number of students scoring below
the 25th percentile on a standardized achievement test on three
alternate methods of diagnosing LD students using the current federal
definition (cutoff points at the 1.0. 1.5. and 3.0 standard deviation
levelsL Using any one subtest from the Woodcock Johnson Achievement
Test or the Peabody Individual Achievement Test.(subtests-~mathematics.
reading. spelling) and the WISC-R Full Scale ID. the authors found

inconsistent results. Of the students in the sample. eight met no

23

identification criteria on any definition. The criteria for identifi-
cation were met by 92% of the LA group on at least one formula. More
LD students met the criteria on four definitions. yet more LA students
met the criteria on two other definitions. 0f the entire sample. 73%
met the identification criteria on the least-stringent ability-
achievement model with a standard score difference of 10 or more
points.

Warner et a1. (1980) reported similar results in their comparison
of adolescent LD and LA students. Although their cutoff level for
identifying LA students was higher than that used in other studies
(33rd percentile or below). the results were similar to those reported

by Algozzine and Ysseldyke (1982a).

WW

Of particular importance is the statistical reliability of any
method used for differential diagnosis. Shepard (1980) commented on the
four most commonly used diagnostic methods and advocated the regression
method as the most statistically reliable. stipulating that scores be
secured from co-normed tests. She indicated that the Harris (1970)
method (determining expected grade equivalent in reading based on
ability by subtracting 5 years from the student's mental age) fails to
consider the less-than-perfect correlation between ability and
achievement. Because of regression effects. the Harris method tends to
identify more bright than dull students as L0. The Bond and Tinker
(1967) method (years in school x IO/lOO +-l.O) assumes that the IQ
score obtained from standardized tests is a ratio scale of measurement.

The method does not consider that the variance in grade-equivalent

24

performance increases with grade level. The z—score method proposed by
Erickson (1975) assumes that achievement and I0 are in the same
relative position as measured by standardized tests. This method (the
.z-score is obtained by subtracting achievement discrepancy from ability
discrepancy after converting by: raw score - group mean divided by
standard deviation) is based on the expectation that the achievement
score is in about the same relative position in the distribution as the
ability score and that regression of measurement is certain if a one-
to-one correspondence does not exist. Shepard (1980) listed several
advantages of the regression method over other methods. As previously
mentioned. she stipulated that both the achievement and ability tests
used to calculate discrepancies should be co—normed to avoid errors due
to differences in standardization populations. However. the practical
value of this provision is questionable. At present. diagnostic tests
that do not meet this criterion (WISC-R. PIAT. Woodcock Johnson. WRAT.
and others) are widely used.

Reynolds (1981) affirmed Shepard's (1980) criticism of grade-
equivalent methods. saying that they ignore the dispersion of scores
around the mean and that the regression between grade and test score is
not equivalent across grades or school subjects. Reynolds did
indicate. however. that the z-score method is satisfactory for
indicating that real differences between ability and achievement exist.
as long as the reliability of the test instrument is included as a
factor in the calculations. Correction for differences in test
reliabilities adjusts for differences due to chance or error of

measurement. and calculated z—scores indicate real differences in

25

performance. Reynolds indicated that the real differences between zr
score performance are divided by the square root of combined test

reliabilities subtracted from one:

Absolute difference between

= Zescore discrepancy

 

V (l - reliability) + (1 - reliability)

The resultant zrscore discrepancy is then compared to the normal curve
for statistical significance. 'Whe values of‘z required at three
commonly employed levels of significance for a one-tailed test are:
1.65. p = .05; 2.33. 12 = .01; 3.08. p = .001. For a two-tailed test.
the values are 1.96. p = .05; 2.58. p = .01; 3.28. ,p = .001" (p. 354).
When the test reliabilities of the instruments used fall within certain
ranges. Reynolds indicated that specific cutoff standard deviation
levels that indicate discrepancy levels meet statistical reliability as
long as the standard deviations for each test instrument are equated by
comparison of equal (or converted to equal) standard scores. For
example. if the test reliabilities from which scores are obtained fall
between .90 and .95. a z-score difference of .66 standard deviations is
significant. Reynolds presented a conversion chart that facilitates
the equating of standard scores when these scores are not equal.
Despite psychometric cautions. the emphasis on quantification of
differences between ability and achievement appears to be gaining
momentum. Warner et a1. (1980) and Algozzine and Ysseldyke (1982b)

indicated a trend by school districts to refer and place those students

26

who are the lowest achieving but not exhibiting any other discernible
handicaps.

The question of performing comparisons to differentiate between LD
and LA students still needs to be addressed. particularly with a method
that has the most statistically reliable basis. If achievement is a
function of learning disabilities. an examination of differences
between ability and achievement may help make appropriate classifica-
tions. When statistically significant differences between ability and
achievement exist. it would appear to be important to note the per-
centage of the nonhandicapped group identified as having significant
differences. as compared with the LD group. Also. the method used to
determine differences between ability and achievement should be
practical. Reynolds! (1981) method would appear to meet both of these
criteria because it offers a statistically reliable calculation that
can be used to indicate the significance of discrepancies. The method
also adjusts for the differences between standardization distributions.

Obtaining a statistically significant discrepancy between ability
and achievement does not necessarily mean the student needs special
education intervention. The literature indicated that there may be a
sizable population of students who are low achieving (achievement not
commensurate with measured ability) who have not been referred for
diagnostic evaluation but who. upon evaluation. demonstrate significant
discrepancies between ability and achievement (Epps et al.. 1982;

Warner et al.. 1980).

27

WW

Early attempts to differentiate the LD from the rest of the
population on the basis of Verbal-Performance IQ test results appeared
promising. Diagnoses were based on specific differences in test
scores. Ackerman. Peters. and Dykman (1971) indicated that
"discordance" among a LD sample was more frequent than in a "normal"
sample. Anderson. Kaufman. and Kaufman (1976) reported statistically
significant differences in test scores between children diagnosed as LD
and the "normal" population. However. they did not find that children
in their sample exhibited unusually large discrepancies. despite the
statistical significance obtained. Piotrowski (1978) conducted obser-
vations that apparently verified Kaufman%;(l976b) findings. although
it became apparent that such analyses would have to acknowledge the
degree of discrepancy in the normal population. When Schooler. Beebe.
and Koepke (1978) compared the normal and LD populations. they found
there were few Verbal-Performance IO differences between the two
groups.

Recent studies investigating significant differences between LD
students. those with other handicaps. and the nonhandicapped population
may be characterized by two general methods of analysis: the use of
statistical cutoffs for different confidence levels and the comparison
of actual differences between experimental and control groups. ‘Veres
(1982) indicated LD students were likely to exhibit differences between
verbal and performance scores. although the direction of the difference
was not significant. Further differentiation of age and IQ levels in

comparing the LD group with the normal group (lJL. referred for

28

evaluation but not classified) appeared to offer no consistently
reliable guidelines or diagnostic rules.

Epps et al. (1982b) attempted to verify the consistency of Verbal-
Performance 10 differences as a diagnostic tool through the discrim-
inant analysis of 48 L0 and 96 nonhandicapped students at three levels
of statistical confidence. Although the sample included children ran—
domly selected from the third through fifth grades. no operational
rules or guidelines for classification decisions were presented.

Indications that the diagnostic utility of comparing verbal-
performance ability differences may be less than reliable have been
presented by a number of researchers. Ysseldyke et a1. (1982) compared
the results of 49 subtests. including verbal-performance analysis. with
a population of 50 L0 and 49 LA students at the fourth-grade level. No
psychometric differences of practical utility between the groups were
observed.

The degree to which Verbal-Performance IO differences are impor-
tant appears to be a judgment by school personnel making diagnostic
decisions. Epps. McGue. and Ysseldyke (1982) used 18 judges trained in
school psychology and special education to evaluate the test results of
99 fourth-grade students. 50 of whom had previously ben classified as
LD and 49 of whom had scored below the 26th percentile on the Iowa Test
of Basic Skills but had not been classified as L0 or handicapped.
Verbal-performance difference was one of 48 criteria used in deciding
whether a student was classified as L0 or not LD. Judges were
evaluated on their degree of leniency; the most lenient judges

classified all students as LD. Factors used in influencing judges'

29

decisions were rank-ordered on the basis of average mean differences of
the two groups. For the lenient judges. verbal-performance differences
were ranked 10 out of a possible 48. For the nonlenient judges.
verbal-performance differences were ranked below 10 (actual degree not
reported). On the basis of this study. verbal-performance difference
was found not to be as important in making classification decisions as
were ability-achievement discrepancies or other test characteristics
such as individual ability and achievement scores.

In summary. there appears to be little evidence that assessing the
degree or direction of Verbal-Performance I0 differences helps differ-
entiate the LD from those with other handicaps and the nonhandicapped
but LA population. Of particular note is the lack of studies con-
cerning the nonhandicapped but LA population who share a common charac-
teristic with the LD (low achievement). Although the Institute for
Research on Learning Disabilities at the University of Minnesota has
completed several studies. sample size and age restrictions on these
studies have been limited. The Institute has asserted a need for

further studies with a focus on operationality.

MW
In Chapter I the concept was stated that subtest scores represent
the degree of cognitive functions. Atypical patterns in subtest-score
scatter were thought to demonstrate atypical learning patterns. which
were thought to characterize a learning disability.
Kaufman (1976a) indicated that the variability of range scatter
differed between LD and normal children; children with higher overall

IOs exhibited more range than did those with lower 105. In further

30

research efforts. Tabachnick (1979). Gutkin (1979). and Thompson (1980)
indicated similar differences between LD and normal children. However.
they advised caution in using the results for interpretive purposes.

