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I .. . 2.55111. fie:- _. .utguuf It‘- .Ifl C Pull u luv ’Olwr. . . ‘1 . is)»; . . ‘61; 3.0.5155!) I n . . 7.. . . u . gtughwfgw -;{A2 .2 , H.431! b girl-05% .2 : 2. . lfolsalihk? 32.12%... 2:12.822}?! . . ii}. .23! #2:... It}; .222; . .... .51.; . . . 2 EA AfanMJWwinA 23“.“; .r 5 f ‘s‘kutA: . t x H2 r. 23.3%. ..§ : . lllfllllllllilHill]llfl'tlllfllllllllllllfillll .’— _ 3 1293 00672 8624 {86% This is to certify that the dissertation entitled A Comparison of Methods for Calculating a Severe Discrepancy Between Ability and Achievement Using the WISC—R, PIAT, and K—ABC presented by Deborah Ellen Bennett has been accepted towards fulfillment of the requirements for Ph.D. degree in School Psychology QZI/ZC U.“- “2 71' /?(C0 (1"- {5“ (Major professor ‘/ Date November 12 , 19 86 MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 A COMPARISON OF METHODS FOR CALCULATING A SEVERE DISCREPANCY BETWEEN ABILITY AND ACHIEVEMENT USING THE WISC-R, PIAT, and K-ABC BY Deborah Ellen Bennett 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 1986 ©1987 DEBORAH ELLEN BENNETT All Rights Reserved ABSTRACT A COMPARISON OF METHODS FOR CALCULATING A SEVERE DISCREPANCY BETWEEN ABILITY AND ACHIEVEMENT USING THE WISC-R, PIAT, AND K-ABC BY Deborah Ellen Bennett Four methods for determining a severe discrepancy between ability and achievement for the purposes of diagnosing students as learning disabled were compared using scores from the Wechsler Intelligence Scale for Children—Revised, The Peabody Individual Achievement Test, and the Kaufman Assessment Battery for Children. Eighty-six students who were referred for academic difficulties were tested with the WISC—R, PIAT, and K-ABC. The score differences between the WISC—R Full Scale IQ and the PIAT subtests as well as between the K-ABC Mental Processing Composite and the K-ABC Achievement subtests were evaluated using four procedures: z-score difference, estimated true score difference, and two regression analysis procedures. The first regression procedure (unadjusted) considered only errors of estimate. The second regression procedure also included an adjustment for test unreliability. A high degree of agreement in the selection of students was found between the z—score difference and estimated true score difference approaches, particularly for tests with high reliabilities. Considerable agreement was also found between the z-score difference, estimated true score difference, and the adjusted regression procedure when tests with high reliabilities were analyzed. Less agreement was found between the unadjusted regression procedure and the z-score, estimated true score, and adjusted regression approaches. The unadjusted regression method generally identified significantly fewer students than the other three approaches. No significant differences were found between student characteristics: age, sex, grade placement, and IQ across methods. When comparing the WISC-R/PIAT discrepancies with the K-ABC MPC/Achievement discrepancies, it was found that the two approaches to the determination of a score difference resulted in different populations of students. Percent overlap ranged from O to 49.2 percent with 8 out of 16 comparisons resulting in less than 25 percent of the same students identified. The high average PIAT standard scores in combination with lower subtest reliabilities appeared to be the primary source of disparity between the two approaches to the calculation of a discrepancy. The PIAT identified fewer students than the K-ABC in all comparisons and selected less than half the number of students in ten of the sixteen comparisons. ACKNOWLEDGMENTS The author would like to thank Dr. Harvey Clarizio and Dr. Susan Phillips for the ideas and advice which have contributed so greatly to the accomplishment of this dissertation. Dr. Herbert Burks has given much time and energy, both in editing this text and in providing guidance throughout my doctoral program. Appreciation is also extended to Dr. Neal Schmitt and Dr. William Mehrens for their valuable comments. A very special thanks goes to my husband, Vince Bralts, for endless hours of listening, advising, encouraging, and believing. The last note of appreciation is for the children: Natasha, Alisha, and Rebekah who make it all worthwhile. ii TABLE OF CONTENTS PAGE LIST OF TABLES... ...... ........ ....... .............. v LIST OF FIGURESOOOOOOO......O.........OOOOOOOOOOOOOOViii LIST OFABBREVIATIONS.0.0.0.9.........O....'.....0.0 ix I. INTRODUCTION ...... ..................... . ..... . I II. LITERATURE REVIEW ............................. 5 A. Severe Discrepancy ................... ...... 6 B. Description and Background of the K-ABC ..... 22 C. K-ABC Validity Studies ......... ............ . 36 D. Critique of the K-ABC ........ ............. .. 60 E. Summary of Literature and Implications for the Present Study .......... .......... ....... 70 III. METHODOLOGY ...... ...................... ........ 75 A. Rationale ............ . ....... ....... ........ 75 B. Goals . ............ ........ .................. 78 C. Definitions and Formulas ... ........... . ..... 80 D. Hypotheses .... ..... . .......... . ............. 92 E. Subjects ........ .... ........................ 94 F. Instruments .... ..... . ....................... 97 G. Procedures ......... ........ . ................ 98 H. Data Analysis .. ......... . .......... . ........ 99 I. Limitations ........ . ....................... 100 iii IV. RESULTS AND DISCUSSION .... ....... 0.000000000000104 V. SUMMARY AND RECOMMENDATIONS.. ..... ..............l75 APPENDIX A: Description of Tests. ........... .........182 APPENDIX B: Data Collection Forms .............. ......192 APPENDIX C: SPSS Program.00.0.0... ...... 0 OOOOOOOOOOO .196 APPENDIX D: Test Intercorrelations ................... 204 APPENDIX E: LiSting Of Zdif'SOooooooo oooooooooooooo .0210 APPENDIX F: Statistical Formulas ..................... 219 LIST OF REFERENCESOOO.........O....OO... ....... ......223 iv LIST OF TABLES TABLE PAGE 1. Student Characteristics.. ........... .............95 2. Means and Standard Deviations of K—ABC, WISC-R and PIAT Subtests and Score Composites.. ........ 105 3. Proportion of Students Showing a Severe Discrepancy Using Four Methods .................. 109 4. Agreement between Method 1 and Method 2 in the Selection of Students......... .............. 112 5. Agreement between Method 1 and Method 3 in the Selection of Students................. ...... 114 6. Agreement between Method 1 and Method 4 in the Selection of Students.......................1l6 7. Agreement between Method 2 and Method 3 in the Selection of Students............... ....... .117 8. Agreement between Method 2 and Method 4 in the Selection of Students.......................119 9. Agreement between Method 3 and Method 4 in the Selection of Students. ..... ...... ........... 120 10. Agreement between Methods for the Range of zdif'So00000090.0000000000000000 ooooooo o oooooooo 136 11. Analysis of Variance for Full Scale IQ's of Identified Students across Methods for Determining a Discrepancy....... ................ 139 12. Analysis of Variance of K-ABC MPC's of Identified Students across Methods for Determining a Discrepancy.. ..................... 139 13. Analysis of Variance of Chronological Age of Students Identified by WISC-R/PIAT Comparisons across Methods for Determining a Discrepancy....l4l 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. Analysis of Variance of Chronological Age of Students Identified by MPC/K—ABC Achievement Comparisons across Methods for Determining a Discrepancy...................................l41 Analysis of Variance of Grade Placement of Students Identified by WISC-R/PIAT Compari— sons across Methods for Determining a Discrepancy.....................................142 Analysis of Variance of Grade Placement of Students Identified by K-ABC MPC/Achievement Comparisons across Methods for Determining a Discrepancy...................................142 Proportions of Students Showing a Severe Dis- crepancy Using WISC-R/PIAT Comparisons by Sex for Methods of Determining a Discrepancy.....................................144 Proportions of Students Showing a Severe Dis- crepancy Using K-ABC MPC/Achievement Comparisons by Sex for Methods of Determining a Discrepancy.......................145 Correlations between Teacher Ratings of Students' Academic Difficulty and Calculated Discrepancies: Reading Recognition..............147 Correlations between Teacher Ratings of Students' Academic Difficulty and Calculated Discrepancies: Reading Comprehension............147 Correlations between Teacher Ratings of Students' Academic Difficulty and Calculated Discrepancies: Arithmetic.......................150 Correlations between Teacher Ratings of Students' Academic Difficulty and Calculated Discrepancies: Total Achievement................150 Numbers of Students Showing a Severe Dis- crepancy between Ability and Achievement Using WISC-R/PIAT Mathematics and K-ABC MPC/ Arithmetic Comparisons............... ........... 153 Numbers of Students Showing a Severe Dis- crepancy between Ability and Achievement Using WISC—R/PIAT Reading Recognition and K-ABC MPC/Reading Decoding Comparisons .......... 154 25. 26. 27. 28. 29. 30. Numbers of Students Showing a Severe Dis- crepancy between Ability and Achievement Using WISC-R/PIAT Reading Comprehension and K-ABC MPG/Reading Understanding Comparisons.....155 Numbers of Students Showing a Severe Dis- crepancy between Ability and Achievement Using WISC-R/PIAT Total and K-ABC MPC/ Achievement Composite Comparisons...............157 Agreement between WISC-R/PIAT Mathematics and K-ABC MPG/Arithmetic in Identifying StUdentSooooocoo.ooooooooooooooooooooooo ....... .160 Agreement between WISC-R/PIAT Reading Recognition and K-ABC MPG/Reading Decoding in Identifying Students............. ............ 16]- Agreement between WISC-R/PIAT Reading Com— prehension and K-ABC MPC/Reading Under- standing in Identifying Students...... .......... 162 Agreement between WISC-R/PIAT Total and K-ABC MPC/Achievement Composite in Identifying Students ..... ... .................... 164 vii LIST OF FIGURES FIGURE PAGE 1. An example comparison of four methods for 10. ll. 12. determining a severe discrepancy: WISC-R/PIAT Mathematics............ ........... ... 90 An example comparison of four methods for determining a severe discrepancy: K-ABC MPC/Arithmetj-Coooooo0000000000o oooooooooooo 91 A comparison of four methods for determining a severe discrepancy: WISC-R/PIAT Mathematics....123 A comparison of four methods for determining a severe discrepancy: WISC-R/PIAT Reading RecognitionOOOOOOO....O......O......O......OOOO0.125 A comparison of four methods for determining a severe discrepancy: WISC-R/PIAT Reading comprehenSj-Onooooooooooo0000000000000...000000000126 A comparison of four methods for determining a severe discrepancy: WISC-R/PIAT Total..... ..... 128 comparison of four methods for determining severe discrepancy: K—ABC MPC/Arithmetic.. ..... 129 m3» comparison of four methods for determining severe discrepancy: K-ABC MPC/Reading DeCOding....O....O...........O......O 000000000000 130 023’ A comparison of four methods for determining a severe discrepancy: K-ABC MPC/Reading UnderstandingooO.......0.0...O.... 000000000000000 131 A comparison of four methods for determining a severe discrepancy: K-ABC MPC/Achievement Composite........ ......... . ..... . ................ 132 A comparison of four cutoffs for the regression analysis approach to determining a severe discrepancy........... ..... ..... ................. 170 Utilization of a regression analysis cutoff line: An example.......... ....... . ............... 172 viii WISC-R K-ABC PIAT FSIQ VIQ PIQ M.A. C.A. G.A. L.D. LIST OF ABBREVIATIONS Wechsler Intelligence Scale for Children- Revised Kaufman Assessment Battery for Children Peabody Individual Achievement Test Full Scale IQ (WISC-R) Verbal IQ (WISC-R) Performance IQ (WISC-R) Mental Processing Composite (K-ABC) Mental Age Chronological Age Grade Age Learning Disability ix I. INTRODUCTION The determination of a "severe discrepancy" between ability and achievement is a critical component in the process of diagnosing a learning disability. In order to be considered for Special Education support services under the learning disabilities classification, a student must first exhibit a level of achievement in one or more specified academic areas which is significantly below his or her "expected level of achievement." The expected level of achievement is typically based upon some estimate of ability, such as the student's score on an individually administered intelligence test. The process of quantifying this discrepancy has been an area of increasing concern for school psychologists, measurement specialists, and educational administrators. It has become more obvious that the method of discrepancy determination which is implemented by a school system can have a substantial impact upon the number and characteristics of students who are serviced in learning disability (L.D.) programs. Unfortunately, there have been few studies which have systematically analyzed the consequences of different discrepancy procedures upon the characteristics of the selected L.D. population. While earlier research has attempted to compare expectancy formulas, little has been done to compare the impact of more recently advocated methods such as the standard score discrepancy (Reynolds, 1981), estimated true score discrepancy (Cone & Wilson, 1981), and regression analysis (Wilson & Cone, 1984) approaches. While considered by most measurement experts to be more acceptable approaches to the quantification of a significant discrepancy, there appears to be a paucity of research which considers the outcome of the actual implementation of each method (Reynolds, 1985; Wilson & Cone, 1984). One of the major objectives of the present research is to compare the numbers and characteristics of students who demonstrate a severe discrepancy using these three methods. Do all three approaches tend to identify the same students or are there systematic differences in such variables as chronological age, IQ, grade placement, and sex? If there are no observed differences, then ease of application and interpretability of results may be the deciding factors in the selection of a discrepancy procedure. On the other hand, substantial differences in the population which demonstrates a severe discrepancy may warrant a closer examination of the psychometric adequacy of the selected approach as well as consideration of more philosophical issues, such as who should be served by programs for the learning disabled. Another related issue involves assessing the impact of test characteristics, such as reliability and validity, upon the quantification of a significant discrepancy. To what extent do these critical variables influence the students who are identified by each method; and is there some minimal requirement in terms of technical adequacy for the tests which are used in the determination of a discrepancy? Although it is beyond the scope of this dissertation to recommend minimal standards for tests, such issues are often overlooked once a discrepancy procedure has been endorsed and implemented. The second major objective of this research is to evaluate the adequacy of the recently published Kaufman Assessment Battery for Children (K-ABC) for use in the determination of a severe discrepancy between a student's ability and achievement. Of particular interest is the comparison of the K-ABC with the well-established and widely used Wechsler Intelligence Scale for Children-Revised (WISC- R) and the Peabody Individual Achievement Test (PIAT). Do the discrepancies found between the Mental Processing Composite (ability component) and the Achievement subtests of the K-ABC correspond with the discrepancies found between the WISC-R Full Scale IQ and the PIAT subtests, or will the selective use of the K-ABC over the WISC—R and PIAT result in the identification of different students? As with the choice of a method for determining a significant discrepancy, the choice of tests to be administered could have a substantial impact upon students selected for learning disabilities programs. The K-ABC is unique in many ways from the WISC-R and PIAT, both in terms of underlying theory and nature of abilities which are sampled. Because the test authors have purposely attempted to depart from the classical approach to intelligence testing, basic questions need to be answered regarding the application of the K-ABC to the diagnosis of learning disabilities. Again, how will use of the K-ABC in the determination of a discrepancy between ability and achievement affect the size and characteristics of the L.D. population? I I . REVIEW OF L ITERATURE The Review of Literature has been written to analyze and discuss two broad areas of research. The first area of investigation involves the development and analysis of various methods for determining a "severe discrepancy" between ability and achievement. The review starts by examining and evaluating simpler discrepancy methods, such as deviations from grade level, and progresses to the more recently advocated and statistically sophisticated approaches to the problem. An attempt has been made to discuss the benefits and disadvantages of each approach and ultimately provide a rationale for selecting the four methods which have been implemented in the present study. The second area of investigation focuses on research related to the Kaufman Assessment Battery for Children. Because of its recency in the evolution of individual assessment, both the theoretical structure and the nature of the tasks included in the battery have been outlined and discussed. Studies which have examined the relationship between the K-ABC and other achievement and intelligence tests offer insights regarding how the results of the K-ABC might compare with the WISC-R and the PIAT. Finally, several critiques of the K—ABC will be summarized. These reviews provide an interesting perspective concerning the accuracy of the K-ABC in reflecting the underlying theoretical constructs selected by its authors. Some basic differences between traditional notions of intelligence and the Kaufmans' concept of "mental processing" are highlighted, and implications of the literature are related to the objectives of the present study. A. Severe Discrepancy Cone and Wilson (1981) have provided a useful categorization of available procedures for determining a severe discrepancy between a student's ability and achievement for the purposes of identifying learning disabilities. The categories offer a helpful structure for comparing the many formulas and include: 1. Deviation from grade level, 2. Expectancy formulas, 3. Standard score comparisons, and 4. Regression analyses. 1. Deviation from Grade Level The deviation from grade level method for determining a severe discrepancy involves the identification of students who score substantially below their grade level on achievement tests. Other sources have referred to this procedure of identifying discrepancy as "years behind" (Forness, Sinclair, & Guthrie, 1983; Erickson, 1975) or simply "low achievement" (Epps, Ysseldyke, & Algozzine, 1985). Cone and Wilson further make the distinction between "constant deviation" and "graduated deviation" procedures. Constant deviation methods require the determination of a fixed discrepancy (e.g., two grade levels) between a student's current grade placement and level of achievement. Graduated deviation procedures allow for variation across grade levels with a smaller deviation required for a "severe discrepancy" at lower grade levels and a larger deviation required at upper grade levels. Reynolds (1981) discusses the disadvantages of using a constant grade level deviation as a diagnostic criterion for learning disabilities. He explains that "the use of grade equivalent scores at a constant discrepancy level irrespective of actual grade placement produces considerable irregularity and distortion in the magnitude of aptitude/achievement discrepancies required for diagnosis of a learning disability across grade levels" (p. 351). A clear example of this irregularity can be seen by comparing the educational significance of a two year below grade level discrepancy for a third grade student with the educational significance of an eleventh grade student who is achieving at the ninth grade level. The increasing range of achievement scores which occurs with the progression to higher grade levels was addressed, at least partially, with the introduction of the graduated deviation procedures for determining discrepancy. Several difficulties, however, are still inherent in this approach. Cone and Wilson point out that a graduated deviation formula (as well as a constant deviation formula) discriminates against higher ability students who may exhibit learning disabilities. The brighter the child, the more unlikely it is that a severe discrepancy will be identified. Supportive evidence comes from a study by Fields (1979) which compared the characteristics of students identified using an expectancy formula, a deviation from grade level procedure, and a standard score comparison procedure. Students identified using the expectancy formula and the standard score comparison procedure had significantly higher Full Scale IQs than the group identified using the deviation from grade level method. Reynolds (1984-85) also criticizes these methods as overidentifying children who fall in the "slow learner" range, including many children who are functioning academically at a level which is consistent with their general intellectual ability and age. "Only for children with IQs of precisely 100 will there be no bias in diagnosis with these models" (p. 457). 2. Expectancy Formulas During the past two decades there has been a proliferation of methods for determining a student's expected level of achievement. Most of these methods utilize some combination of ability (typically IQ) and age or grade level. Cone and Wilson (1981), Danielson and Bauer (1978), Epps, et a1. (1985), O'Donnell (1980), and Harris and Sipay (1980) describe and critique several of these formulas. For the purpose of this review, a limited number of the most widely used formulas will be discussed. Many of the difficulties encountered with the use of these selected procedures are also inherent in other expectancy formulas. One of the simplest and most widely applied procedures for quantifying a student's expected level of achievement is the formula advocated by Kaluger and Kolson (1969): (IQ x CA)/100 - 5 which yields an expected grade level for each student. While useful for students who have entered school at age five and who have not subsequently repeated a grade, the formula becomes more difficult to interpret for students who deviate substantially from this norm. A second formula which attempts to adjust for the amount of time that a student has spent in school is the revised Bond and Tinker (1973) formula: # of years in school X IQ/100 + 1 This formula has been criticized for the same reasons that the deviation from grade level procedures have been criticized, specifically that there is a tendency to overidentify slow learners as learning disabled (Cone & Wilson, 1981). The advantage of this formula over the deviation from grade level procedure is that an attempt is made to incorporate a child's ability level in the determination of a learning discrepancy. 10 Johnson and Myklebust (1967) propose a third method for the determination of achievement expectancy which includes the child's ability level, chronological age, and "grade age": Expected grade equivalent = (MA + CA + GA)/3 - 5 Cone and Wilson suggest that this formula better accounts for the increasing range and variability of students at higher grade levels than the previously cited formulas. Finally, the formula which has received the most critical attention in recent years is the modified Harris formula which was proposed by the Bureau of Education for the Handicapped in 1976. The "Federal formula" originated from the 1970 Harris formula for expected grade level: Expected grade equivalent = (2MA + CA)/3 - 5 By substituting a standard score (IQ) for mental age and setting a severe discrepancy at half a child's expected grade equivalent or below, the Harris formula was modified to the following: Severe discrepancy = CA(IQ/300 + .17) - 2.5 Perhaps because of attempts at widespread implementation of this procedure, a number of strong criticisms were leveled at the proponents of the formula. Cone and Wilson (1981) summarize many of the points ll initially presented by Danielson and Bauer (1978). First, as with several of the previous procedures for the quantification of a severe discrepancy, this formula tends to identify a disproportionate number of slow learners. Secondly, younger children are more likely to be identified as exhibiting a discrepancy between ability and achievement than older children. The formula also will identify more children using certain tests than others because of the failure to consider errors of measurement. This last criticism, however, is applicable to all expectancy formulas. Finally, only 58 percent of children currently receiving support services under the learning disabilities classification would be identified using the Federal formula. In a study which compared the proportion of students who demonstrated a severe discrepancy using a number of different expectancy formulas, Forness, et a1. (1983) found considerable variation in both the incidence of identification and the agreement regarding which children demonstrated a discrepancy. In a sample of 92 children who had been hospitalized for evaluation or short-term treatment of behavior and learning problems, 32 percent were identified as learning disabled using the deviation from grade level procedure, 18.5 percent were identified using the Bond and Tinker formula, 21.7 percent were identified using the Kaluger and Kolson formula, and 24 and 25 percent of the children demonstrated a severe 12 discrepancy using the 1975 Harris formula and the Federal formula, respectively. Not surprisingly, there was almost perfect agreement between the Federal formula and the Harris formula in identifying children as having a discrepancy between ability and achievement. Somewhat lower agreement was shown between the other procedures, with deviation from grade level being the least consistent procedure among the methods described in this review. Expectancy formulas have been questioned on a variety of technical grounds, some of which have been discussed in the preceding paragraphs. Wilson and Cone (1984) point out that expectancy formulas ignore the reliabilities of the measures which are incorporated into the calculations, as well as the intercorrelations between the tests. Reynolds (1984-85) objects to expectancy formulas because they attempt "mathematical operations that are not considered appropriate for the types of measurement being employed" (p. 452). The treatment of age and grade information as interval data or ratio data in the calculation of a discrepancy leads to meaningless and misleading results according to Reynolds and others. (More will be said about this concern when discussing standard score procedures for determining a discrepancy.) Cone and Wilson (1981) echo and amplify Reynolds' concerns regarding the use of expectancy formulas, emphasizing the fact that none of the formulas "addresses l3 errors of measurement, regression toward the mean, norm group comparability, a priori knowledge of incidence, or the increased range and variability of obtained scores for students at higher grade levels" (p. 363). Furthermore, the comparison of grade or age equivalents across tests or, even within tests, is troublesome because of the lack of equal variability of this type of score. As a result of the numerous technical difficulties encountered when using these procedures, most psychometricians patently argue against implementation of the expectancy formulas in determining a discrepancy. 3. Standard Score Comparisons A number of authors (Erickson, 1975; Reynolds, 1981) have promoted the use of standard score comparisons as a more appropriate method of dealing with the quantification of a severe discrepancy. These procedures typically involve calculating the difference between comparable standard scores (same mean and standard deviation) on an ability test (typically IQ) and on an achievement test. It is expected that the achievement standard score will be in approximately the same relative position in the distribution as the ability estimate. One form of standard score comparison is the z-score discrepancy procedure outlined by Erickson (1975) in which each test or subtest score is linearly transformed to a z— score by subtracting the group mean from the observed score and dividing the residual by the test standard deviation. 14 Generally an arbitrary cut—off, with the achievement measure one to two standard score units below the ability measure, is established as a criterion for a severe discrepancy. Reynolds (1981) has attempted to establish the significance of a standard score discrepancy by dividing the z-score difference by the standard error of the difference score. While improving upon the technical quality of the standard score procedure, the statistically significant difference between the z-scores does not always translate into a difference with educational significance. Erickson (1975) stresses the importance of empirically establishing cut-off scores which reflect the characteristics of students in each comparison group. There are several advantages in using a standard score procedure rather than an expectancy formula in the calculation of a severe discrepancy. Shepard (1980) points out that the Z-score method takes into consideration both ability and grade level when determining a difference. It also adjusts for differences in variability across grades by using the standard deviation for a particular grade. Additionally, standard scores allow for comparisons across tests, subtests, and age levels. While the standard score procedures appear to offer advantages over the more traditionally used expectancy formulas, there are still difficulties which arise with the use of the Z—score method. Undoubtedly the major problem with this approach is the failure of the standard score 15 procedure to account for the regression between ability and achievement which results from less than perfectly correlated measures. Shepard (1980) explains that "because the actual correlation [between IQ and achievement] is usually more on the order of 0.6, there will be a regression to the mean. It can be shown both mathematically and theoretically that bright children have above average achievement, but their relative position (i.e., Z-score) tends not to be as high as it is in the IQ distribution. Conversely, children with low IQs will, on the average, have relatively higher achievement status than IQ status, although they will still be below the mean" (p. 83). The effects of the regression phenomenon can be seen quite clearly in a study by Fields (1979) which demonstrated that the z—score procedure identified students with higher IQs than did either the deviation from grade level or Bond and Tinker procedures. Erickson (1975) also presented results which indicate average IQs of 110.3, 92.9, and 88.1 for children identified using the z-score, Bond and Tinker, and deviation from grade level procedures, respectively. Reynolds (1985) describes the erroneous reasoning of those who call for a discrepancy of one standard deviation between ability and achievement in order to create a pool of eligibility of 16 percent of the student population (one standard deviation below the mean falls at the 16th 16 percentile of a normal distribution). He points out that if two test scores are positively correlated, which ability and achievement test scores invariably are, "the distribution of scores created by subtracting the scores of a set of students on both tests from one another will not be the same as the two univariate distributions" (p. 454). Ultimately the new distribution will have a much smaller standard deviation, serving to identify a smaller number of students as exhibiting a severe discrepancy than originally intended. This problem is further exacerbated by exclusionary practices such as eliminating from consideration children who have IQs less than 85 or children who are not performing below grade level. On the other hand, Reynolds discusses the impact of multiple comparisons which typically occur when evaluating a child for learning disabilities. The practice of comparing a student‘s IQ with a number of achievement scores results in a greater incidence of "severe" discrepancies simply on the basis of chance. Clearly there are a number of difficulties which are inherent in the use of standard score comparisons in the determination of a severe discrepancy. The problems tend to compound depending upon the specific practices and definitions of severe discrepancy which are implemented by a given state or district. Cone and Wilson (1981) describe an alternative approach which takes into account the measurement errors l7 inherent in the ability and achievement tests that are chosen for the calculation of a standard score discrepancy. Knowing the reliabilities of each test, it is possible to calculate the estimated true score for each observed score using the following formula: (X - X) + X The estimated true scores, thus, consider errors of measurement resulting from less than perfectly reliable measures. This factor becomes increasingly significant when comparing two tests with substantially different reliabilities, such as the WISC-R Full Scale IQ and the less reliable PIAT achievement subtests (Cone & Wilson, p. 365). Salvia and Ysseldyke (1978) recommend dividing the difference of the estimated true scores by the standard error of measurement of difference scores in order to determine the significance of the score discrepancy. Cone and Wilson (1981), however, suggest that the more accurate error term for the comparison is the standard error of measurement of the estimated true score difference, described by Stanley (1971), where: SEA A _ 2 2 _ Tx-T _,/}xx (l-rxx) + ryy (l ryy) Cone and Wilson (1981) consider this approach to the determination of a discrepancy to be "the next evolutionary step in the standard score comparison procedure" (p. 365). 