Clarizio and Bernard (1981) found that attention-factor scores
differentiated the LD from the educable mentally impaired and nonclas-
sified groups but not from the emotionally impaired group. This study
supported the contention that. as a group. the LD score relatively
lower on subtests categorized under attention-concentration. In
reviewing the differences between profiles. however. Clarizio and
Bernard indicated that these scores were not useful in discriminating
between groups or in making accurate predictions for diagnoses.

Veres (1982) compared the scatter indices of a group of children
classified as LD with a nonclassified population and compared
recategorized subtests. similar to the study by Clarizio and Bernard
(1981). Veres' analyses found no useful diagnostic rule. even when
factors of age and I0 level were cross-tabulated.

Algozzine and Ysseldyke (1982a) investigated whether ability-
subtest scatter is a useful diagnostic tool in differentiating
nonhandicapped LA from L0 students. When the results of 99 fourth-
grade children (50 identified as LD and 49 labeled LA) were compared.
no significant differences were found. Using a cutoff level of 10
points between the highest and lowest subtest scores. 21% of the LD and
77% of the LA samples were found to exhibit a significant degree of
subtest scatter. Ysseldyke et a1. (1982) reported little variance when
their sample of LD students was compared with nonhandicapped LA

students. Using mean-difference scores. which included analysis of

31

ability-subtest scatter. the authors concluded that "we do not yet have
good enough data regarding the extent to which identification as LD

. . . is beneficiaLfl They emphasized that further evaluation of
similar populations (i.e.. LA students) should be considered.

Epps. Algozzine. and Ysseldyke (1982) compared the performance on
ability tests of randomly selected students. LD students. and nonhandi-
capped LA students. The study included 144 students in the third
through fifth grades. Several operational definitions were explored.
including the degree of subtest scatter. The results indicated that. in
correlating degree of subtest scatter with other definitions including
ability-achievement discrepancy and verbal-performance difference. the
degree of scatter had a negative relationship with identification of LD
students. ‘That is. when the greatest number of LD students were iden-
tified by any other definition. the degree of subtest scatter was
small.

In summary. researchers have used recategorized subtests and
analyzed degree of scatter and mean deviation with LD students and
those with other handicaps. as well as with nonhandicapped but LA
students. 'There is some indication that plausible differentiation may
result from using subtest-scatter analyses. However. a number of

researchers have contrary opinions about this.

Wm
This study was directed toward comparing LD with LA students to

evaluate methods proposed in the literature as being useful in

differential diagnosis. The investigator adjusted for limitations

32

found in previous studies that had left results open to interpretation.
The major assumption was that:
Comparisons of LD with LA students on standardized test results
will not lead to decision rules that are useful in differential
diagnosis when general ability and achievement characteristics.
ability-achievement discrepancies. verbal-performance ability

differences. and degree of ability-subtest scatter are used as the
basis for comparisons.

WWW
Various writers have suggested that misidentification of LD and LA

students (false positive) is prevalent in current practice (Hallahan &
Kaufman. 1978; Ysseldyke 8. Algozzine. 1979). Although some studies
have addressed this issue (Veres. 1982; Ysseldyke et a1“. 1982). there
is a general lack of evidence concerning the usefulness of the differ-
ential-diagnosis methods examined in the present research. Studies
that have evaluated these methods have produced results that are open
to various interpretations. Small sample size. grade restrictions.
inadequate controls. the influence of discriminant functions (moderator
variables). and opposing findings have characterized the studies
reported in the literature.

.Sample_size_and_cgmpgsjtign. With the exception of Warner et a1.
(1980). who reported difficulty finding enough students below the 33rd
percentile. studies have been limited primarily to fourth- and fifth-
grade students (Algozzine & Ysseldyke. 1982b; Epps et al.. 1982; Shinn
et al.. 1982). Algozzine and Yssel dyke. Epps et al.. and Shinn et al.
reported that some students included were referred. others randomly

selected. and yet others included whose basis for classification

33

decisions was not clear (Algozzine & Ysseldyke. 1982a; Epps et alu
1982; Norman & Zigmond. 1980; Shepard. 1983).

jnadaquatg_cgntzgls. In previous studies. assessment results have
been compared without controlling for the differing validities and
reliabilities of tests. Also. correlations between student performance
on achievement tests have not been explored (Epps et al.. 1982; Shinn
et al.. 1982; Ysseldyke et al.. 1982).

Won. The influence of moderator variables such
as sex. age. grade. referral reason. and IQ level on study results
appears to be limited. Ysseldyke et a1. (1982) used a stepwise linear
discriminant function model to assess the influence of test scores on
performance differences between LD and non-LD students. Researchers.
however. have not reported the influence of moderator variables
partially because the necessary demographic information was unavailable
(Shinn et al.. 1982; Ysseldyke et al.. 1982).

,Qppgsing_find1ngs. The use of ability-achievement discrepancy
formulas has been explored in a number of studies. but there was
little consensus about their statistical reliability for diagnostic
purposes. Shepard (1980) indicated that the regression method is
statistically reliable (if used with co-normed tests). whereas Reynolds
(1981) advocated the zrscore method for determining statistically
significant differences. Support for either method has not been
reported; some investigators (Algozzine & Ysseldyke. 1982a; Shepard.

1983) have examined the effectiveness of other methods.

34

mm
The results of this study may demonstrate the diagnostic utility

of certain methods that are currently used for differential diagnosis.
The percentage of false-positive and false-negative diagnoses that do
not affirm the decisions of Educational Placement and Planning
Committees (EPPCs) may be demonstrated.

The sample size of this study was substantial (N = 404) and
comprised a broad spectrum across grades (first through twelfth) so
that method effectiveness could be compared across grade ranges.

The same standardized tests (dependent on age) were used to assess
all students included in this study. Therefore. no variability in
performance may be attributed to different test measures. The LA group
was selected on the basis of specific achievement-score levels.
Selected diagnostic methods were applied to alternate comparisons in an
attempt to indicate differing usefulness. 'The relationship between
student performance and achievement subtests was examined.

The influence of discriminant functions (moderator variables) was
analyzed for their effect on group differences when these differences
were found to be statistically significant.

The students selected for this study were relatively typical of
those referred for psychological evaluation in rural and suburban
areas. All students had been referred for evaluation after attracting
attention in the school environment and were classified by EPPCs as
either L0 or not eligible for special education services. Equal
probability of classification in either category was reasonably assured

by the nature of the EPPCs. ‘These multidisciplinary teams of profes-

35

sionals followed specific procedures for identifying the handicapped.
as mandated by the state of Michigan (effective since 1973). Consid-
eration of ecological factors other than test scores was part of the
classification procedures. and specific steps were taken to ensure
parental involvement. These professional teams were also responsible
for initiating educational plans for students classified as handi-

capped.

The results of this study should provide information on the
usefulness of methods used in differential diagnosis that are absent in
the current literature. 'The comprehensiveness of the study in terms of
sample size and selection should lend credibility to the results. which
can be generalized to the referred population when LD and LA classifi-

cation decisions are the issue.

CHAPTER 3
METHOD

W

The data used in this study were collected during the 1975-76
school year by the Michigan Department of Education. Special Education
Services. Bernard (1978) described many of the essential features of
these data.

Of the 645 school districts in Michigan. 45 agreed to participate
in the data-collection project. Each of the school districts provided
data on all children considered by EPPCs regarding their eligibility
for special education programs and services. ‘The data submitted by
school psychologists encompassed 57 factors. including reason for
referral. WISC-R or other IQ scores. grade placement. chronological age.
sex. WRAT or other achievement scores. and the decisions of the EPPCs.

Data were collected on a total of 1.552 students with a grade
range from 0 through 12.9 (reported in tenths) and a mean grade
placement of 4.8. The age range of the students was from 1.3 through
24.9 years. with a mean age of 10.5.

Of the 1.552 student evaluations submitted. 356 were reevaluated.
The data derived from these reevaluations were not included in this
study. to avoid bias in classification decisions and also because no
information was available about previous classifications or length of

time the student had been receiving special education services.

36

37

The EPPCs assigned the students to five categories: learning
disabled (417). educable mentally impaired (228). emotionally impaired
(137). physically or otherwise handicapped (138). and those students
not found eligible for special education (422). Classification

decisions were not available on 210 students.

Inflamm
Data germane to this study were available for 230 L0 students and

174 students determined not eligible for special education services who
had been included in the data-collection project. Students were
included in the present study if they were classified by EPPCs as L0 or
not eligible for special education services and if their scores from
the Wechsler battery. word recognition subtest scores from the Wide
Range Achievement Test. and grade levels were reported. Students not
eligible for special education were included if they scored below the
26th percentile on the word recognition subtest. Of this group. 125
students scored below the 17th percentile.

The sample used in this study is not purported to be representa-
tive of the special education or general populations in Michigan at the
time of data collection. School districts participated voluntarily in
the data-collection project. 0f the 645 school districts in Michigan.
45 agreed to participate. Suburban and rural districts reported data
for 84.9% of the students included in the study. A sizable percentage
of the students (38.8%) were evaluated by 11% of the participating
districts. A marked percentage (86.6%) of students were male; females
accounted for only 13.4% of the sample. This representation is

disproportionate to the number of females in the general population.