18 Shortcomings of this method, however, include the failure to consider "the main source of regression which is due to the inherent relationship between IQ and achievement" (p. 365). 4. Regression Analysis In an attempt to address many of the concerns related to the standard score procedures for determining a score discrepancy, Wilson and Cone (1984) and Reynolds (1985) have described a procedure which takes into consideration the regression of aptitude on achievement when assessing a "severe" discrepancy. Using the standard regression or prediction equation, an expected value of the achievement score (Y'), based upon the relationship between the aptitude measure and the achievement measure (rxy), can be calculated: U) Y+r XY_S_ X The observed value for the achievement measure (Y) can thus be subtracted from the expected value (Y'). The discrepancy represented by this residual is considered severe if it equals or exceeds the value: 2 xY (Za)sy l - r After presenting and critiquing several alternatives, Reynolds argues that this model is the only acceptable method for determining a severe discrepancy available at 19 this time. He recommends adjusting 23, however, for test unreliability. Both test reliabilities and intercorrelations are therefore included in the calculation of a discrepancy. The following formula represents Reynolds' regression analysis procedure: xy ) - 1.65 SE§_Yi A = _ 2 ./ _ A_ where SEY‘Yi l rxy l ry yi = 2 _ and ry_y ryy + rxx rxy 2rxy 2 Y A Y - Y1 = (za 5y 1 — r 2 l-rx When making a single comparison, a z of 1.65, a corresponding to the traditional 0.05 confidence level for a one-tailed test, is recommended. When making multiple comparisons, a more conservative value of 2a is suggested. Wilson and Cone (1984) summarize the advantages of the regression approach: "Unlike other approaches, it considers regression, measurement errors, and incidence. The expectancy formulas are biased in terms of intelligence and age, and they do not consider measurement errors and regression effects. The variations of the IQ-standard score difference approach consider measurement errors but not regression effects, and they cannot provide a priori estimates of incidence" (p. 107). 6. Grade Equivalents vs. Standard Scores Before completely dismissing expectancy formulas which utilize grade equivalents in favor of the more 20 psychometrically sound regression procedure, it is useful to examine some of the arguments which support the retention of more descriptive, developmental scores. Phillips and Clarizio (1986) point out that status standard scores which describe a student's relative standing within a comparison group (either age or grade), do not allow for comparisons across groups. This information is often desirable when determining the appropriate instructional level for children being evaluated for learning problems. It is also suggested that status standard scores fail to consider the increased within-grade variability which occurs at higher grade levels. In other words, the same standard score may, in fact, represent different degrees of learning impairment for children at different grade levels. Descriptive information regarding a student's actual level of performance is lost through attempts to provide normative data regarding the child's relative academic standing. Hoover (1984) also makes the distinction between status standard scores which compare the student's performance within a single reference group and developmental scores, such as grade and age equivalents, which compare the student's performance with "that of a series of reference groups which differ systematically and developmentally in average achievement" (p. 8). Hoover argues that both types of scores are needed in the interpretation of a child's performance. He cautions % ____ __ 21 against abandoning grade equivalents because of the useful and interpretable information which such scores provide about a student's development in basic skill areas. Although no specific recommendations are made by either Phillips and Clarizio or Hoover regarding the quantification of a severe discrepancy, it would appear valuable to retain some form of developmental information when considering an educational diagnosis. The obtuse manipulations which accompany regression analysis may serve to obscure the educational meaning of the resultant discrepancy. For this reason, a comparison of methods’ which provide grade level information with methods which utilize standard scores (status) would seem to be a worthwhile endeavor. It might thereby be possible to evaluate, not only incidence of discrepancy and the agreement among methods, but also the relative gain achieved through use of status indicators versus developmental scores. For the purposes of this study, however, three approaches to the calculation of a severe discrepancy between ability and achievement have been chosen for comparison. These methods represent the most widely used and endorsed procedures currently recommended by Michigan school districts (from a review of practices submitted by 10 districts). Although the various districts employ different "rules of thumb" in the determination of a severe discrepancy, the basic methods can be characterized as: 22 l. z-score discrepancy, 2. estimated true score differences, and 3. regression analysis. For the present study, each approach to the quantification of a discrepancy will be implemented using the algorithms provided by the authors reviewed in this section rather than using modified procedures. A more complete description of these algorithms appears in the Methodology section. B. Description and Background of the K-ABC The Kaufman Assessment Battery for Children (K—ABC) is a recently developed, individually administered test battery designed for use with children between the ages of two and a half and twelve and a half (Kaufman & Kaufman, 1983a, 1983b). It consists of sixteen subtests, ten of which represent a "mental processing" component, and six of which represent an "achievement" component. The Mental Processing subtests can be further divided into Sequential Processing tasks and Simultaneous Processing tasks. This distinction is based upon neuropsychological research (Luria, 1966), cognitive theory (Neisser, 1967), and factor studies (Das, Kirby, & Jarman, 1975) which support the existence of separate types of mental functioning: sequential (or successive) and simultaneous (or holistic). The distinction between the Mental Processing component and the Achievement component is further based upon the Cattell-Horn model of "fluid" versus "crystallized" intelligence (Cattell, 1968). 23 The purpose of this section of the literature review is to provide a brief description of the component subtests of the K—ABC and discuss the research which supports the development of the battery. This general background will provide a basis for later examining the studies which consider the relationship between the K-ABC and more traditional tests (section C), as well as critiques which review the extent to which the K—ABC accurately reflects its underlying theoretical models (section D). 1. Description of the K—ABC subtests Klanderman, Perney, and Kroeschell (1985) have provided a summary of the K-ABC subtests, including a brief description of each task, the ages of administration, and the scale in which each task is included. This summary is included below. A more comprehensive description of each subtest can be found in the Interpretive Manual of the K-ABC. Sequential Processing Scale a. Hand Movements (ages 2 1/2 to 12 1/2) The examinee performs a series of hand movements in the same sequence as the examiner performed them. b. Number Recall (ages 2 1/2 to 12 1/2) The examinee repeats a series of digits in the same sequence as the examiner said them. C. Word Order (ages 4 to 12 1/2) The examinee touches a series of silhouettes of 24 common objects in the same sequence that these objects were named orally by the examiner. Simultaneous Processing Scale a. Magic Window (ages 2 1/2 to 4 1/2) The examinee identifies a picture which is rotated behind a narrow window and, hence, only partially visible to the child at any one time. b. Face Recognition (ages 2 1/2 to 4 1/2) The examinee selects from a group of people the one or two faces that were just exposed briefly. c. Gestalt Closure (ages 2 1/2 to 12 1/2) The examinee names an object or scene pictured in a partially completed "inkblot" drawing. d. Triangles (ages 4 to 12 1/2) The examinee assembles two to nine triangles, all identical, into an abstract pattern that matches a model. e. Spatial Memory (ages 5 to 12 1/2) The examinee recalls the placement of pictures on a page that was just exposed briefly. f. Matrix Analogies (ages 5 to 12 1/2) The examinee selects a concrete picture or an ab- stract design which best completes a visual analogy. 9. Photo Series (ages 6 to 12 1/2) The examinee places photographs of an event in chronological order. Achievement Scale 25 a. Expressive Vocabulary (ages 2 1/2 to 4 1/2) The examinee names an object pictured in a photograph. b. Faces and Places (ages 2 1/2 to 12 1/2) The examinee names a well-known person, character, or place pictured in a photograph. c. Arithmetic (ages 3 to 12 1/2) The examinee demonstrates knowledge of numbers and mathematical concepts, counting and computational skills, and other school-related arithmetic abilities. d. Riddles (ages 3 to 12 1/2) The examinee infers the name of a concrete or abstract concept when given a list of its characteristics. e. Reading/Decoding (ages 5 to 12 1/2) The examinee identifies letters and words. f. Reading/Understanding (ages 7 to 12 1/2) The examinee demonstrates reading comprehension by following commands that are given in sentences. (Klanderman, et al. p. 524) 2. Simultaneous and Successive Processing: Das-Luria Model Luria (1966) was the first to suggest the distinction between successive and simultaneous modes of integration. Based upon case histories of cortical lesions and subsequent processing dysfunctions, Luria described three functional units of the brain. The first unit or "block" includes the upper and lower brain stem, the reticular formation, and the hippocampus and is associated with arousal or activation of the cortex. In terms of intellectual functioning, the first block is related to motivation and the maintenance of an optimal level of arousal for performing an activity or task. The second block of the brain is located in the posterior region of the neocortex and includes the occipital, temporal, and parietal lobes. This unit is hierarchically structured with a primary projection zone involved in the reception and analysis of information, a secondary projection zone involved in the organization and coding of information, and a tertiary projection zone involved with the integration of information which has already been coded. Moving from the primary zone to the tertiary zone, an increasing degree of lateralization of functions occurs (i.e., the left hemisphere and the right hemisphere of the secondary and tertiary zones become increasingly specialized). The third block of the brain, as described by Luria (1973), is located in the anterior region of the cortex and is involved with the planning and programming of behavior. "The frontal lobes not only perform the function of synthesis of external stimuli, preparation for action, and formation of programs, but also the function of allowing for the effect of the action carried out and verification that it has taken the proper course" (p. 93). 27 In examining the consequences of lesions in the occipital-parietal areas (second functional unit), Luria observed that simultaneous organization of stimuli was disturbed. On the other hand, damage to the fronto- temporal region of the cortex interfered with the successive processing of information. This led to the hypothesis that the cortex was involved in two distinctly different modes of integrative activity: simultaneous integration "which has the property of surveyability and refers to any system of relationships" (Das & Molloy, 1975, p. 213) and successive integration which "refers to processing of information in a serial order...a system of cues consecutively activates the components" (Das, Kirby, & Jarman, 1975, p. 89). Other neuropsychological research has demonstrated differential functioning of the right and left hemispheres of the brain. Sperry (1970) studied the effects of split— brain surgery performed to reduce the symptoms of severe epilepsy. The surgical procedure involves the severing of the corpus callosum, the primary connection between the right and left hemispheres. Using sensitive psychological assessment procedures, Sperry discovered that split-brain surgical-patients were unable to integrate information received through the right and left hemispheres: "A patient may see an object in his left visual field, and be able to pick it out with his left hand from a hidden array of objects (both the left visual field and left hand 28 connect directly to the right hemisphere), but be unable to name the object or identify it with his right hand" (Kaufman, 1979, p. 97). Further research on cerebral specialization has demonstrated that the left hemisphere is more specialized for verbal, analytic, temporal, and digital operations while the right hemisphere is more adept at processing non— verbal, holistic, spatial, analogic, creative and aesthetic information (Bogen, 1969; Bogen, DeZure, Tenhouten & Marsh, 1972; Gazzaniga, 1970; Nebes, 1974, as reported in Kaufman, 1979). Lezak (1976) suggests that differences between the hemispheres exist not only in what is processed but how information is processed. The left hemisphere is described as organizing information on the basis of conceptual similarity while the right hemisphere organizes information on the basis of structural similarity. An apple and a peach are alike to the left brain because they are both fruits, while they are alike to the right brain because they are both round (Kaufman, 1979, p. 98). The distinctions which have been drawn between the left brain and the right brain are remarkably similar to the dichotomy described by Luria between the frontal— temporal and the occipital-parietal areas of the brain. The split-brain research would suggest that the right brain is responsible for the holistic, simultaneous processing of information while the left brain appears to be more specialized for processing successive, temporally related 29 information. While it is beyond the scope of this review to interpret this discrepancy, it is sufficient to say that research in the area of cortical functioning consistently demonstrates the dual nature of information processing. The existence of a simultaneous—successive dichotomy appears to be well-founded in theory, despite the uncertainty of its neurophysiological etiology. Based upon Luria's neuropsychological research, Das, Kirby, and Jarman (1975) developed an information processing model to explain stimulus integration. It was hypothesized that information integration involves four basic processing units: the input, the sensory register, the central processing unit, and the unit for output. Input is presented to the sensory register in either a parallel (simultaneous) or serial (successive) manner. Once registered, the information is transmitted to the central processing unit. It is speculated that the sensory register accepts complex information in a parallel fashion but "transmits" this information to the central processing unit in a serial manner. Das, Kirby and Jarman (1979) divide the central processing unit into three components: "that which processes separate information into simultaneous groups, that which processes discrete information into temporally organized successive series, and the decision making and planning component which uses the information so integrated by the other two components" (p. 50). Referring to Luria's 30 functional units of the brain, it can be seen that each of these processing components has an hypothesized relationship to a specific functional area of the cortex. The occipital-parietal area is associated with simultaneous processing, the fronto-temporal area is associated with successive processing, and the anterior lobe is associated with planning and "thinking." Das and his colleagues are quick to point out, however, that an individual has access to both simultaneous and successive modes of processing, and the "decision" to utilize one mode or the other is determined by the individual's habitual mode of processing as well as the nature of the task. Additionally, when responding to a task, the individual may utilize simultaneous or successive processing which is independent of the way in which the information was coded. The example given involves a memory task which could alternatively require serial recall or the recall of categories. A number of research studies have subsequently confirmed the existence of the simultaneous and sequential processing dichotomy. Das, Kirby, and Jarman (1975) selected a variety of cognitive tasks which they administered to normal and retarded children. A two dimensional, successive—simultaneous, solution resulted from factor analysis. The dimensions were found to be equally descriptive for the normal and retarded children. Molloy (Das, et al., 1975) factor analyzed the scores of six and ten year old children on a similar battery of tests 31 (with the addition of two timed tasks: Word Reading and Color Reading). The results of the analysis yielded a three factor solution: simultaneous integration, successive integration, and speed, which was consistent across age groups. Further investigation by Molloy demonstrated that the three factor solution was also consistent in describing the test performance of fourth grade students from different socioeconomic levels. Das (1973) examined the performance of Canadian children and high-caste Indian children on the battery of tests and found the three factor solution to be consistent across cultures. A follow-up study by Das and Molloy (1975) added tests of intelligence (Lorge-Thorndike Digit Span and Performance IQ) and measures of reading achievement to the original battery of cognitive tests. For a group of fourth grade students, the factors of simultaneous processing, successive processing, and speed emerged once more in the factor solution. Predictably, Digit Span loaded on the successive dimension while Performance IQ loaded on the simultaneous dimension. Reading achievement emerged as a separate factor with high loadings noted on the vocabulary and comprehension components of the reading achievement test. A systematic attempt to identify differences between IQ groups (high, normal, low) in the utilization of simultaneous and successive synthesis was undertaken by 32 Jarman and Das (1977). Factor analysis of the intercorrelations from a number of cognitive tests for the low IQ group yielded three factors which were labeled simultaneous synthesis, successive synthesis and speed, and successive synthesis in performing auditory-visual matching. Analysis of the intercorrelations for the normal IQ group revealed two factors: simultaneous synthesis and successive synthesis, while analysis of the high IQ group intercorrelations yielded three factors: simultaneous synthesis, successive synthesis, and speed. It was concluded that simultaneous synthesis was highly stable across IQ groups. Successive synthesis was also found to be quite stable across IQ groups. Although not addressed in this paper, an interesting parallel can be seen between the Das, et a1. (1975) research and the Jarman and Das (1977) findings. In both cases, the low IQ groups preferred sequential processing for a specific task which is more efficiently solved with a simultaneous approach. Given the observation that the general IQ from school records (Das, et al., 1975) loads on the simultaneous factor, one might speculate that the simultaneous factor represents a higher level of abstraction than the sequential, successive factor. In fact, the successive dimension is described primarily by rote memory tasks (digit span, serial recall, free recall, etc.) across studies. Das (1984) also has observed that sequential processing skills tend to develop earlier than 33 simultaneous skills and predominate at lower age levels. In a study by Cummins (reported in Das, et al., 1975) an entirely different battery of tests was administered to high school students. The tasks included syllogisms, similarities, paired—associate concrete words, memory span, digit span, paper folding test, and utility test (divergent thinking). Factor analysis yielded a three factor solution: simultaneous processing, successive processing and divergent thinking. Naglieri, et al. (1981), also concerned about generalizability of the studies by Das and his colleagues, sought to cross-validate the simultaneous and successive processing dimensions using novel tasks. The battery of tests developed for this study was subsequently modified and expanded to form the Mental Processing component of the K-ABC. The tasks chosen for analysis included Concept Formation (requiring the child to distinguish pictures which represented a given concept), Memory for Places (recalling the location of objects presented on a page), Triangles (construction of designs from plastic triangles), Overlapping Designs (construction of hexagons from irregular geometric shapes), Hand Patterning (replication of a series of hand movements), Sequential Hand Movements (similar to Hand Patterning with increasing number of (movements), Memory for Words (recollection of a series of common words by pointing to pictures of the words), Raven's Progressive Matrices, and Block Design, Digits Forward, and 34 Digits Backward from the Wechsler Intelligence Scale for Children-Revised. A two—factor varimax rotated solution revealed clear- cut simultaneous and sequential processing factors. Progressive Matrices, Block Design, Triangles, Overlapping Design, Concept Formation, and Memory for Places loaded strongly on the simultaneous processing dimension while Digits Forward, Digits Backward, Hand Patterning, Sequential Hand Movements, and Memory for Words all loaded on the sequential factor. 3. Fluid versus Crystallized Intelligence Horn and Cattell (1966) propose a different, hierachical model of intelligence. The model includes five general factors with the two most important dimensions being fluid intelligence and crystallized intelligence. Both fluid and crystallized intelligence are viewed as components of general intelligence, but fluid intelligence is applied to tasks which are novel to the examinee while crystallized intelligence is believed to reflect education and experience. Other, less significant components include general visualization, general fluency, and general speed. The Cattell-Horn model (1966) distinguishes between an individual's ability to solve problems which are largely independent of past experiences and formal educational training (fluid intelligence) and the individual's ability to apply aspects of formal training to more familiar 35 problem solving situations (crystallized intelligence). With this distinction in mind, Kaufman and Kaufman have attempted to incorporate "fluid" tasks into the Mental Processing component of the K-ABC while including items which require "crystallized" abilities in the Achievement component. Of interest for the purpose of this research is the examination of the Cattell—Horn "fluid-crystallized" theory of intelligence and the extent to which the K-ABC Mental Processing and Achievement components correspond to this theoretical dichotomy. Since the distinction between "ability" and "achievement" is implicit in the determination of a severe discrepancy between a student's observed and expected levels of achievement, the extent to which a test or set of tests is capable of separately measuring fluid and crystallized components of intelligence is of interest. A closer examination of the accuracy of the K-ABC in representing the Das-Luria and Cattell—Horn models will appear in Section D. While the K-ABC grew from the work of researchers and theorists who demonstrated the existence of a simultaneous/sequential information processing dichotomy, it will be seen that the K-ABC Mental Processing subtests may fall short of adequately assessing these two components (Das, 1984). Likewise, critics (Sternberg, 1984; Bracken, 1985) seriously question the application of Cattell's fluid and crystallized components of intelligence to Kaufman's Ls____.__ 36 categorization of "mental processing" and "achievement" tasks. Before reviewing critiques of the K-ABC, however, several correlational and factor studies will be examined to determine the relationship of the K-ABC to well- established and widely used intelligence and achievement tests. C. K-ABC Validity Studies In attempting to anticipate differences which might be observed between the use of the K-ABC Mental Processing Composite and the Wechsler Full-Scale IQ in the determination of a severe discrepancy between ability and achievement it is useful to review the literature which addresses the comparability of the two instruments. Several validity studies have been conducted which have systematically compared the scores from the K-ABC, the WISC-R, and standardized achievement tests in populations of students referred and not referred for academic problems. 1. Normal Children Kaufman and Kaufman (1983b) have described a number of correlational studies which were conducted as part of test development and standardization procedures for the K—ABC. Of particular interest is the research which examined the relationship between the K-ABC composite scores and the WISC-R scale scores. When examining a combination of three samples of 37 normal children (n = 182) the test authors report a correlation of 0.70 between the WISC—R Full Scale IQ and the K-ABC Mental Processing Composite. Somewhat weaker relationships were observed between the Full Scale IQ and the K-ABC Sequential Processing (r = 0.47) and Simultaneous Processing (r = 0.68) standard scores. The strongest score correspondence was reported between the Wechsler Full Scale IQ and the K-ABC Achievement Composite (r = 0.78). Kaufman and Kaufman suggest that this strong relationship is attributable to heavy reliance on verbal skills and factual knowledge in determining the Wechsler Full Scale IQ, skills which are also measured on the achievement subtests of the K-ABC. The authors interpret these correlations as evidence that the Wechsler scales and other traditional measures of intelligence are "to a large extent measures of children's school related accomplishments" (p. 111). The K—ABC Mental Processing tasks are viewed as estimates of more "fluid" abilities while the Achievement tasks (and many of the Wechsler Verbal Scale tasks) represent "crystallized" abilities according to the Kaufmans' interpretation of the Cattell—Horn processing dichotomy. Additional studies which examined the predictive validity of the K-ABC Achievement Composite through correlations with a number of standardized achievement tests are also reported in the Interpretive Manual of the 38 K-ABC. Murray and Bracken (Study #28*) found a correlation of 0.52 between the K—ABC Mental Processing Composite and the PIAT Total standard score for a sample of 29 normal children. A predictably higher correlation of 0.72 is reported between the K—ABC Achievement Composite and the PIAT Total standard score with correlations between the MPC and individual PIAT subtest scores ranging from 0.34 (Spelling) to 0.65 (Reading Comprehension). Other research by Lewis and Swerdlick (Study #25) assessed the relationship between the Iowa Tests of Basic Skills and the K-ABC standard scores for a group of 18 normal children following a six month interval. Correlations were obtained between the ITBS Composite standard score and the K-ABC Mental Processing Composite (r = 0.58) and between the ITBS Composite and the K-ABC Achievement standard score (r = 0.89). Childers, Durham, and Bolen (Study #10) provide further evidence of the predictive validity of the K-ABC through research which examined the relationship between the K—ABC and the California Achievement Test for 45 normal children. Following a twelve month interval, correlations of 0.65 between the CAT Total Battery and the K-ABC Mental Processing Composite and 0.77 between the CAT Total Battery and the K-ABC Achievement Composite were obtained. Studies which have examined the concurrent validity of *Studies which were included in the standardization research (Kaufman & Kaufman, 1983b) are referenced by the study numbers which appear in the K—ABC Interpretive Manual. 