38

but is consistent with sex ratios in L0 populations. It is unknown
whether the reasons for referral are characteristic of the school-
referred population. Students referred for academic reasons
constituted 87.6% of the sample; those referred for behavioral and
physical reasons accounted for 10.1% and .9% of the sample.
respectively. The socioeconomic status of this sample was weighted.
with 1% from high levels. 51.5% from middle levels. and 22% from low

levels. Characteristics of the sample are reported in Table 1.

Mums

The students included in the study were those who had been
classified by EPPCs as L0 or not eligible for special education
services with no discernible handicap. It is unclear what factors the
EPPCs used in making these decisions. However. it is known that all
students had attracted attention in the school environment and were
referred for evaluation because of academic. behavior. or physical
reasons. The majority of students (87.6%) were referred for academic
reasons.

The researcher assumed that the EPPCs followed guidelines for the
identification of handicaps as mandated by the state of Michigan
(effective since 1973) and. more important. that the classification
decisions were accurate. 'Thus it was assumed that the effectiveness of
methods used in the present study to affirm EPPC classification
decisions could be evaluated.

Students who were classified by EPPCs as LD were included in the

study. regardless of their level of ability or achievement scores. if

Table 1. Sample characteristics

39?

 

 

 

 

 

 

Group
LD LA<26th LA< 17th
6 fl. 1 E. z .5
Total number (230) (179) ('25)
Sex
Male 81 (186) 72 (16A) 76 ( 95)
Female 19 ( #3) 28 ( #9) 2h ( 30)
Socioeconomic Status
High 2 ( 3) o ( o) o ( 0)
Middle 69 (123) 69 ( 85) 6S ( 56)
Low 29 ( 52) 31 ( 38) 35 ( 30)
Type of District
Urban 12 ( 26) 9 ( IS) 10 ( 12)
Suburban 27 ( S7) 18 ( 31) 18 ( 23)
Rural 61 (132) 73 (123) 72 ( 90)
Type of Referral
Behavior 8 ( 17) 1h ( 29) 8 ( 10)
Academic 91 (206) 86 (198) 92 (119)
Physical 1 ( 3) 1 ( 1) O ( 0)
IQ Level
0 thrOugh 7h 11 ( 26) 9 ( 15) ll ( 19)
75 through 89 9| ( 99) 50 ( 87) 56 ( 70)
90 through 110 42 ( 97) 37 ( 65) 30 ( 37)
111 through 130 3 ( 7) 1 ( 2) I ( I)
13I through ISO 3 ( 6) 3 ( 5) 2 ( 3)
Mean IQ (g2) 88.00 (12.38) 86.69 (10.01) 84.93 ( 9.58)
Age Ranges
5- 8 32 ( 7A) 35 ( 61) 31 ( 39)
9-11 28 ( 64) 36 ( 62) 32 ( 40)
12-14 25 ( 58) 18 ( 3|) 25 ( 31)
15-17 13 ( 30) 10 ( 18) 10 ( 13)
18-22 1 ( 3) o ( I) I ( I)
Mean Age (g2) 10.67 (3.27) 10.22 (2.87) 10.50 (2.83)
Grade Ranges
l- 3 39 ( 89) 97 ( 81) Ah ( 55)
u- 6 20 ( 47) 22 ( 39) 22 ( 27)
7- 9 26 ( S9) 19 ( 33) 22 ( 28)
10-12 15 ( 35) 12 ( 21) 12 ( 15)
Mean Grade (52) 9.99 (3.01) h.43 (2.78) 9.62 (2.76)

 

Note: Totals vary because of missing data.

available data.

Where totals vary,

percentages are of the

40

data germane to this study were reported. 'The 230 students in the LD
group had reported scores from the Wechsler Battery. word recognition
subtest scores from the Wide Range Achievement Test (Jastak.& Jastak.
1965). and grade-level indicators. Students who were classified as not
eligible for special education services with no discernible handicap
were included if there were scores from the Wechsler Battery. grade-
level indicators. and if their scores from the word recognition subtest
fell below the 26th percentile. These 174 students constituted the LA
group. Of this number. 125 students scored below the 17th percentile
on the test of word recognition.

In the data analysis conducted for the present study. comparisons
were made between the 230 L0 students and the 174 LA students who
scored below the 26th percentile (LA<26th). Identical analyses were
conducted between the LD group and the 125 LA students who scored below

the 17th percentile (LA<l7th).

Demdentlaflabjes

General ability and achievement characteristics of both groups
were compared by computing the degree of variance between group means.
The z-score discrepancy method (Reynolds. 1981) was used for
calculating ability-achievement discrepancies between full-scale IO
scores and word recognition subtest scores. As noted in Chapter 3.
Reynolds reported that a z-score discrepancy model would be useful in
ascertaining whether there was statistically significant variation
between ability and achievement scores on standardized tests. Reynolds
indicated that when test reliabilities from which scores are derived

fall within the range of .90 to .95. an absolute difference of .66

41

standard deviations or more indicates that a significant difference
exists. The reliabilities of the tests used in this study exceeded
this range; therefore. the results represent a conservative estimate of
statistically significant differences. Reynolds'inethod was applied in
two ways: absolute differences between ability and achievement scores
and directional differences (mathematical signs used in calculations).

The variance in achievement subtest scores (word recognition.
spelling. and reading) was calculated by two methods: range (highest
minus lowest (Algozzine & Ysseldyke. 1982a; Epps et aL» 1982) and mean
deviation (difference between the student's overall achievement mean
and the most variant achievement score.

The degree of scatter (variance) on ability tests was calculated
by three methods: range (highest minus lowest scaled score; Algozzine
& Ysseldyke. 1982a; Epps et al.. 1982). range (NDEV. variance by three
or more scaled score points from the student's mean; Kaufman. 1976a;
Veres. 1982). and mean deviation (difference between the student's IO
mean and scaled scores which exceeds that required at the .15

confidence level).

W155
Although statistically significant differences may be obtained in

some of the analyses included in this study. they do not necessarily
offer direct evidence on the question of utility. Diagnostic rules are
useful if they aid in differential diagnosis. That is. the rule can be
applied to student characteristics and can result in appropriate

classification decisions that do not exceed an acceptable error level.

42

Deno and Mirkin (1977) suggested that a student should be performing at
half the rate of the average student to require intervention from
special education services. This rule is relatively straightforward.
with a criterion establishing the need for services. However. the
method of implementation (how achievement is assessed) may contain
errors that result in misdiagnosis.

The diagnostic criteria and methods reviewed in Chapter 2 and used
as dependent variables in this study were applied to student test
performance results. They can be considered useful in differential
diagnosis if they affirm the EPPC classification decisions and
differentiate at least 85% of the LD from the LA students. Although
this level of usefulness is better than chance. it is an arbitrary
criterion proposed in this study. It is. however. more generous than
the criterion established by interpretation of the federal regulations
for the identification of learning disabilities. which allows no error
in classification. The percentage of students in each group who would
have been misdiagnosed by the criteria and methods used are reported as
false-positive and false-negative decisions and are compared with the

85% level to validate differential diagnostic usefulness.

Siiiisilcnl_lnfiatm§n1
For purposes of this study. any statistical procedure that
resulted in variance between groups at a .05 or greater level of
confidence was judged to be significant. The Statistical Package for
the Social Sciences (Hull & Nie. 1981) was used for analyses.
Correlation analyses were conducted on achievement subtest scores.

dependent variables. and moderator variables. Pearson product-moment

43

correlations and resultant probability levels were used to determine
whether to conduct further analyses assessing the influence of these
variables. When the variables were highly correlated (.p g .05). it was
assumed that a degree of interdependence existed. and analyses were
conducted using the most inclusive variable.

The significance of variance between groups on general ability and
achievement characteristics was derived from pooled t-tests because
variance was assumed to be unequal unless otherwise found.

Univariate analyses of variance were calculated between groups on
all dependent variables. These analyses were conducted on an overall
design with all discriminant functions included. A full factoral model
adjusting for unequal cell frequencies set initial levels of variance
with which resultant discriminant function analyses could be compared.
A model of univariate variance was used to calculate the degree of
influence moderator variables had on the variance of dependent
variables.

The percentage of false-positive and false-negative diagnoses was
calculated to indicate the usefulness of dependent variables in terms

of diagnostic utility.

1111101115595

This study was designed to evaluate the effectiveness of criteria
and methods used for differential diagnosis of L0 as compared to LA
students. Comparisons to EPPC classification decisions were essential
to this evaluation. The hypotheses tested in this study are as

follows:

44

Hypothesis 1: Comparisons of the general intelligence character-
istics of LD and LA students will not lead to a useful decision
rule in differential diagnosis.

Hypothesis 2: Comparisons of the general achievement character-
istics of LD and LA students will not lead to a useful decision
rule in differential diagnosis.

Hypothesis 3: Comparisons of ability-achievement discrepancy
levels of LD and LA students will not lead to a useful decision
rule in differential diagnosis.

Hypothesis 4: Comparisons of ability-test scatter indices of LD
and LA students will not lead to a useful decision rule in
differential diagnosis.

Hypothesis 5: Comparisons of verbal-performance ability test
results of LD and LA students will not lead to a useful decision
rule in differential diagnosis.

CHAPTER 4

RESULTS

Quentin

The primary focus of this research was to analyze the performance
of LD and LA students on standardized ability and achievement tests to
determine if useful diagnostic decision-making rules could be
validated. Of particular importance was the distinction between
statistical and applied practical value. Although some analyses may
provide statistical evidence affirming theoretical concepts. their
ability to differentiate between handicapped (LD) and noneligible (LA)
students should be of concern to those individuals making educational
decisions.