39 the K-ABC are also useful in providing insights into the relationships between the K-ABC and various measures of achievement. Kamphaus (Study #20) evaluated the agreement between the K-ABC MPC standard scores and the Woodcock Reading Mastery Tests Passage Comprehension and the KeyMath Diagnostic Arithmetic Test Written Computation standard scores for a large group of normal children. Coefficients of 0.63 between the K-ABC MPC and the Passage Comprehension subtest and 0.82 between the K-ABC Achievement standard scores and the Passage Comprehension subtest scores were obtained. Somewhat lower correlations were reported between the K-ABC and Written Computation subtests (r = 0.47 MPC/Written Computation and r = 0.59 Achievement/ Written Computation). Cummings and McLeskey (Study #13) examined the relationship between the K-ABC Achievement standard score and the PIAT subtest scores for 31 normal children. The results of the study indicate coefficients ranging from 0.63 (Spelling) to 0.82 (Reading Recognition) for PIAT subtests scores. A correlation of 0.89 was obtained between Total PIAT standard score and the K-ABC Achievement standard score. Additional studies reporting the relationship between the K—ABC and Wide Range Achievement Test for normal children show correlations in the range of 0.45 to 0.73. In a recently reported study, Naglieri (1985b) investigated the relationship between normal children's (n 40 = 51) performance on the McCarthy Scales, the K-ABC, and the PIAT. A moderate correspondence was found between scores on the McCarthy General Cognitive Index and the K-ABC Mental Processing Composite (r = 0.55). The McCarthy General Cognitive Index was found to be strongly related to academic skills with a correlation of 0.74 between the PIAT Total standard score and the GCI. The correlation coefficient between the K—ABC Mental Processing Composite and the PIAT Total standard score was somewhat lower (r = 0.57) while the coefficient between the K—ABC Achievement standard score and the PIAT Total standard score was 0.86. In spite of the substantial correlation between the PIAT and the K-ABC Achievement standard scores, the PIAT subtest scores have been reported to be consistently higher than their K-ABC Achievement counterparts. The most extreme example of this mean score difference can be seen when comparing the average K-ABC Reading/Understanding standard score (104.5) with the average PIAT Reading Comprehension standard score (117.7). Naglieri (1985b) suggests a need to determine which subtest scores most closely correspond to the student's actual academic functioning. In spite of these mean score differences, the findings described in this study are very similar to the relationships reported by Murray and Bracken (Study #28 and 1984) and other studies reported in the Interpretive Manual which have evaluated the relationships between the K-ABC Mental Processing and other ability tests, such as the 41 WISC-R. The findings of the validity studies for normal children generally provide impressive evidence for construct, predictive, and concurrent validity of the K- ABC. A close correspondence between results obtained from the K-ABC Achievement subtests and PIAT achievement subtests could be anticipated on the basis of the coefficients, although the average standard scores on the PIAT achievement subtests may be somewhat higher than the K-ABC Achievement standard scores. Of additional interest are the reports that the correlations between the K—ABC Mental Processing Composite and Achievement scores tend to be smaller than the correlations between the WISC-R Full Scale IQ and similar measures of achievement. While this finding is consistent throughout many research studies, it should be noted that the Naglieri and Haddad (1984) study failed to demonstrate this pattern of score relationships. 2. Learning Disabled Students Several studies which examined the performance of identified learning disabled students and learning disabilities referrals on the K-ABC are also reported in the K-ABC Interpretive Manual. As with the reported research with normal subjects, many of these studies have evaluated the relationship of the K-ABC with other well— known and widely used ability and achievement tests. The results of these studies provide clues regarding the impact of the use of the K-ABC on diagnostic decisions. Kaufman 42 and Kaufman (1983b) report the consolidated results of four studies which investigated the relationship between the K- ABC and the WISC-R for learning disabled students (n = 138). The correlations between the Wechsler Scales and the K-ABC Global Scores are very similar to those reported for normal subjects with a coefficient of 0.74 obtained between the K-ABC MPC and the WISC-R Full Scale IQ and a correlation of 0.71 reported between the K-ABC Achievement standard score and the WISC—R Full Scale IQ. The Kaufmans interpret these results as additional evidence of the construct validity of the K—ABC with learning disabled students. A similar pattern of test intercorrelations was obtained for a group of 60 children who were referred for learning disabilities (Gunnison, Masunaga, Town, & Moffitt, Study #17), although the coefficients were somewhat smaller than the correlations reported for the normal and learning disabled samples. The slightly lower correlations presumably resulted from a restriction of range on the K-ABC rather than from any inherent differences in the variable relationships (Kaufman & Kaufman, 1983b). Gunnison, et al. (Study #17), Naglieri and Haddad (Study #32), and Klanderman, Kroeschell, and Licht (Study #23) examined the relationships between the K—ABC Achievement subtests and scores obtained by learning disabled students on other individually administered achievement measures. The results of these studies 43 indicate correlations ranging from 0.59 to 0.66 between the PIAT and K-ABC Arithmetic subtests and from 0.40 to 0.71 between the WRAT and K—ABC Arithmetic subtests. Correlations between the WRAT Reading subtest and the K—ABC Reading/Decoding and between the PIAT Reading Recognition and the K-ABC Reading/Decoding ranged from 0.60 to 0.87 (Kaufman & Kaufman, 1983b). Kaufman and Kaufman further describe the general profiles which typified the learning disabled students who _ participated in the standardization studies (Gunnison, et al., Study #17; Hooper & Hynd, Study #19). For this group of children, Simultaneous standard scores were, on the average, 2 to 5 points higher than Sequential Processing standard scores. Gestalt Closure represented the strongest Mental Processing subtest for the learning disabled and dyslexic children. Within the Achievement area, the average Riddles subtest score was the highest for this group of students. Subtests which were the most difficult for the learning disabled students included Matrix Analogies, Photo Series and Spatial Memory. It is suggested that learning disabled students experience difficulty on tasks which require the integration of both sequential and simultaneous processing abilities while performing relatively well on tasks which are measures of pure simultaneous processing. Gunnison, et al. (1982) report that 70 percent of the significant discrepancies between Simultaneous and Sequential Processing scores 44 reflected stronger Simultaneous than Sequential abilities for learning disabilities referrals. Studies by Klanderman, et a1. (#23), Snyder, et al. (#39), and Naglieri and Haddad (#32) showed an equal proportion of discrepancies in both directions (Kaufman & Kaufman, 1983b, p. 139). Of particular interest are studies which have investigated the relationships between K-ABC Mental Processing subtest patterns and performance on various measures of achievement. McRae (1981) tested 65 normal children with the PIAT Reading Recognition and Reading Comprehension subtests and, subsequently, identified four groups of students as "high recognition-high comprehension," "high recognition-low comprehension," "low recognition-high comprehension," or "low recognition-low comprehension" on the basis of the PIAT scores. Upon testing these groups with the K—ABC, McRae found a significant relationship between reading comprehension and simultaneous processing, with the group identified as high recognition-low comprehension scoring significantly lower than the other groups on the Simultaneous Processing Scale. Kaufman and Kaufman (1983b) summarize the findings of the standardization research with learning disabled students, learning disabilities referrals, and dyslexic children, suggesting that these students perform better on Gestalt Closure, Triangles, and Riddles subtests while exhibiting most difficulty with Hand—Movements, Word Order, 45 Faces and Places, Arithmetic, Reading/Decoding and Reading/Understanding subtests. Consistently higher (half a standard deviation) standard scores on Simultaneous than on Achievement Global scores are also reported for this group of handicapped children (pp. 142-143). In a study of 32 exceptional children (19 learning disabled and 13 educable mentally retarded) Obrzut, Obrzut, and Shaw (1984) examined the relationship of the WISC—R and the K-ABC standard scores. The results of the study demonstrated a stronger relationship between the K-ABC MPC and the WISC-R Full Scale IQ (r = 0.77) than between the K-ABC MPC and the K-ABC Achievement scores (r = 0.54). For the learning disabled group, the average K-ABC Simultaneous score was eight and a half standard score points higher than the Sequential Processing score, findings which are consistent with results reported in the K-ABC Interpretive Manual. In addition to the research conducted as part of the K-ABC standardization process, several studies have been undertaken to investigate the generalizability of the three factor (Sequential/Simultaneous/Achievement) structure of the K—ABC for children with learning difficulties. Keith (1986) performed a principal components factor analysis on the K-ABC subtest scores of 585 children who were referred for psychological evaluation. Seventy-six percent of these students were referred for problems in school achievement. When only the Mental Processing 46 subtests were included in the factor solution, the highest loadings on the first, unrotated factor were achieved with the Photo Series, Triangles, Spatial Memory, and Word Order subtests, suggesting that these subtests are the best measures of general intelligence or "g." Varimax rotation yielded two factors, simultaneous and sequential processing, findings which are consistent with previous studies with normal children. Keith concludes that "the K- ABC MP Scale's factor structure seems quite stable for normal and exceptional children" (p. 243). When Achievement subtests were included with the MP subtests in the factor analysis, however, a somewhat different structure emerged. The Achievement subtests and the MP Photo Series subtest loaded highest on the first, unrotated factor, suggesting that the Achievement subtests may, in fact, be a better estimate of "9" than most of the Mental Processing subtests. The rotated factor solution yielded a three factor solution which Keith alternatively labels: I. Simultaneous, II. Achievement, III. Sequential or I. General Ability/Reasoning, II. Reading Achievement/Verbal, and III. Verbal Memory. A four factor solution yielded a separate factor for reading with high loadings achieved on Reading Decoding and Reading Understanding subtests. Keith notes that the factor structure obtained for referred children closely approximates the results of previous studies with normal children (Keith, 1985; Keith & 47 Dunbar, 1984; Kaufman & Kaufman, 1983b), confirming that the battery is operating quite consistently across groups. The interpretation of the factor structure, however, is not as clear as Kaufman and Kaufman indicate in the K-ABC Interpretive Manual. In another recent study, Kaufman and McLean (1986) performed a joint factor analysis of the K—ABC and the WISC-R using scores from 198 learning disabled and/or referred students. Citing a previous joint factor study using normal children (Kaufman & McLean, 1985) which demonstrated a merger of each of the K-ABC factors with a previously established WISC-R dimension (i.e., K—ABC Achievement with WISC—R Verbal Comprehension, K—ABC Simultaneous with WISC-R Perceptual Organization, and K-ABC Sequential with WISC-R Freedom from Distractibility), the authors question whether a similar structure would be obtained with children with learning difficulties. The results of the study indicate strong evidence of a characteristic ACID profile on the WISC-R (low scores on Arithmetic, Coding, Information, and Digit Span). In contrast, very little variability was noted among the K—ABC MP subtest scaled scores. Performance IQ was slightly higher than Verbal IQ (VIQ: 93.1, PIQ: 96.4) on the Wechsler while the mean Simultaneous Processing score (93.3) was slightly higher than the mean Sequential Processing score (91.4) on the K-ABC. Joint factor analysis yielded defensible three and 48 four factor solutions. The three factor solution corresponded to the previous solution obtained with normal children, showing a merger of the WISC-R and K-ABC factors. The four factor solution suggests that the joint structure might be characterized by Simultaneous/Perceptual Organization, Achievement/Verbal, Sequential/ Distractibility, and Reading Ability. The four factor solution for L.D. and referred children agrees with the factor solution obtained by Keith (1986), indicating that certain of the subtests (in particular, the K-ABC Achievement subtests) function differently for L.D. children than for normal children. This is not surprising considering that many of the L.D. and referred students were probably experiencing reading difficulties. The authors also argue, however, that the strength of the first three factors in this analysis provides further support for the construct validity of the K-ABC with learning disabled students. Using the standardization data from the WISC-R, Lawson and Inglis (1985) examined the unrotated factors from a principal components analysis and found two significant factors, the first representing general intelligence or "g" and the second representing a verbal—nonverbal continuum. For learning disabled students, they discovered that "the degree of deficit shown by L.D. children on any particular subtest...is almost exactly proportional to the amount of verbal content of that subtest as expressed by its Factor 49 II coefficient" (p.80). In an attempt to replicate this finding with the K-ABC, Inglis and Lawson (1986) submitted intercorrelations from the K-ABC standardization sample to principal components analysis and again obtained two significant unrotated factors: I. a general factor and II. a verbal— nonverbal factor. Number Recall (-.50), Word Order (-.42), Faces and Places (-.08), Riddles (-.08), Reading Decoding (-.26) and Reading Understanding (-.24) all had negative loadings (representing "verbal" subtests) while Hand Movements (.03), Gestalt Closure (.47), Triangles (.40), Matrix Analogies (.21), Spatial Memory (.38), Photo Series (.30), and Arithmetic (.01) had positive loadings (representing "nonverbal" subtests). To determine the utility of Factor II in explaining the performance of learning disabled students, Inglis and Lawson correlated the Factor II score coefficients with the mean subtest score of the L.D., L.D. referrals, and dyslexic samples from the K-ABC Interpretive Manual. Positive, statistically significant coefficients were obtained in all cases (.55, .64, and .67, respectively), suggesting that, as with the Wechsler subtest scores, the amount of deficit shown by children with learning difficulties tends to be proportional to verbal content. While not preempting the rotated three or four factor solutions offered by other researchers (Keith, 1986; Kaufman & McLean, 1986), Inglis and Lawson suggest that the 50 verbal-nonverbal continuum provides a useful and generalizable structure for interpreting learning difficulties. Contrasting the Inglis and Lawson study, Hooper and Hynd (1986) performed an analysis of K-ABC subtest score patterns for normal and dyslexic students. Citing previous research (Bannatyne, 1968, 1971; Das, 1984; Das, et al., 1979; Rugel, 1974) which has demonstrated that sequential processing difficulties constitute the primary processing problems for disabled readers, Hooper and Hynd hypothesized that dyslexic children would score significantly lower than normal children on the K-ABC Sequential Processing subtests. Analysis of scores from 55 dyslexic and 30 normal readers (sample from Hooper & Hynd, Study #32) showed that Hand Movements, Number Recall, Word Order, Matrix Analogies, each Achievement subtest, the Sequential Factor, the Achievement Factor, and the Mental Processing Composite all significantly differentiated between the groups in favor of the normal readers. The Matrix Analogies subtest was the only Simultaneous Processing subtest which significantly distinguished between groups. Descriptive discriminant analysis revealed Reading Decoding, Faces and Places, Arithmetic, Number Recall, Matrix Analogies, Reading Understanding, Hand Movements, and Riddles to be significant predictors of group membership, while predictive discriminant analysis revealed that the K-ABC correctly classified 86.7 % of normal and 51 92.7 % of dyslexic readers. The authors conclude that the results "implicate sequential processing deficits in the development of reading disability...The study lends additional support to this notion with the significant accuracy with which the K-ABC, particularly the Sequential and Achievement subtests could predict group membership" (p. 201). Other studies suggest that profile analysis with learning disabled children may be speculative, at best. In a study with 33 learning disabled students, Naglieri and Haddad (1985) demonstrate higher average standard score for the Sequential Processing Scale than for the Simultaneous Processing Scale. Additionally, the PIAT Total standard score is slightly lower than the K-ABC Achievement Composite. Although no individual achievement subtest scores were reported for the K—ABC, this evidence might indicate that the average K-ABC Achievement subtest score is more comparable to the Average PIAT subtest score than suggested by the Naglieri (1985b) study with normal children. Also of note is a "somewhat lower" (5 standard score points) K-ABC Mental Processing Composite than WISC-R Full Scale IQ. This finding is consistent with results reported for learning disabled students in the K-ABC Interpretive Manual and may be attributable to the change in performance of standardization samples over time (Naglieri & Haddad, 1984, p. 54). 52 Correlations between the K—ABC Mental Processing Composite and the PIAT and WRAT subtests were generally similar to those obtained between the WISC-R Full Scale IQ and the respective achievement subtests. Interestingly, the relationship between the Simultaneous Processing Scale and the PIAT Total Test score was significantly higher (r = 0.71) than the relationship between the Sequential Processing Scale and the PIAT Total (r = 0.30). Naglieri and Haddad suggest that the disparate findings of this research may be attributable to the small sample size, the variable procedures used in identifying the learning disabled children, or the heterogeneous nature of the sample. Another study which questions the validity of distinctive learning disabilities profiles on the K-ABC was conducted by Naglieri (1985a). Using matched groups of learning disabled (n = 34), borderline mentally retarded (n = 33), and normal children (n = 34), Naglieri failed to find significant differences between the WISC-R Full Scale IQ and the K—ABC Mental Processing Composite across groups. For the learning disabled children, the mean ability estimates from the two measures were 96.8 (Full Scale IQ) and 96.1 (Mental Processing Composite). Even more importantly, the results of the study failed to find significant differences between the mean K-ABC Simultaneous—Sequential discrepancy or between the mean K—ABC Mental Processing-Achievement discrepancy across the 53 three groups of children. Naglieri concludes that "a Simultaneous-Sequential Scale disparity may not typify learning disabled children under the current system of state and federal guidelines" (p. 138). Through a careful analysis of subtest score profiles for the learning disabled and borderline children, Naglieri discovered that, on both the WISC-R and K-ABC, the exceptional children performed best on tasks which had a simultaneous component (WISC—R: Picture Arrangement and Object Assembly; K-ABC: Gestalt Closure and Photo Series) while demonstrating more difficulty with tasks which were largely sequential or academic in nature (WISC-R: Digit Span, Information, Arithmetic, and Vocabulary; K-ABC: Number Recall, Word Order, Hand Movements, and Reading subtests). Naglieri also found that the exceptional children performed poorly on the Matrix Analogies subtest of the K-ABC. These results are generally consistent with the profiles of learning disabled children reported by Kaufman and Kaufman in the K-ABC Interpretive Manual. It is suggested that the complexity of the exceptional children's performance on the K—ABC, with both strengths and weaknesses displayed on the sequential and simultaneous processing tasks, contributes to the inadequacy of a simple simultaneous-sequential dichotomy in characterizing the performance of these children. In examining the intercorrelations between the WISC-R and K—ABC Global Scales standard scores, Naglieri reports a 54 higher correlation between the WISC-R Full Scale IQ and the K-ABC Achievement standard score (r = 0.89) than between the K-ABC Mental Processing Composite and the K—ABC Achievement scores (r = 0.74). He interprets this finding as supportive evidence for the conclusion that the WISC-R Verbal Scale has a substantial achievement component (an argument initially made by Kaufman and Kaufman (1983b), but countered by Keith & Dunbar (1984) and Keith (1985, 1986). It is further argued that it is inappropriate to use two measures of achievement (WISC-R and an individually administered achievement test) when determining an ability/achievement discrepancy for the classification of learning disabled students. The reader is uncertain, at the conclusion of the research report, whether Naglieri is suggesting that a K—ABC Mental Processing/Achievement discrepancy is a more appropriate procedure for classification purposes. If there are no significant differences in the average discrepancies across normal and exceptional groups, this procedure must be seriously questioned, as well. An additional source of confusion centered on Naglieri's failure to distinguish the direction of the sequential/simultaneous difference when performing his analysis of variance on mean differences across groups. When reviewing his table of mean differences, it is apparent that the average Sequential Scale score is seven and a half points lower than the average Simultaneous 55 Scale score for children with learning disabilities. This difference is very consistent with Kaufman and Kaufman's report of a Simultaneous Processing score which is a half standard deviation above the Sequential Processing score for this group of exceptional children. For normal children, Naglieri reports a Sequential Processing score which is slightly higher than the average Simultaneous Processing score. The failure to uncover significant Simultaneous/Sequential differences across groups appears to have resulted from the consolidation of all differences, regardless of the direction of difference. The same uncertainty is apparent, though less pronounced, in the results from the Mental Processing/Achievement discrepancy analysis. Another recent study by Klanderman, Perney and Kroeschell (1985) compares the performance of 44 learning disabled children on the K-ABC, the WISC-R and the Peabody Picture Vocabulary Test (PPVT-R). They found that the Verbal Scale of the WISC-R correlated strongly with the K—ABC Achievement Scale (r = 0.79). Additionally, the Simultaneous Scale of the K-ABC showed a strong relationship with the WISC-R Performance scale (r = 0.82). When the correlation matrices were factor analyzed, it was found that the subtest factor loadings were somewhat different for this group of children than for normal children, with Hand Movements loading on the "Simultaneous" factor and only Number Recall and Word Order loading on the I —. 56 "Sequential" factor. The authors interpreted this finding as suggestive that "the learning disabled group processes material somewhat differently than normative populations" with a tendency to "use a combined processing method and slightly more simultaneous processing for the Hand Movements task" (p. 526). While these results might be indicative of a possible processing distinction between normal and learning disabled children, the study also provides supportive evidence for an alternative factor structure of the K—ABC; one based upon a verbal-nonverbal distinction. Number Recall and Word Order are the only two K—ABC Mental Processing subtests which are primarily dependent on verbal-auditory processing. Das (1984) also notes that the Hand Movements subtest loads on the Simultaneous factor for children above 10 years of age. The fact that Klanderman, et a1. do not provide a specific breakdown of age levels of children included in their study, as well as the fact that children up to age 13 years, 2 months were included in their sample (upper age of the K-ABC is 12 1/2 years) creates further concern regarding the validity of the results of this study. The examination of K—ABC research conducted with learning disabled, dyslexic, and L.D. referred students offers a number of insights regarding the performance of these students on the K—ABC. It is intuitive that the Achievement subtests would 57 differentiate children with learning problems from normal children (particularly Reading subtests for dyslexic children). More interesting are the patterns of MP subtest scores which were found for the exceptional children. Summarizing the findings from the various studies, Kaufman and Kaufman (1983b) suggest that the Hand Movements and Word Order subtests are the most difficult for learning disabled students while the Gestalt Closure subtest is among the easiest. They conclude that learning disabled students experience difficulty on tasks which require the 1 integration of both simultaneous and sequential processing while performing well on tasks which are measures of pure simultaneous processing. Inglis and Lawson (1986) indicate that Number Recall and Word Order are the most difficult Mental Processing subtests for children with learning problems, reflecting a difficulty of these students in performing tasks with a verbal component. Hooper and Hynd (1986) found Hand Movements, Number Recall, Word Order, and Matrix Analogies to be the most difficult and discriminating K-ABC MP subtests for their sample of dyslexic students, suggesting that there are sequential processing deficits in the development of reading disability. Photo Series was found to be the easiest subtest for the dyslexic children. Naglieri (1985a) reports that his sample of L.D. children achieved the lowest scores on Hand Movements, Number Recall, and Matrix Analogies while performing the best on Gestalt Closure and 58 Photo Series subtests. While there are some apparent inconsistencies among these studies, it appears that, in general, the sequential subtests: Hand Movements, Word Order, and Number Recall tend to be more difficult for the children with learning problems. Matrix Analogies is the most difficult of the Simultaneous subtests, while Gestalt Closure (and less consistently, Photo Series) is generally an easier task for the exceptional children. Several difficulties are encountered when trying to generalize the research findings. To begin, different types of children were included in the research samples. Dyslexic, learning disabled, and learning disabilities referrals were variably represented in the studies. The results may be better generalized to "children with learning difficulties" than specifically to learning disabled students. It will be recalled that McRae (1981) found simultaneous processing deficits to be more closely related to reading comprehension difficulties, results which contrast with those of the research with "dyslexic" children (Hooper & Hynd, 1986). Future research may need to more clearly differentiate the type of learning disability which is being studied. Secondly, several of the studies (Inglis & Lawson; Kaufman & McLean; Hooper & Hynd) make use of data from the K-ABC standardization samples which may contribute to overlapping results. While Kaufman and Kaufman discuss specific studies in the 59 Interpretation Manual, the samples are often consolidated, making it difficult to pinpoint confounding effects. In spite of these shortcomings, it appears that the learning disabled students and/or "children with learning difficulties" may have more difficulty with sequential/verbal type tasks than tasks of a predominantly simultaneous nature. Matrix Analogies, which is considered a measure of integrated functioning, may be contributing to the failure of a Sequential/Simultaneous discrepancy to distinguish learning disabled students. Of note is the close correspondence of the sequential subtests of the K-ABC to the distractibility factor of the WISC-R (Kaufman & McLean, 1986). The three subtests contributing to the distractibility factor (Arithmetic, Coding, Digit Span) have been previously implicated in the performance of learning disabled students. It is possible that the same underlying processes are operating for the Sequential subtests. Finally, in spite of evidence that reflects different processing strategies for learning disabled students, there is considerable support for Kaufman and Kaufman's original factor structure with learning disabled children. Patterns of test intercorrelations as well as the factor analytic studies provide strong evidence for the generalizability of the two factor structure of the Mental Processing scale. The Achievement scale, quite understandably, may be functioning somewhat differently for the learning disabled 60 students. The debate regarding the best description of the K—ABC factors is still unresolved. D. Critique of the K-ABC In spite of Kaufman and Kaufman's careful attempts to adhere to theory in the development of the K-ABC, there have been a number of critical reviews which have questioned their success in accomplishing this goal. Of particular interest has been the extent to which the Das— Luria successive-simultaneous processing distinction has been accurately represented by the Kaufman Sequential and Simultaneous subtests (Bracken, 1985; Das, 1984). There have been additional concerns regarding how well the Mental Processing and Achievement subtests measure "fluid" versus "crystallized" intelligence according to the Cattell-Horn model of intelligence (Bracken, 1985; Sternberg, 1984). Several authors (Jensen, 1984; Keith, 1985) have suggested that the abilities assessed by the K-ABC might, in fact, be characterized by alternative models. When discussing the match between the K-ABC and the Das-Luria model of information processing, Bracken (1985) questions the ability of only three subtests (Word Order, Number Recall, and Hand Movements) to accurately assess the sequential processing dimension defined by the model. It is suggested that the restricted and specific nature of the K-ABC Sequential tasks "reduce the sequential processing demands of the K-ABC to simple sequential visual and auditory short term memory" (p. 23). This simplistic 61 nonverbal approach to the assessment of sequential abilities contrasts with the Das, Kirby, and Jarman (1979) comprehensive description of sequential processing as "perceptual, conceptual, or mnestic in nature, with conceptual sequential processing representing complex intellectual behaviors (p. 89). Bracken further suggests that the K-ABC Sequential Processing component tasks have very little correspondence with "complex intellectual behaviors and classroom instruction" (p. 25). Jensen (1984) echoes this concern by describing the K-ABC Sequential tasks as reflective of "Level I" abilities. According to his hierarchical theory of intelligence, Level I abilities are measured by tasks which require rote, short term memory. This contrasts with the more complex cognitive abilities reflected in Level II processing. Jensen further argues that Face Recognition and Spatial Memory subtests of the Simultaneous Processing scale are also reflective of the simpler Level I, short- term memory tasks and that other Simultaneous tasks are inadequate for assessing more complex intellectual abilities. Das (1984), perhaps the most qualified critic of the correspondence of the K—ABC to the Das-Luria model of intelligence, argues that the Kaufmans have used a very restricted interpretation of Luria's observations regarding brain organization when developing the Mental Processing subtests of the K-ABC. It will be recalled that Luria 62 proposed three functional divisions of the brain, the first associated with arousal, the second associated with coding of information, and the third involved with planning and decision making. Das suggests that the only type of cognitive processing measured by the K—ABC involves Luria's