Analyses were conducted on two groups of students: 230 L0
students (grades 1 through 12) and 174 LA students scoring below the
26th percentile on a test of word recognition. Of the latter group.
125 students scored below the 17th percentile on the word recognition
test. Comparisons were made between the LD students and both groups of
LA students. Sample characteristics were discussed in Chapter 3 and
were presented in Table 1.

In this chapter. each hypothesis is restated in the testable null
form. The results of the statistical analyses are presented and

discussed. A final section includes findings that are of general

‘IS

A6

interest but are not necessarily related to the hypotheses

investigated.

mmmmmmmmmmm
Winn:

Hypothesis 1 was formulated to compare the ability test
performance of the two groups of students (LD and LA).

Hypothesis 1: Comparisons of the general intelligence character-

istics of LD and LA students will not lead to a useful decision

rule in differential diagnosis.

The means. standard deviations. and t—test Erratios and
probability levels comparing the means are given in Table 2 for each
group and each comparison. Casual inspection of the means and standard
deviations indicates a degree of difference that would be of little
value to diagnosticians. The differences between means ranged from
(L24 points when the LD and LA<26th groups were compared on performance
abilities to 3.07 points when the LD and LA<l7th groups were compared
on verbal abilities. Given the format of the WISC-R and the WAIS and
the degree of measurement error (3.19). such differences would be of
little diagnostic value.

When t-tests were used to calculate the significance of group mean
differences. two comparisons indicated statistical significance. 'The
difference between the LD and LA<l7th groups for Full Scale means was
2.82 points. which was significant at the .01 level. The Verbal IO
difference between the LD and LA<l7th group means was 3.07 points.
which was significant at the .01 level. Are these differences in test
results useful for purposes of diagnostic utility? Table 3 indicates

the degree of misidentification that would occur if ability test means

'17

 

 

 

 

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sum—v<4 a; Luva<4 o;

 

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.mo_aEmmn:m coozuon muococoww_o acmu_u_cmmm Lem m_o>o_ >u___nmnoLa ocm monumcum amouuh .N o_nmh

118

 

 

 

 

 

 

 

 

 

 

 

Table 3. Summary of use of ability and achievement characteristics to classify students
Correct Incorrect Percent Percent Percent
Measure Classification Classification False False Incorrect
LA LD LA LD Positive Negative Overall
Use of Ability Characteristics
LD and LA<26th
“1225“” 102 120 72 110 1.1 118 1.5
Verbal IQ 90 119 89 111 98 #8 98
Pergormance 83 128 9‘ '02 52 1.1; 158
L0 and LA<l7th
”:32 5‘3" 82 117 1.3 113 31. 1.9 M.
Verbal IQ 78 132 47 98 38 A3 hi
Peraormance 70 ‘3] 55 99 Ah A3 63
Use of Achievement Characteristics
LD and LA<26th
Reading 71. 11.9 100 81 S7 35 1.5
Recognition
Spelling 81 127 93 103 53 ‘15 I19
Arithmetic 100 11.0 74 9o 1.3 39 '11
LD and LA<l7th
Reading 50 1&9 75 81 6O 35 ha
Recognition
Spelling 52 127 73 103 58 AS 50
Arithmetic 72 9O 53 190 #2 61 5h

 

’49

were used as diagnostic criteria to classify students in the three
groups. Forty-three of the LA<l7th group and 113 of the LD group
obtained scores on Full Scale 10 measures that were closer to the other
group's mean than to their own group's. The degree of overall
incorrect classification that would result if group means were used as
a basis for diagnosis was 44%. Similar results were obtained for
Verbal IO mean comparisons. with an overall error rate of 41%.
Applying this method to determine diagnostic utility where differences
between group means were not statistically significant indicated an
even higher degree of misidentification; the highest overall incorrect
percentage was between the LD and LA<26th groups on measures of Verbal
and Performance 10. In all analyses. the degree of misidentification
that would occur if observed differences between groups on the ability
test were used for classification exceeded the level set in this study
as acceptable for diagnostic utility (15%). Therefore. Hypothesis 1

was not rejected.

WWW

Hypothesis 2 was formulated to compare the achievement test
performance of the two groups of students (LD and LA).

Hypothesis 2: Comparisons of the general achievement character-

istics of LD and LA students will not lead to a useful decision

rule in differential diagnosis.

The means. standard deviations. and t-test E—ratios and
probability levels comparing the means are given in Table 2 for each
group and each comparison. Inspection of these indices indicated that

differences between the groups were too small for diagnostic purposes.

Actual differences between achievement test means of the LD and LA<26th

50

groups ranged from 0.0 to .22 for word recognition results. With the
exception of arithmetic. the LA groups obtained means that were higher
than those of the LD group. It should be noted that the higher mean
(2.87) obtained by the LA<l7th group. as compared to the mean obtained
by the LA<26th group (2.86) on arithmetic was not due to statistical
error. The LA group had been subdivided on the basis of their scores
on reading recognition.

Analyses of variance computing group differences in achievement
score range did not yield statistically significant results. The
results of these analyses for both methods are presented in Tables Al
and A2 in the Appendix.

Do the differences in achievement test results offer any
diagnostic value for classification purposes? Table 3 indicates the
degree of misidentification that would occur if achievement test group
means were used to classify students. The degree of overall incor-
rectness that would result if proximity of the student's score to the
group mean score was used for classification exceeded the level for
diagnostic utility (15% incorrect). The lowest overall incorrect
percentage was 41%. which was obtained for L0 and LA<26th group
comparison on arithmetic results. In this comparison. 74 students in
the LA<26th group and 90 L0 students had scores that were closer to the
other group's mean. Based on the degree of misclassification that
would occur if the degree of difference between group means on
achievement test results was used to classify students. Hypothesis 2

was not rejected.

51

WW

Hypothesis 3 was formulated to compare LD and LA students in terms
of discrepancies between ability and achievement test results.
Hypothesis 3: Comparisons of ability-achievement discrepancy

levels of LD and LA students will not lead to a useful decision
rule in differential diagnosis.

MW
We:

Using Reynolds'(1981) formula. the numbers and percentages of
each group were calculated for various zrscore discrepancy levels. The
results are presented in Table 4. The results indicated that no group
met the criterion for diagnostic utility (85% affirmation rate). as
defined in this study.

Of the LD group. 35% had discrepancy levels that fell within the
nonstatistically significant range (0.0 through 0.65 standard
deviations). as reported by Reynolds. When discrepancy levels were
reviewed by grade ranges. the figures remained fairly consistent with
the overall percentages for grades 1 through 12. The highest
percentage of students in the LD group who were identified as being
correctly classified by this method were in grades 10 through 12; 69%
of these students exhibited statistically significant discrepancies.
Discrepancy-level calculations for the LA groups indicated that
approximately 50% of both groups. overall and in specific grade ranges.
had discrepancies within the statistically significant range. If the
discrepancy method is useful for differentiating between the LD and the

LA student. it was not verified by the results reported in this study.

Table 4.

52

discrepancy levels

Percentages and numbers of students scoring at z-score

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Group
Discrepancy Levels
(Standard Deviations) LD LA<26th LA<l7th
Z N_ 2 N_ 2 N_
Grades 1 Through 12
2.00 through 4.00 10 (23) 6 (11) 6 ( 7)
1.50 through 1.99 11 (25) 4 ( 7) 5 ( 6)
1.00 through 1.49 27 (61) ll (20) 12 (15)
0.66 through 0.99 17 (40) 24 (42) 24 (30)
0.00 through 0.65 35 (81) 54 (94) 54 (67)
Grades 1 Through 3
2.00 through 4.00 8 ( 7) 7 ( 6) 5 ( 3)
1.50 through 1.99 10 ( 9) 5 ( 4) 5 ( 3)
1.00 through 1.49 24 (21) 11 ( 9) I3 ( 7)
0.66 through 0.99 l9 (17) 20 (16) 18 (10)
0.00 through 0.65 39 (35) 57 (46) 58 (32)
Grades 4 Through 6
2.00 through 4.00 6 ( 3) 3 ( 1) O ( O)
1.50 through 1.99 11 ( 5) 0 ( 0) 0 ( o)
1.00 through 1.49 32 (15) 10 ( 4) 11 ( 3)
0.66 through 0.99 17 ( 8) 31 (12) 30 ( 3)
0.00 through 0.65 34 (16) 56 (22) 59 (16)
Grades 7 Through 9
2.00 through 4.00 12 ( 7) 9 ( 3) 11 ( 3)
1.50 through 1.99 14 ( 8) 9 ( 3) 11 ( 3)
1.00 through 1.49 27 (16) 6 ( 2) 7 ( 2)
0.66 through 0.99 15 ( 9) 27 i 9) 29 ( 8)
0.00 through 0.65 32 (19) 48 (16) 43 (12)
Grades 10 Through 12
2.00 through 4.00 17 ( 6) 5 ( l) 7 ( 1)
1.50 through 1.99 9 ( 3) O ( 0) O ( 0)
1.00 through 1.49 26 ( 9) 24 ( 5) 20 ( 3)
0.66 through 0.99 17 ( 6) 24 ( 5) 27 ( 4)
0.00 through 0.65 31 (11) 48 (10) 47 ( 7)
Note: Percentages are approximate and are reported to the nearest

whole number.