second block or information coding. There is no attempt to assess either arousal or planning, which seriously restricts the utility of the K-ABC as a comprehensive measure of cognitive processing. Not only are there inadequate provisions for assessing all of the components of the Luria model, but the perceptual modality used in evaluating simultaneous information coding is restricted exclusively to visual processing. Das recommends that both simultaneous and successive processes be evaluated through more than one modality, and preferably through auditory, visual, and kinesthetic modalities. Like Jensen and Bracken, Das observes that all Sequential Processing tasks on the K-ABC are memory tasks. He also notes that, by age 10, the Hand Movements subtest, the only primarily visual sequential task, has a higher factor loading on the Simultaneous dimension, leaving only two verbal subtests to adequately measure sequential processing for older children. This pattern of factor loadings was also discussed in the earlier review (Section C) of the Klanderman, et al. (1985) study with learning disabled children. Das observes that, after age 10, a verbal-nonverbal dichotomy might better characterize the 63 Mental Processing subtests. It is unclear however, how this dichotomization would correspond with the Wechsler Verbal—Performance distinction. Keith (1985) has offered an alternative interpretation of the K-ABC based upon independent confirmatory factor analysis. Instead of the Sequential/Simultaneous dichotomy, Keith suggests that the Mental Processing factors might better be characterized as "verbal memory" and "nonverbal reasoning." When both Mental Processing subtests and Achievement subtests are included in the factor solution, Keith finds dimensions which reflect verbal memory, verbal reasoning, nonverbal reasoning, and reading achievement (p.18). While Keith cautions that the factor structure obtained does not disprove the Sequential— Simultaneous processing structure of the K—ABC, he concludes that the results of his analysis "certainly do not support the K-ABC theory as much as the manuals would suggest" (p. 18). Keith's interpretation would correspond quite closely, however, with Jensen's observations that the K-ABC Sequential component is largely represented by Level I, short—term memory skills as well as Das' reinterpretation of the Mental Processing tasks as better represented by a verbal—nonverbal distinction after age 10. Other critics include Sternberg (1984) who questions the purported ability of the K—ABC to assess a child's problem solving and information processing styles. He suggests that, because the tasks involved on the K-ABC are 64 not pure measures of sequential or simultaneous processing, and because the assessment of information processing style is restricted to tasks rather than to individuals, it is unclear how the K-ABC results contribute to the understanding of a child's approach to problem solving. The observation that the Photo Series subtest was moved from the Sequential to the Simultaneous Processing Scale after it failed to load on the initial (and more intuitively appealing) sequential factor, as well as the inconsistent split loading of the Hand Movements subtest on the sequential and simultaneous factors, would offer support for Sternberg's arguments. Sternberg also expresses concern over the attempt to limit the assessment of verbal abilities to the Achievement component of the K-ABC. He cites the major emphasis that most major psychometric and information processing theorists place upon verbal abilities in the measurement of intelligence. Evidence offered by Kaufman and Kaufman (1983b) and Naglieri (1985b) which demonstrates the consistently higher correlation between the K-ABC Achievement Scale and other measures of intelligence than between the MPC and traditional IQ is interpreted by Sternberg as lack of convergent-discriminant validity for the K-ABC. Kaufman, on the other hand, argues that the higher correlation between achievement and traditional intelligence measures offers proof of the contamination of intelligence with achievement. The MPC is viewed by its 65 authors as the more "pure" measure of "fluid" intelligence. Others, such as Bracken (1985), counter with observations that "the MPC correlates as well or better than traditional IQ tests with measures of achievement," findings which "indicate that the K-ABC Mental Processing Scale, in spite of efforts to separate intelligence from achievement, is related to achievement as much or more so than the traditional intelligence tests" (p. 25). Bracken's observations are based upon the disparate findings of studies by Naglieri and Haddad (1984) and Murray and Bracken (1984) which demonstrate equal, or higher correlations between the MPC and achievement measures than between the WISC-R Full Scale IQ and similar achievement measures. Thus, it appears that the attempt to separate fluid from crystallized intelligence according to the Cattell- Horn model of intelligence may have been less than completely successful. Bracken (1985) returns to Cattell's original characterization of fluid and crystallized intelligence, citing Cattell (1969): "Crystallized ability is not identical with scholastic achievement. Many scholastic skills depend largely on rote memory, whereas what factor analysis shows is crystallized ability in that section of school learning involving complex judgement skills that have been acquired by the application of fluid ability" (p. 114). In examining the Achievement subtests of the K—ABC, Bracken would classify only the Riddles 66 subtest as an adequate measure of crystallized ability. He further concludes that "equating the K-ABC Achievement Scale with crystallized intelligence is not an accurate representation of the Cattell—Horn model" (p. 25). Bracken also finds the MPC of the K—ABC to be a less than convincing representation of Cattell's fluid ability component of intelligence. Like Jensen, who finds an over— representation of lower level, short—term memory tasks in the Sequential Processing subtests, Bracken observes that all of the Sequential Processing subtests are restricted to assessing associative memory skills, and two of the seven Simultaneous subtests are primarily measures of short-term memory. Consequently, only five of seven Simultaneous subtests and only five of ten Mental Processing subtests are measures of non—memory related fluid intelligence (reasoning, judgment, analogies, etc.). Perhaps the most notable short-coming of the K—ABC identified by its critics is its failure to adequately tap higher level cognitive abilities. Unlike traditional intelligence tests which rely on more higher level mental abilities (what Jensen would refer to as "g"), the K-ABC seems to be over—represented by short—term, associative memory tasks. The lower correlations between the MPC and K-ABC‘ Achievement Scale than between traditional IQ tests and the K—ABC Achievement Scale have been interpreted by critics as evidence that, in fact, "the K-ABC Achievement Composite measures ability more than Achievement and measures ability better than the MP Scale" (Keith, 1985, p. 10). Keith cites evidence from Swerdlik and Lewis (1983) which demonstrates that the correlation between the WISC-R Verbal Scale and the K-ABC Achievement Scale was larger than the correlation between the K-ABC Achievement Scale and the Composite Achievement score on the Iowa Tests of Basic Skills. If, in fact, the Achievement Scale was measuring achievement, 3 higher correlation might be anticipated between the two achievement tests. Clearly, there are alternative explanations for the observed relationship between traditional ability tests (particularly verbal intelligence) and the K—ABC Achievement Composite. When comparing the subtest scores of the K-ABC Mental Processing Composite with the WISC—R subtest results, what might be anticipated in terms of profile differences? Kaufman (1979) published an article on cerebral specialization and intelligence testing in which he discussed the Wechsler Scales in terms of tasks which involved right hemisphere, holistic, simultaneous processing and tasks which required left hemisphere, sequential processing, as well as tasks which appeared to require integrated functioning of the two cerebral hemispheres. Since the K—ABC Mental Processing Composite is based upon this information processing distinction, those Wechsler tasks which appear to require more holistic, simultaneous processing should show a stronger relationship 68 with the Simultaneous Processing Scale of the K-ABC while those which are more dependent on sequential, analytical abilities should correlate more strongly with the Sequential Scale. Regarding holistic processing, Kaufman notes that, of the WISC-R subtests, only Picture Completion and Object Assembly require distinctly simultaneous "right brain" processing. Other Performance subtests are seen as requiring a combination of simultaneous and sequential processing. The Verbal subtests, although primarily characterized as sequential, "left brain" tasks, in most cases demand an integration of visual-spatial and temporal— language skills. Noted examples include the mental arithmetic (Arithmetic) and digits backward (Digit Span) tasks of the Verbal Scale. It is also observed that the heavy reliance on verbal instructions on all but the Object Assembly and Picture Completion subtests of the Wechsler increases the necessity for "left brain" involvement for efficient and effective task solution. Kaufman describes research with split—brain patients which shows clearly the need for the integration of simultaneous and sequential processes for the accurate solution of Picture Arrangement and Block Design subtest items. Indeed, most academic tasks such as reading require not only a sequential, left brain component, but also the perceptual functions of the right brain (letter and pattern recognition). Without the interaction of the hemispheres and the respective specialized functions, the child will 69 likely experience some degree of learning difficulty. Several reseachers (Dencla, 1974; Witelson, 1977) have hypothesized that learning difficulties such as developmental dyslexia have resulted from faulty interhemispheric integration. Witelson (1977) has speculated that the individual with developmental dyslexia has "two right hemispheres and none left." Das (1984) observes that successive or sequential processes appear to develop earlier than simultaneous abilities. It might be expected, therefore, that until the age of six a child will have more difficulty solving simultaneous tasks than sequential tasks. By grade three, however, Das, Snart, and Mulcahy (1982, as reported in Kaufman & Kaufman, 1983b) have shown that the performance of learning disabled children is depressed on both simultaneous and sequential processing tasks. It appears, then, that depressed scores on tasks which require either simultaneous or sequential or integrated processing (most WISC-R tasks) could show a relationship to learning disabilities. On the other hand, intact simultaneous and sequential abilities would not necessarily predict learning success if there is faulty integration of the two processes. The WISC-R might be faulted for its inability to isolate simultaneous from successive processing difficulties. On the other hand the K-ABC may be viewed as deficit in tapping more complex skills which require 70 integrated processing and which are more representative of abilities required for school learning. Yet, even as argued previously, the K-ABC Mental Processing subtests are not pure measures of a single processing style and, in fact, load to varying degrees on both the primary and secondary factors (especially Hand Movements). One is still left with the question regarding the extent to which the solution of a sequential task such as Hand Movements has been mediated by simultaneous or successive processing. E. Summary and Implications for the Present Study In reviewing the research related to the present study, four general areas of literature have been discussed: 1. Methods for determining a severe discrepancy between ability and achievement, 2. Description and background of the Kaufman Assessment Battery for Children (K—ABC), 3. K-ABC validity studies, and 4. Critical reviews Of the K-ABC. The first section of the review addressed problems involved in the determination of a severe discrepancy between ability and achievement when considering a student for eligibility under the Special Education Learning Disabilities classification. Several approaches to the calculation of a severe discrepancy were presented and critiqued on the basis of Cone and Wilson's (1981) classification of methods: 1. Deviation from grade level, 2. Expectancy formulas, 3. Standard score procedures, and w---___ _ 1‘ 71 4. Regression analysis. Advantages and disadvantages of each approach were discussed. Because of the current widespread use and statistical advantages of the z-score discrepancy, estimated true score difference, and regression analysis procedures, these three methods have been selected for comparison in the present study. By contrasting these procedures, it will be possible to examine the effect of considering various sources of error in the calculation of a significant score discrepancy. Among the sources of error are errors of measurement resulting from the less than perfect reliabilities of selected tests and errors in predicting achievement from ability due to less than perfect correlations between tests. The second section of the literature review was concerned with examining the theoretical background, development, and structure of the Kaufman Assessment Battery for Children. The Das—Luria model of simultaneous and successive mental processing and the Cattell-Horn model of fluid and crystallized intelligence were presented and related to the tasks which were selected for the K-ABC Simultaneous, Sequential, and Achievement Scales. A summary of correlational studies which examined the relationship between the K-ABC, WISC—R, and PIAT was presented in section three of the review. General findings which would support the comparability of discrepancies calculated using the WISC—R Full Scale IQ and PIAT 72 Achievement subtests with the K-ABC Mental Processing Composite (MPC) and K-ABC Achievement subtests include: 1. The high, positive correlations between the Full Scale IQ and the Mental Processing composite and 2. The high, positive correlations between the PIAT subtests and the K-ABC Achievement subtests. The evidence which demonstrates a similar pattern and magnitude of test intercorrelations for normal and learning disabled students offers support for the generalizability of results from students with normal children to learning disabled populations. Results which might predict different outcomes from WISC—R Full Scale IQ/PIAT comparisons and K-ABC MPC/K-ABC Achievement comparisons include the reported tendency for PIAT standard scores to be higher than the respective K—ABC Achievement scores, as well as the tendency for the WISC-R Full Scale IQ to be slightly higher than the K-ABC MPC. The finding that the correlation between the K-ABC MPC and achievement subtests tends to be lower than the correlation between the WISC-R Full Scale IQ and achievement subtests could also influence discrepancies which are obtained using methods which consider test intercorrelations (i.e., regression analysis procedures). Finally, although the reliabilities of the WISC-R Full Scale IQ and the K-ABC MPC are comparable, the reliabilities of the PIAT subtests are consistently lower than the respective K-ABC Achievement subtests. The lower PIAT subtest reliabilties could serve 73 to decrease the relative incidence of significant discrepancies when using methods which consider this source of error (i.e., z-score discrepancy and estimated true score difference approaches). The last section of the review involved a critical examination of the underlying structure of the K-ABC, as well as a closer look at the relationship of this structure to the Wechsler Intelligence Scales. The discussion