53

W
W

Reynolds (1981) was concerned with the absolute difference between
ability and achievement test results when calculating the degree of
discrepancy (for statistical purposes). On the other hand. the
directionality of the zrscore when mathematical signs were not ignored
was surprising. When the difference between the IQ score and the IQ
test mean was greater than the difference between the achievement test
score and the achievement test mean. a negative zrscore was obtained.
When such calculations resulted in a negative Zescore. the student was
achieving better than what would be expected on the basis of the
ability (IO) assessment. The percentages and numbers of students in
each group who scored at negative zrscore discrepancy levels is
reported in Table 5. 0f the LD group. 12% achieved better than
expected at a statistically significant level. and 25% had actual z-
scores that indicated this directionality. Given the degree of corre-
lation between achievement subtest scores (reported under general find-
ings). it seems doubtful that low achievement was a major factor in
classifying at least 12% of the LD group (25% if statistical signifi-
cance was ignored). 'This finding may explain. in part. the classifica-
tion of the LA students as not eligible for services. If better-than-
expected achievement was part of the diagnostic process and if no other
contributing factors were identified that influenced classification as
LD. at least 8% of the LA<26th group and 6% of the LA<l7th group
appeared to be doing better than expected on school-related tasks.

As indicated in Chapter 2. a number of formulas have been

developed to quantify ability-achievement discrepancies. The current

54

Table 5. Percentages and numbers of students scoring at Efscore
discrepancy levels with negative directionality

 

 

 

 

 

 

 

 

 

 

 

 

 

Group
Discrepancy Levels LD LA<26th LA<l7th
(Standard Deviations)
2 N_ 2 N_ 2 ‘N
Grades 1 Through 12
-0 66 through -4.0 12 (28) 8 (14) 6 ( 7)
-0.0l through -4.0 25 (58) 29 (50) 27 (34)
Grades 1 Through 3
-0.66 through -4.0 19 (17) 10 ( 8) 5 ( 3)
-0.0l through -4.0 34 (30) 3O (24) 29 (16)
Grades 4 Through 6
-O.66 through -4.0 11 ( 5) 5 ( 2) O ( 0)
-0.01 through -4.0 I9 ( 9) 21 ( 8) 15 ( 4)
Grades 7 Through 9
-O.66 through -4.0 8 ( 5) 6 ( 2) 7 ( 2)
-0.01 through -4.0 20 (12) 39 (13) 36 (10)

 

Grades 10 Through 12

 

-O.66 through -4.0 3 ( 1) 10 ( 2) l3 ( 2)
-o.01 through -4.0 20 ( 7) 24 ( 5) 27 ( 4)

 

Note: Percentages are approximate and are reported to the nearest
whole number

55

federal definition specifically states that a condition of learning
disabilities is: 'Whe child does not achieve commensurate with his or
her age and ability levels in one or more of the areas listed (USOE.
1977. p. 65082). The results presented in this study indicate that a

sizable percentage of the LD group did not meet that criterion.

WW

To assess the degree of variance between groups. univariate
analyses of variance were calculated between groups in five grade
ranges. with zrscore discrepancy levels as the dependent variable. The
results of these analyses appear in Table A1 and A2 in the Appendix.
Table 6 indicates the variance of discrepancy levels between grade
ranges when both the LD and LA<26th groups were combined. This
analysis was conducted to assess if particular grade ranges could be
identified in which the degree of discrepancy was most prominent.
Homogeneous grade ranges (not differing by more than the degree
required for statistical significance) appeared to be grades 4-6. 7-9.
and 10-12. Grades 1-3 appeared to be the most variant; the mean for
these grades was 6.03. which varied from the next closest grade range
(grades 7-9) by .48 points.

To assess for sources of variation within grade ranges. analyses
of variance were conducted for the LD and LA<26th groups at grade
ranges in separate analyses. The degree of variation between grade
ranges for the LA<26th group was not significant (p = .91). as
indicated in Table 7. A11 grade ranges were homogeneous; none differed

by the range required for statistical significance at the .05 level.

56

Table 6. Analysis of variance--discrepancy levels at grade ranges:
LD and LA<26th groups

 

 

 

Source of Variation d:_ Mean Square [fRatio '3
Between grades 3 14.97 4.12 .01
Within grades 400 3.63
Means
Grades 1-3 = 6.03 Grades 7-9 = 6.51
Grades 4-6 = 6.67 Grades lO-12 = 6.89
Grand Mean = 6.40

 

Table 7. Analysis of variance--discrepancy levels at grade ranges:
LA<26th group

 

 

 

Source of Variation 3:. Mean Square EfRatio '3
Between grades 3 .53 .19 .91
Within grades 170 2.85
Means
Grades 1-3 = 6.06 Grades 7-9 = 6.27
Grades 4-6 = 6.26 Grades 10-12 = 6.19

Grand Mean = 6.16

 

Significant variation between grade ranges was found to exist in
the LD group. Table 8 indicates the source of variation as grades 10-
12 being significantly different from grades 1-3. Figure 1 shows this
variation. as well as the variation between groups at all grade ranges

other than grades 1-3.

57

Table 8. Analysis of variance-~discrepancy levels at grade ranges:

 

 

 

LD group
Source of Variation .g: Mean Square ffRatio .2
Between grades 3 18.58 4.47 .00
Within grades 226 4.16
Means
Grades 1-3 = 6.00 Grades 7-9 = 6.89
Grades 4—6 = 6.72 Grades 10-12 = 7.31

Grand Mean = 6.58

 

Levels

 

 

 

O‘O‘NV
UT

U1
U‘l

 

U1
0

 

1-3 4—6 7-9 10'12
Grade Ranges

LD
LA<26th

><
ll II

Figure 1. Discrepancy level means at grade ranges for
L0 and LA<26th groups.

58

Univariate analyses of variance with discrepancy level as the
dependent variable were conducted between the LD and LA<l7th groups.
As reported in Table A2. no statistically significant variance was
found to exist between groups (p = .20). When the groups were
combined. there was significant grade-range variability (p = .03).
Table 9 indicates the combined-group means; Figure 2 illustrates the
variance.

Table 9. Analysis of variance--discrepancy levels at grade ranges:
LD and LA<l7th groups

 

 

 

Source of Variation d:_ Mean Square [fRatio .2
Between grades 3 11.32 3.10 .03
Within grades 354 3.65
Means
Grades 1-3 = 6.12 Grades 7-9 = 6.74
Grades 4-6 = 6.60 Grades 10-12 = 6.92

Grand Mean = 6.48

 

7.0
6.8
E 6.5
>
G)
"’ 6.2
5.9

 

 

1-3 4-6 7-9 10‘12

Grade Ranges

Figure 2. Discrepancy 1evel means at grade ranges for L0
and LA<l7th groups.

59

In summary. the LD group was found to exhibit statistically
significant variance in discrepancy levels. whereas no statistically
significant variance was noted in the LA<26th or the LA<l7th groups.
There did appear to be statistically significant variance between the
LD and LA<26th groups for all grade ranges except grades 1-3. Variance
between the LD and LA<l7th groups was found not to exist; however. when
grade ranges of both groups were combined. statistically significant

differences did exist between grade ranges.

W
W

Although the univariate analyses between groups using discrepancy
levels as a dependent variable indicated statistical significance. they
shed no light on the question of diagnostic utility. Using Reynolds'
(1981) formula for absolute differences between ability-achievement
performance. discrepancy-level scores were used to compare groups. If
a LD student exhibited a discrepancy level equal to or exceeding .66
standard deviation. he/she was judged to be correctly classified (even
though a reliable difference between ability and achievement does not
necessarily indicate a need for special education services).
Conversely. if a LA student exhibited.a.66 standard deviation or
greater discrepancy. he/she was judged to be incorrectly classified.
The results of these analyses are presented in Table 10.

From inspecting the data presented in Table 10. it is apparent
that the z-score discrepancy-level method does not satisfy the
criterion for diagnostic utility. as set in this study. Although 65% of

the LD group were correctly classified using this method. 46% of the LA

60

groups were incorrectly classified. For the practitioner who wishes to
be correct 60% and 59% of the time. such a method would be useful. Of
the LA<26th group. 805tudents exhibited discrepancy-level scores that
met the criterion for statistical significance and would subsequently
be diagnosed as LD (false positive) if this method was used for
classification. Of the LA<l7th group. 58 students met the same
criterion. whereas 81 of the LD group would be judged as non-L0 (false
negative). The overall incorrect percentages (40% and 39%) reflect the
error when both false-positive and false-negative indicators are
combined. Based on the results of these analyses. Hypothesis 3 is not
rejected.

Table 10. Summary of the use of z-score discrepancy levels to
classify students

 

 

 

 

LD LA<26th
Correct classification 149 94
Incorrect classification 81 80
Percent false positive .. 46
Percent false negative 35 ..
Percent incorrect overall--40

LD LA<l7th
Correct classification 149 67
Incorrect classification 81 58
Percent false positive .. 46
Percent false negative 35 ..

Percent incorrect overall--39

 

61

.Ab1l1Ix:Iest_Subtast_§cattez_comnatlsons

Another proposition presented earlier concerned the amount of
scatter in ability subtest scores of the L0 as compared with the scores
of the LA student. Hypothesis 4 addressed these comparisons.

Hypothesis 4: Comparisons of ability-test scatter indices of LD

and LA students will not lead to a useful decision rule in

differential diagnosis.

Ability-test subtest scatter was used to compare groups and was
calculated in three ways: range (highest minus lowest scaled score).
Kaufman's NDEV measure (variance from the student's mean by three or
more points by scaled scores). and mean deviation (variance from the
student's mean by the most variant scaled score). This within-person
variance was calculated in numerical quotients from which mean
comparisons were made. Only those scaled-score deviations from the
student's mean that exceeded the difference required at the .15 level
of confidence were used in calculating mean deviated scatter.

Table 11 contains the group means for the three measures of
calculated scatter.- Casual inspection of the data in this table

indicates that no differences are apparent that would be of diagnostic

utility.

Table 11. Group means for three measures of IO scatter

 

 

Group Range NDEV Mean Deviation
LD 10.83 1.23 1.67
LA<26th 9.97 .05 2.52

LA<l7th 9.97 .64 2.34

 

62

Wang
W

Analyses of variance using each method of calculating scatter as a
dependent variable were performed to ascertain whether significant
group differences existed. The results of these analyses are reported
in Tables Al and A2. Scatter calculated using the NDEV method was
found to be significantly variant between the LD and LA<26th groups
(p = .02). Table 12 reflects the degree of variance between group

means when grade-range comparisons were not made.

Table 12. Analysis of variance--IO scatter (NDEV): LD and LA<26th

 

 

 

groups
Source of Variation .0: Mean Square lffRatio .2
Between groups 1 132.27 5.213 .02
Within groups 402 26.33

Means

Grand Mean = -0.713

 

To assess for causal factors. analyses of variance were performed
for each group at grade ranges. Tables 13 and 14 illustrate the degree
of variance within groups at different grade ranges. Figure 3
illustrates the degree of variance between groups at the four grade
ranges.

The degree of variance between grade ranges within the LA<26th
group was found not to be significant. All grade-range means were

homogeneous; variance did not exceed the range required at the .05

63

level of confidence. Similar variance was found to exist within the LD
group. When the groups were compared. however. statistically
significant grade-range differences were found to exist. particularly
at grade range 1-3. with a variance of 2.38 points between the LD and
the LA<26th groups.

Table 13. Analysis of variance--IO scatter (NDEV) at grade ranges:

 

 

 

LD group
Source of Variation g:_ Mean Square FfRatio ‘2
Between groups 3 71.47 2.05 .11
Within grades 226 34.88
Means
Grades 1-3 = -2.27 Grades 7-9 = -0.29
Grades 4-6 = -1.42 Grades 10-12 = -0.13

Grand Mean = 1.23

 

Table 14. Analysis of variance--IO scatter (NDEV) at grade ranges:
LA<26th group

 

 

 

Source of Variation d:_ Mean Square ffRatio .2
Between grades 3 4.01 .28 .84
Within grades 170 14.55
Means
Grades 1-3 = -0.11 Grades 7-9 = 0.02
Grades 4-6 = -O.31 Grades 10-12 = 0.60

Grand Mean = -0.05

 

64

0.60

0.30

-0.60
-O.9O
-1.20
-i.50
-1.80
-2.10

-2.40

 

 

1-3 4-6 7-9 10-12
Grade Ranges

LD
LA<26th

X0
11 11

Figure 3. 10 scatter (NDEV) means at grade ranges:
LD and LA<26th groups.

WWW):

Does this statistically significant variance between groups have
value for decision-making rules? Table 15 presents the results of
classification decisions based on the degree of scatter for the three
methods. Using range and mean-deviation methods. the proximity of the
student's score to his/her group mean was used as the basis for
classification. When the score was closer to the other group's mean

than to the student's own mean. the method used misclassified the

65

 

 

 

 

 

 

 

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acoOLom ucoocom acoocom uooccooc_ HouLLOU

 

mucooaum >w_mmm_o 0u moOLuoE couumum mo om: mo >Lm553m .m. o_nmh

66

student. Using the NDEV method. students were classified according to
the degree of scatter. A student was correctly classified as LD if
his/her scaled scores varied three or more points from the mean of
his/her overall ability test performance. A LA student was correctly
classified if his/her scaled scores varied less than three points from
the mean of his/her overall ability test performance.

Inspection of the data presented in Table 15 indicates that the LD
group would be misclassified to a greater extent than the LA groups.
when the NDEV and mean-deviation methods are used. The range method
(highest minus lowest scaled score) is the most promising for correct
classification of the LD group. although it still does not meet the
criterion set in this study for diagnostic utility. No one method was
able to differentiate between groups with a degree of misclassification
of 15% or less. When percentages of misclassification were combined.
the error rate ranged from 43% to 66%. Based on the analyses conducted
and the degree of misclassification that would occur using methods for

calculating IO scatter. Hypothesis 4 is rejected.

WW

As discussed in Chapter 3. researchers have postulated a
difference between verbal-performance ability test scores that may
distinguish the LD student from others who do not possess any
discernible handicap. As Kaufman (1976b) noted. a difference of 12
points between these scores is required for statistical significance at
the .05 level of confidence. Hypothesis 5 states that observed
differences between the groups included in this study will not assist

in the formulation of useful decision rules.

67

Hypothesis 5: Comparisons of verbal-performance ability test
results of LD and LA students will not lead to a useful decision
rule in differential diagnosis.

To evaluate Hypothesis 5. students included in the study were
compared using two methods of analyzing verbal-performance 10 score
differences: Kaufman's difference of 12 or more points and a mean
deviated method in which each scaled score was included in the
calculations if it differed from the student's overall ability test

Inean by the difference required at the .15 confidence level (reported

in the test manual).

W

The percentages and numbers of students for each group as they
scored on the two methods are reported in Table 16. Inspection of the
data indicates that no marked percentages of students in any group
scored at one level on either method or the directional aspects of one
method. Forty-eight percent of the LD students in grades 1 through 12
obtained scores that equaled their performance ability scores on the
mean deviation method. Similar results (35% and 33%) were indicated
for the LA groups. 'The method using 12 or more point differences failed
to differentiate any group at the level set in this study for useful
decision rules (85%). Fifty-eight percent of the LD group had verbal-
performance differences of less than 12 points. as did 70% of the
LA<26th group and 67% of the LA<l7th group.

WWW
WEED—Gm

Analyses of variance were conducted using two methods as dependent

variables. The results of the analyses are reported in Tables Al and

Table 16.

(38

Percentages and numbers of students scoring at mean deviated and actual
differences between Verbal-Performance le

 

 

 

 

Mean Deviated Actual
v<P v-P v>P v<P v-r v>P ViP<12
23121292123232!

£3
A11 grades 19 (44) 48 (110) 33 (76) 22 (51) S (12) 15 (34) 58 (I33)
Grades 1-3 19 (17) 45 ( 48) 27 (24) 18 (I6) 7 ( 6) 29 (18) 55 ( 49)
Grades 4-6 29 (12) 47 ( 22) 28 (13) 17 ( 8) 6 ( 3) 19 ( 9) 57 ( 27)
Grades 7-9 20 (12) 39 ( 23) 41 (24) 24 (14) 3 ( 2) 7 ( 4) 66 ( 39)
Grades 10-12 9 ( 3) 49 ( 17) 43 (15) 37 (13) 3 ( 1) 9 ( 3) 51 ( 18)
3822959
All grades 22 (38) 35 ( 61) “3 (75) 6 (10) 4 ( 7) 20 (35) 70 (1221
Grades 1-3 22 (18) 41 ( 33) 37 (3o) 6 ( 5) 6 ( 5) 11 ( 9) 77 ( 62)
Grades 4-6 23 ( 9) 28 ( ll) 49 (19) 5 ( 2) 3 ( l) 31 (12) 62 ( 24)
Grades 7-9 21 ( 7) 36 ( 12) 42 (14) 6 ( 2) 3 ( 1) 27 ( 9) 64 ( 21)
Grades Io-12 19 ( 4) 24 ( 5) s7 (12) 5 ( 1) o ( o) 24 ( 5) 71 (115)
Lfiillsb.
All grades 22 (28) 33 ( 4|) 45 (S6) 7 ( 9) 2 ( 2) 24 (30) 67 ( 84)
Grades I-3 24 (I3) 38 ( 2|) 38 (2|) 4 ( 5) 2 ( I) 7 ( 9) 73 ( 40)
Grades 4-6 19 ( 5) 30 ( 8) 52 (14) 4 ( 1) o ( o) 33 ( 9) 63 ( 17)
Grades 7-9 25 ( 7) 29 ( 8) 46 (13) 7 ( 2) 4 ( 1) 29 ( 8) 61 ( 17)
Grades 10-12 20 ( 3) 27 ( 4) 53 ( 8) 7 ( 1) 0 ( 0) 27 ( 4) 67 ( 10)

 

Note:

V-P column in Mean Deviated category

required for significance at the .15

Percentages are approximate and are reported to the nearest whole number.

indicates any difference less than what is

level.

69

AZ. No variance approaching the .05 level of confidence was found to

exist for either method.

Diagnostic_0tilltx_o£
WW9:

To assess the question of diagnostic utility. comparisons were
made between the classifications by EPPCs and the effectiveness of these
methods to confirm such classifications. 'Table 17 presents the results
of the comparisons. Using the actual-difference method (12 or more
points). 63% of the LD group were incorrectly classified. Five percent
of the LD group had equal verbal and performance scores. and 58% had
verbal and performance scores that were not equal but were less than
12. These false-negative classifications far exceeded the level for
useful decision-making rules (15%). In comparison. 26% of the LA<26th
group and 31% of the LA<l7th group were classified as false positive
(having differences of 12 or more points). The mean-deviation method
offered more congruence of classification decisions for the LD group.
yet it still markedly exceeded the level for usefulness (15%). 0f the
LD group. 48% were incorrectly classified (false negative) using this
method. The overall percentage error rates for both methods ranged
from 47% to 55%. which offers little support for the diagnostic utility
of these methods for useful decision-making rules. Based on the

analyses conducted in this study. Hypothesis 5 cannot be rejected.

We:
The findings presented in this section relate to the hypotheses

and methods presented in Chapter 3. Some of the findings might not

focus directly on the usefulness of decision-making rules. but they are

7O

 

 

 

 

 

 

 

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mucoosum >m_mmm_o Cu moococomw_o oucmEc0uc0a1_mnco> *0 mm:

Io >cmEEJm .N_ 0.4mh

71

presented here to clarify certain aspects of the groups studied and the
methodology used. The tables referred to in this section are found in

the Appendix.

WWW

Pearson product-moment correlations were computed between the
achievement test results of all groups included in this study.
Between-group correlations were also calculated. The results of the
correlational analyses indicated that variability in the two groups'
performance on the three subtests (word recognition. spelling.
arithmetic) was minimal. The performance of the LD group and that of
the LA groups on these measures were highly correlated. The
coefficients ranged from .552 to .923. all of which were significant at
the .001 level of confidence. The correlations of achievement
performance between the groups indicated similar results. ‘The
coefficients ranged from .638 to .849. and all were significant at the
.001 level of confidence. Hypothesis 2 stated that comparison of
general-achievement characteristics would not lead to useful decision-
making rules for differentiating between groups. ‘The results presented
here would appear to verify this assertion. Performance on the
achievement test included in this study indicated no statistically

significant variance between the two groups of students.

WWI-elation

With the exception of discrepancy-level calculations. the
dependent variables used in this study were assessed in two or more

ways. Two methods were used to evaluate Verbal-Performance IQ

72

differences. three methods were used with ability-subtest scatter. and
two methods were used to evaluate achievement variability. Pearson
product-moment correlations were computed between the methods. to
assess the statistical relationship. ‘The methods used within each
analysis were highly correlated with each other. ‘The coefficients
ranged from .19 to .93. all of which were significant at the .00 level

of confidence.

W

The degree of correlation (Pearson product moment) between
covariates served as a basis for exclusion in the analyses of
discriminant functions reported in this section. In Chapter 3. it was
indicated that the influence of discriminant functions (moderator
variables) would be investigated when overall analyses of variance were
statistically significant. The selection of covariates included in
these analyses was based on the relationship between covariates. as
determined by correlation significance. Table A5 presents the results
of the correlations between covariates. Covariates of IO level. sex.
and primary referral reason were found to be correlated at a statis-
tically significant level with all other covariates but not with each
other. Therefore. these covariates were found to be independent of
each other in terms of the degree of influence on variance between

groups.

Wm:

A univariate analysis with covariates uses a linear regression

format that adjusts for the variance between groups caused by the

73

discriminant function (moderating variable). The resultant E-ratios
and significance levels are derived after these adjustments are made.
Comparing the resultant statistical significance with the overall
analysis (covariate included) gives an indication of the effect of the
covariate on the degree of variance observed in the overall analysis.
Covariates of IQ level. sex. primary referral reason. type of district.
socioeconomic status. and age were defined as covariates in this study.
Grade range was included in all overall analyses. 10 level. sex. and
primary referral reason were found to be significantly related to all
other covariates. but they were independent of each other. The
influence of these covariates on statistically significant between-
group variance was evaluated.

D1screpancy:1exel_yaniance. To ascertain the degree of influence
covariates had on the variation between groups. separate univariate
analyses with covariates were conducted. ‘The results of these analyses
are reported in Tables A6 and A7. Primary referral reason and sex were
not found to be significant in producing the observed variation between
groups in the overall analysis. The significance levels of t-values
indicating covariate effect did not approach the .05 level of
confidence. and there was no significant change in the variation when
compared with the overall analysis. IO level appeared to have a
significant effect in producing the variation in the overall analysis.
A .t-value of 19.25 with significance at 0 for the LD and LA<26th group
comparison and a t-value of 18.10 with significance at 0 for the LD and
LA<l7th group comparison indicated the IO-level effect. The adjusted

means with variance not influenced by IO level are depicted in Figures

74

4 and 5. Comparison of these means with the nonadjusted means shown in
Figure 1 indicates a high degree of similarity in both mean differences
and overall direction. The effect of IO level. while statistically
significant. did not appear markedly to influence group differences.

IO level appeared to have the same effect for the LD and LA<l7th group

 

 

comparisons.
7.5
7.0
m 6.5
'6
6 6.0
" Q
5.5
5.0
1'3 4'6 7-9 10-12
Grade Ranges
X = LD
0 = LA<26th
Means
1.3 LA<26th
Grade Range 1-3 = 5.67 Grade Range 1-3 = 5.91
Grade Range 4-6 = 6.58 Grade Range 4-6 = 6.34
Grade Range 7-9 = 7.10 Grade Range 7-9 - 6.50
Grade Range 10-12 = 7.31 Grade Range 10-12 = 6.30

Figure 4. Adjusted discrepancy level means at grade ranges:
LD and LA<26th groups.

75

7.0 //
6.5

 

 

 

U1 N
'8
3 6 O
_1
5.5
5.0
1'3 4-6 7'9 10-12
Grade Ranges
X = LD
0 = LA<17th
Means
Lg LA<l7th
Grade Range 1-3 = 5.67 Grade Range 1-3 = 5.91
Grade Range 4-6 = 6.58 Grade Range 4-6 = 6.34
Grade Range 7-9 = 7.10 Grade Range 7-9 = 6.50
Grade Range 10-12 = 7.31 Grade Range 10-12 - 6.30

Figure 5. Adjusted discrepancy level means at grade ranges:
LD and LA<17th groups.

IQ_scai:su;1fl0£¥l_1aniange. To ascertain the degree of influence
covariates had on the significant variation between groups. separate
univariate analyses with covariates were conducted. ‘The results of
these analyses are reported in Tables A6 and A7. None of the covari-
ates (10 level. sex. primary referral reason) was found to be signifi-
cant in producing the observed variation in the overall analysis. The
significance levels of t-values indicating covariate effect did not
approach the .05 level. and there was no statistically significant

change in the variation when compared with the overall analysis.

CHAPTER 5

DISCUSSION

Sumac:

The ability and achievement test performance of 404 students
selected from a sample of 1.552 students from 45 school districts in
Michigan was analyzed to determine if methods proposed in the
literature could assist in formulating useful decision-making rules for
classification purposes. Two hundred thirty students classified as LD
were compared with 174 LA students selected on the basis of their
achievement scores on a test of word recognition. Methods calculating
.z-score discrepancy levels. ability-test subtest scatter. verbal-
performance ability differences. and general ability and achievement
characteristics did not meet the criterion set in this study for
usefulness in differential diagnosis. Methods were deemed useful if
they affirmed classification decisions made by EPPCs for 85% or more of
the students in the groups studied. The methods used to calculate
discrepancy levels and ability subtest scatter indicated statistically
significant differences at the .05 level of confidence. However. they
were not found to be useful for practical diagnostic purposes.

In this chapter. conclusions and recommendations are discussed
under the following areas: clinical practice. public policy.

directions for educational research. and limitations of the study.

76

77

Waging

Comparison of the general ability and achievement characteristics
of the LD and LA students included in this study offered little
direction to the diagnostician who wishes to use the results for
classification purposes. Although statistically significant variation
was found to exist between the LD and LA<l7th groups. this variation
offered little in terms of formulating useful decision rules. When
proximity to the student's mean was used as the basis for
classification. the degree of overall error was 44% for Full Scale IQ
comparisons and 41% for Verbal IO comparisons. The high degree of
correlation (p = .001) between achievement test results). both within
groups and between groups. spoke little to any variation in terms of
achievement. Group characteristics of IO levels offered little for the
purposes of differentiation. Forty-two percent of the LD group and 30%
of the LA<26th group had IO levels in the range of 90 to 111. Six
percent of each group had 105 above 110; 52% of the LD group and 67% of
the LA group had 105 below 90.

The range of ability and achievement scores was found not to vary

between samples on any of the methods used. In this study. the
diagnostic utility of using ability and achievement performance to
differentiate between groups was found to be highly unproductive.
Using ability and achievement characteristics for differential purposes
was found to produce an unacceptably high error rate. with a range from
41 to 54%.

The use of ability-test scatter as a diagnostic tool offers just

as little promise. ‘The most promising method appeared to be the range

78

method (highest minus lowest scaled score). which identified only 70%
of the LD and approximately 30% of the LA students. Simply put. this
method. though most successful. leaves much to be desired for realistic
classification purposes.

Verbal-performance differences using two methods were unsuccessful
in differentiating between the LD and LA students in this study.
Although the actual 12-point-difference method was most successful in
identifying classifications. the percentage of false-positive and
false-negative diagnosis far exceeded an acceptable level.

The only discriminant factor (covariate) that produced changes in
significant overall analyses was found to be IO level. Even with that
effect. the general trend of discrepancy levels among groups was quite
consistent.

In conclusion. none of the diagnostic methods tested in this study
was found to have an acceptable level of utility (85%). It would seem
that. to the extent that the sample of students used in the study was
representative of the population referred for educational diagnoses.
the use of general achievement and ability characteristics. z-score
discrepancy levels. ability-test scatter. or ability-test verbal-
performance differences for classification may be well intentioned but
not accurate or realistic.

Educational practitioners who use the standardized test data
included in this study and who focus on the methodology studied here
should be advised that these methods have little practical value for
classification purposes. Neither the literature nor the present study

supports these practices. This statement is not intended to discourage

79

judgments based on individual student processes observed in assessment.
but rather to discourage strongly the practice of serving some students
and denying others special programs on the basis of criteria that have

no realistic basis.

WWW
EubJJLEolm

The methods used in this study failed to distinguish between a
classification of LD and a nonhandicapped classification of low
achievement. The data presented here suggest that considerable
confusion may result when an attempt is made to distinguish school-
defined LD students from their LA peers. In fact. this study failed to
do so using student samples that were more characteristic of the
referred population at large than those used in recent studies
comparing the LD with the LA student. Public policy should disregard
the notion that a label is considered a valid and separate category if
it serves only a portion of the school population with no discernible
impairment other than low achievement. A sufficiently large population
of students is believed to exist. if this study's samples are
representative of the general referred population. who are not being
served. The reasons for this condition are still unclear. Public
policy makers should be charged with identifying student characteris-
tics and more clearly specified classification. without which neither
clinical practice nor research can advance very far from the present
state. Of central concern to this study is the question. Does the
handicap of learning disabilities exist as it is presently defined in

the federal definition? The results of this study suggest a negative

80

response. Is the concept of learning disabled. as a separate and
distinct group from the general population who is experiencing diffi-
culty in the school environment. realistic? Again. the results of this
study suggest a negative answer. The possibility exists that direction
of efforts is realistic in creating a category of educationally handi-
capped and assisting educational personnel to develop the flexibility
needed to address the needs of a sizable portion of the school popula-
tion. Researchers and practitioners should lend their expertise to
policy makers. whenever possible. in an attempt to define appropriate
categories for services. Active participation by both parties may help
ensure congruence between practical educational practices and
legislative intention.

The number of students who would qualify for special education
services under the current federal definition. even with an
achievement-ability discrepancy level set marginally low. did not
constitute a two-thirds majority in any group studies. Sixty-seven
percent of the LD group and between 46 and 50% of the LA groups
demonstrated a reliable discrepancy between ability and achievement. a
figure too low for diagnostic utility. Even more surprising was the
number of students scoring with negative directional discrepancies:

12% of the LD and 8 and 6% of the two groups of LA students. Even
though between-group variance was found to exist. the number of
students affecting such variance would well have been due to chance.
The degree of misidentification that would result if the discrepancy
method was applied for classification purposes exceeded. by far. an

acceptable level. Thirty-five percent of the LD and 46% of the LA

81

students would receive either a false-positive or a false-negative
diagnosis. Given the federal definition for the determination of a
learning disability. it is surprising that a sizable number of the
students included in the LD group in this study exhibited no signifi-
cant discrepancy between ability and achievement. ‘The stringent
requirements of the definition indicate that children may only be
determined to have a learning disability if they do not achieve commen-
surate with their age and ability in one or more areas. ‘The results of
this study may well indicate that congruence between the nature (valid-
ity and purpose) of standardized tests and the uses to which they are
applied does not exist. Using standardized tests to affirm teacher
judgment is prevalent and highly accepted (Shinn et al.. 1982). but the
ability of such tests to differentiate between handicapping conditions

may well be questioned.

WWW

None of the analyses performed in this study met the criterion for
usefulness in differential diagnosis as set in this research. Cer-
tainly the overall error rate was more generous than what is presently
required in interpreting the federal regulations and than what would be
acceptable to practitioners making educational decisions. Research
efforts should be directed toward clarifying the nature of handicaps.
the factors educators view as important to educational progress. and
the appropriate measurement of these factors before realistic educa-
tional schema can be developed.

The fallibility of diagnostic decisions is an area of research

that needs to be explored. The accuracy of methods used for

82

differential diagnosis should be of concern to practitioners and those
responsible for legislating standards for identifying the handicapped.
The degree to which present special education populations meet the
criteria mandated by state and federal regulations may provide an
information base from which realistic criteria can be formulated.
Aligned with these efforts should be an information base regarding the
factors that are instrumental in initial placements of students. ‘The
degree to which test scores and ecological factors. as well as daily
classroom behavior. influence the decisions of placement teams may
provide information relative to criteria for the presence of a
handicap. School personnel seem best able to assess the qualities
necessary for academic progress. Using such information as diagnostic
directions in the assessment process may assist in formulating
practical definitions of the handicapped.

The majority of students included in this study were referred for
academic reasons. Although this may not be representative of the
entire referred population. the factors influencing teacher referrals
should be pursued. What criteria do teachers use in deciding to refer
a student for evaluation? Teacher awareness of individual differences
and the degree to which students are viewed as requiring intervention
may assist in developing appropriate definitions of handicaps.

Although it appears highly unlikely that results of the analyses
performed in this study will vary upon replication. research may well
be continued on samples that are as representative of the general
population as the samples included in this study were of the referred

population. It seems likely that large samples of students with

83

specified low achievement scores can be obtained across the spectrum of
grades. .Analyses of characteristics and comparative studies with
identified LD students may well offer validations that provide insight
into recategorization of classifications (McKinney. 1984).

Other research efforts should be directed toward comparing
functional differences between the L0 and LA populations. Abandoning
current practices that are not valid does not mean simply relying on
teacher judgment. Informal measures of assessment may allow for
efficient. expedient quantification of functional classroom performance
as the basis for selecting students who should receive LD services.
Comparative studies using representative samples across the school-age
population appear to be nonexistent. but such studies might help
classify and serve students experiencing academic difficulty. For
example. although the male-female ratio in this study is characteristic
of the general LD population. the issue of bias in referral and
placement of females versus males needs exploration. Theoretically.
there are few differences in the ability and achievement levels of
males and females in the general population. If this is true. there
may be a population of LD students who are not being referred and
served in special programs.

Diagnostic-utility questions related to the specificity of
handicapping conditions need to be addressed. Until this is

accomplished. assessing group differences is redundant.

84

Limitations
Certain limitations were inherent in the study. and they should be

noted when the results are generalized to the school-age population.
Limitations regarding sample selection. methodology. and interpretation

of results are of particular importance.

Won
1. As noted in Chapter 3. the classification decisions of the

EPPCs were accepted as accurate. Uncertainty about the factors used in
making these decisions is of concern when this population of LD and
noneligible students is represented as being characteristic of the
general or special education populations.

2. All of the students included in this study were referred for
evaluation after attracting attention in the school environment.
Generalizing the results to nonreferred students may not lead to
accurate classification decisions or assessment techniques.

3. The source of the sample (mainly suburban and rural) and
socioeconomic level (predominantly middle level) indicate biases that
might affect generalization of the results. ‘There might be a broader
population of LD and LA students to whom the results of this study
cannot be generalized.

4. Although the presence of a discrepancy between ability and
achievement was a consideration in classifying LD students. there is no
assurance that this was a primary consideration.

5. The data reported in this study were collected during the
1975-76 school year. Curriculum and methodological changes. as well as

the nature of special education services. may well influence the

85

variability and composition of present LD students as compared with
those included in this study.

6. The variability of psychometric competency used in data
collection is unknown. Although all of the data used in this study
were collected by certificated school psychologists. the variability of

assessment situations might have produced inconsistent results.

11191119091291

1. The results of this study were derived from standardized test
performance. Analyses of group differences on informal or competency-
based tests may yield significantly different results.

2. The achievement-test results used in this study were limited
to three areas that might not reflect the academic:(competency-based)
tasks required in the general school environment. Hence generalization
of the results to academic assessments other than those included in

this study may be invalid.

Results

1. A primary concern in current diagnostic practices is the use
of z—score discrepancy formulas to indicate practical (functional)
differences between ability and achievement. The method used in this
study is purported to measure statistically significant differences.
Generalizing that a calculated statistically significant discrepancy
indicates a need for special education services is strongly dis-

couraged.

APPENDIX

86

87

 

 

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39

Table A3. Means, standard deviations, correlation coefficients, and significance levels
between subtest scores for Wide Range Achievement Test performance

 

Subtests

 

Subtests Word Recognition Spelling Arithmetic

 

Mean §D_ Coe SL Mean §2_ Coe SL Mean §2_ Coe SL

 

LD and LA<26th

 

Word Recognition 2.60 1.77 2.45 1.59 .849 .001 2.86 1.59 .679 .001
Spelling .849 .001 .679 .001
Arithmetic .849 .001 .679 .001

 

L0 and LA<17th

 

 

 

 

 

 

 

Word Recognition 2.53 1.70 2.38 1.45 .833 .001 2.87 1.56 .638 .001
Spelling .833 .001 .638 .001
Arithmetic .638 .001 .638 .001
L0

Word Recognition 2.49 1.81 2.53 1.66 .789 .001 2.86 1.61 .552 .001
Spelling .789 .001 .554 .001
Arithmetic .552 .001 .554 .001 .554 .001

LA<26th
Word Recognition 2.71 1.72 2.53 1.66 .919 .001 2.86 1.61 .853 .001
Spelling .919 .001 .823 .001
Arithmetic .853 .001 .823 .001

LA<17th
Word Recognition 2.57 1.58 2.38 1.38 .923 .001 2.87 1.54 .821 .001
Spelling .923 .001 .796 .001

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94

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