raised questions regarding the accuracy of the K—ABC in representing its underlying theoretical models. It was generally concluded that, relative to most traditional tests of intelligence, the K-ABC is over-represented by less complex, short-term memory tasks. The attempt by Kaufman and Kaufman to minimize the verbal component of the K-ABC may have further reduced the diagnostic utility of the battery in school settings. In spite of efforts to represent a simultaneous/sequential processing dichotomy through task selection, it was shown that certain subtests, such as Hand Movements, have loadings on both simultaneous and sequential factors, and that the magnitude of these loadings varied across age groups. Independent confirmatory factor analysis demonstrated that an equally plausible model based upon verbal memory and nonverbal reasoning dimensions could be applied to the K-ABC Mental Processing subtests. It is difficult to determine the full impact of test content on the resulting performance of students with 74 learning difficulties. The conclusion that profile analysis with learning disabled students is speculative, at best, makes attempts at subtest score prediction even more questionable. It may be useful, however, to return to studies which demonstrate divergent patterns of subtest score performance for learning disabled students when interpreting differences which might emerge between performance on the K-ABC and WISC-R. Among the reported trends are Kaufman and Kaufman's (1983) findings that L.D. children tend to perform somewhat better on the K-ABC Simultaneous Processing tasks than on Sequential Processing tasks, as well as Naglieri's (1985b) findings that learning disabled children tend to earn higher scores on the WISC-R Picture Arrangement and Object Assembly subtests and on the K—ABC Gestalt Closure and Photo Series subtests. In conclusion, the studies reviewed present a wide variety of factors which could potentially influence the discrepancies which are obtained when comparing the WISC-R Full Scale IQ and PIAT subtests and the K—ABC MPC and K—ABC Achievement subtests across selected methods for calculating a significant discrepancy. These factors will be considered when interpreting the results of the present study. III. METHODOLOGY A. Rationale In attempting to answer the questions which were generated in the previous sections, two general areas of investigation were pursued. The first area of research addresses the issues surrounding the adequacy of selected procedures in quantifying a "severe discrepancy" between ability and achievement for purposes of identifying students under the special education learning disabilities classification. A systematic analysis of several techniques which are currently endorsed and utilized by diagnostic teams will allow a comparison of the impact of each method on the size and characteristics of the population identified as learning disabled. While previous studies have focused on the comparison of the proportion of students who demonstrate a severe discrepancy between ability and achievement using divergent criteria, this study will additionally attempt to describe characteristics, such as IQ, sex, and chronological age, of students who are systematically included or excluded from a learning disabilities classification based upon the severe discrepancy criterion which has been implemented. Also, unlike previous studies which have examined differences 75 76 between single types of discrepancy calculation procedures, for example, differences between expectancy formulas or differences between standard score methods, this study will compare two standard score discrepancy formulas and two approaches to the more recently advocated regression analysis procedure. The comparison of discrepancies obtained through each of these procedures should help to clarify some of the practical, as well as theoretical, benefits and disadvantages of using various approaches when calculating discrepancies. Another major difference between this study and most of the prior research in the area is the nature of the sample of students which has been selected. Many studies have chosen to evaluate test information from students who have been previously classified as learning disabled. The number of students who would be classified or declassified by various discrepancy procedures is then determined. Often such studies involve a consolidation of achievement test information which disguises the criteria upon which initial decisions were based. Also, in retrospect, it is nearly impossible to identify the discrepancy formula which was implemented in the original diagnosis of such students. This study will examine a group of students who have been referred for evaluation because of learning difficulties. As a result, it will be possible to determine the extent to which a wider range of student characteristics interact with various discrepancy criteria. Also retained in the 77 analysis will be scores from a number of achievement subtests. The inclusion of these scores will allow an analysis of the numbers and characteristics of students who demonstrate a severe discrepancy in different academic areas under the selected definitions. The second part of the study has been designed to compare the recently developed Kaufman Assessment Battery for Children (K-ABC) with the more established and widely used Wechsler Intelligence Scale for Children-Revised (WISC-R) and Peabody Individual Achievement Test (PIAT) to determine the adequacy of the new battery in the determination of a severe discrepancy for learning disabilities classification. Since the K-ABC consists of a Mental Processing component which is analogous to the WISC-R Full Scale IQ and an Achievement component which can be considered analogous to the PIAT, it is of interest to evaluate differences in a discrepancy determination which might result through the use of the K-ABC. With the increased usage of the K-ABC by practitioners, the convenient comparison of the Mental Processing Composite with the various achievement subtests for determination of discrepancy seems a natural extension of assessment procedures. The importance of determining the validity and the impact of this diagnostic strategy is obvious. It will be recalled that, in a study which examined differences in K-ABC score profiles, Naglieri (1985) found no significant differences between the mean Mental 78 Processing—Achievement discrepancy for learning disabled, mentally retarded and normal groups. Again, the consolidation of achievement subtest scores can serve to conceal differences in specific academic areas. Additionally, the evaluation of mean differences between test scores can hide the direction of the differences. With learning disabled students, it is anticipated that ability estimates will exceed achievement estimates. Normal and mentally retarded students, on the other hand, might exhibit differences in either direction. A purpose of this study will be to evaluate both the magnitude and the direction of the discrepancy between the Mental Processing Composite and the K-ABC Achievement subtests and contrast these differences with the discrepancies obtained in WISC-R Full Scale IQ-PIAT achievement subtest comparisons. B. Goals The goals of the proposed research can be summarized as follows: Part I 1. Compare the proportion of students who demonstrate a significant discrepancy between ability and achievement using four procedures: a. Z-score discrepancy (Method 1) b. Estimated true score differences (Method 2) c. Regression analysis I: Wilson & Cone (Method 3) d. Regression analysis II: Reynolds (Method 4). 79 2. Determine the extent of agreement between each pair of methods in the identification of students who demonstrate a significant discrepancy between ability and achievement. 3. Determine systematic variation in characteristics: IQ, chronological age, sex, and grade placement for students demonstrating a severe discrepancy between ability and achievement using the four selected procedures. Part II Compare the following WISC—R Full Scale IQ/PIAT subtest discrepancies with corresponding K-ABC Mental Processing/Achievement subtest discrepancies: a. FSIQ—PIAT Arithmetic with MPC—KABC Mathematics b. FSIQ—PIAT Reading Recognition with MPC-KABC Reading/Decoding c. FSIQ-PIAT Reading Comprehension with MPC—KABC Reading/Understanding d. FSIQ-PIAT Total with MPC—KABC Achievement 1. Determine the proportion of students who demonstrate a discrepancy between ability and achievement. 2. Determine the extent to which there is agreement between pairs of tests in identifying students who demonstrate a significant discrepancy between ability and achievement. 80 C. Definitions and Formulas 1. Method 1: Z-score discrepancy In order to compare a standard score for ability measures with the standard scores for achievement measures, the procedure recommended by Reynolds (1981) for the determination of a significant standard score difference will be applied. For each ability-achievement comparison, the following calculations will be made: a. Calculate Z for the ability measure Zx = X ; X x where X = WISC-R Full Scale IQ or K-ABC Mental Processing Composite K = mean standard score for FSIQ or MPC ox = standard deviation of scores for FSIQ or MPC b. Calculate Z for the achievement measure where Y PIAT or KABC achievement subtest score Y = mean standard score for PIAT or K—ABC achievement subtest score 0 = standard deviation of scores for PIAT or K-ABC achievement subtest 81 c. Calculate the difference in z scores for the two tests d. Divide the difference by the standard error of the difference scores D Zdif /(l-rxx) + (l-ryy) where rxx = reliability of FSIQ or MPC (internal consistency) ryy = reliability of PIAT or K-ABC achievement subtest (internal consistency) e. Compare Zdif to Za = 2.05 = 1.65 from the standard normal table. For the purposes of this study, the .05 level of sig— nificance has been chosen with a corresponding Za of 1.65. A one-tailed test was selected because the comparisons of interest involve discrepancies in which ability scores exceed achievement scores. 2. Method 2: Estimated true score differences Following the procedure outlined by Stanley (1971) and Cone and Wilson (1981), true scores will be estimated for each observed ability and achievement test score and the significance of the difference in true scores will be calculated: 82 a. Calculate estimated true 2 scores for ability and achievement measures xx x ZTY _ ryyzy where rxx' ryy' Zx, and ZY are previously defined b. Calculate difference between estimated true Z SCOI‘ES c. Calculate standard error of the estimated true score difference SEA A _ 2 2 _ Tx-Ty ‘y/fxx (1"rxx) + rYY (l rYY) xx and rYY are previously defined d. Divide the true Z score difference by the standard where r error of estimated true score difference DA A _ Tx-T zdif - -§§:-- A Tx—Ty e. Compare zdif to Za = 2.05 = 1.65 from the standard normal table. 3. Method 3: Regression Analysis Method 3 employs the regression analysis procedure which was outlined by Wilson and Cone (1984). For purposes of comparison with other standard score methods, it will be assumed that the mean standard score for the population being sampled is 100 and the standard deviation is 15 for 83 each test under consideration (WISC-R, K-ABC, PIAT). Intercorrelations between tests have been drawn from either test manuals or other published sources which have reported the relationships. Correlations between the K-ABC Mental Processing Composite and the K-ABC Achievement subtests were obtained from the intercorrelation matrices for seven age groups (6 to 12 1/2 years) which were presented in the K-ABC Interpretive Manual. The correlations were 2— transformed (Fisher 2 transformation), averaged, and converted back into correlations which were then included in the discrepancy equations. The correlations between the WISC-R Full Scale IQ and the PIAT subtests were obtained from a research study by Wikoff (1979) which investigated the WISC-R as a predictor of achievement. Wilson and Cone advise determining appropriate means, standard deviations, and intercorrelations for each population under consideration. Therefore, it should be cautioned that the statistics borrowed from the broader standardization group may vary to some extent for the population of students which are currently being studied. These variations could influence the number of students demonstrating a discrepancy between ability and achievement. Reynolds (1984-85) advises using the statistics from "a large, stratified, random sample of normally functioning children" (p. 472) which offers some support for the choice of statistics from the standardization group for these analyses (Methods 1 84 through 4). The following steps are involved in the calculation of a severe discrepancy for Method 3: a. d. Calculate the predicted 2 score for achievement 2? = rxy(zx) where rxy is the correlation between the ability test and the achievement subtest and 2x is previously defined Subtract the observed Z from the predicted Z“ Y Y DZYZY = zy ' zy where Zy is previously defined Divide the difference by the standard error of estimate DZyZy zdif = 2 /€—' rxy Compare zdif to Za = Z.05 = 1.65 from the standard normal table. 4. Method 4: Regression Analysis II Method 4 is based upon the regression analysis formula recommended by Reynolds (1984-85). Unlike the previous regression analysis approach in which Zdif is compared to a Za. Z = 1.65, Reynolds recommends comparing zdif to a modified The zmod is an adjustment of Za for the unreliability —— cfiaM-Ffl— 85 of the subtests which are being compared. With perfectly reliable tests, zmod will equal Za, and score differences which are significant for Method 4 will also be significant for Method 3. Reynolds suggests using the following equation for calculating a discrepancy: - . = - 2 _ A Y Y1 (2 SD 1 rxy ) 1.65 SEy-yi where SE§_Yi = l-rxy °/l- ry_yi and r‘ = r + r r 2 - 2r 2 Y‘Yi YY XX XY XY 2 l-rxy S. Phillips (personal communication) has suggested that the correct form of this equation for standard score comparisons is: _ _ > _ A _ 2 zdif — zx (rxy) zy (2a 1.65 sazy_zyi ( 1 rxy ) where za would equal 1.65 for one-tailed comparisons and SEzy-zyi= l- ry-Yi Using the latter equation, the following steps would be taken in the calculation of a discrepancy: a. Calculate Zdif as in Method 3, above _ DZ§ZY z - _ ________ dif /1 ' rxy 86 b. Calculate zmod (note: zmod is Za corrected for the unreliability of the tests) - 1.65 SE A = Z _ ZY zyi Z mod a where Za = 1.65 and SEzy-zyi= ¢/l_ ry-Yi c. Compare Zdif to zmod' 5. Comparison of Discrepancy Methods In order to compare the four standard score procedures for determining discrepancy (Methods 1, 2, 3, and 4), the formulas were solved for 2a = 1.65 and plotted. Sample statistics were selected to demonstrate the relationships between the methods and the impact of test reliabilities and intercorrelations on the obtained discrepancies. Two graphs were developed representing the following situations: Graph 1: rxx = .96; ryy = .74; rxy = .58 Graph 2: rxx = .94; ryy - .87; rxy = .71 Linear equations were developed for each method in the following manner: a. Method 1: Z score difference zx_zy /l - rxx + 1 - ryy = 1.65 87 substituting /d - .96 + 1 - .74 = 1.65 reducing and rearranging ZY = —.90 + 2x b. Method 2: Estimated True Scores rxxzx _ rYYzY V/Lxx2<1 - rxx) + ryyz(1 - ryy) = 1.65 substituting 096 Zx - .74 ZY ’/.962 (1 - .96) + .742 (1 - .74) = 1.65 reducing and rearranging zy = -.95 + 1.30 zx c. Method 3: Regression Analysis (Wilson & Cone) rxy(zx) - ZY /Fl - rxyzfii = 1.65 substituting 88 reducing and rearranging zy = -1.35 + .58 2x d. Method 4: Regression Analysis (Reynolds) _ > _ A _ 2 2x (rxy) ZY (Za 1.65 SEzy-zy; ( l rxy ) substituting zx(.58) - z .74 + .96(.58)2 - 2(.58)2 Y =(1.65 - 1.65 1 - /[1 - .582 1 - .582 reducing and rearranging ZY = -.482 + .582x e. The four linear equations are graphed for the ability and achievement range of interest for each of the two conditions above (See Figures 1 and 2). It can be seen that the number of students identified will vary depending upon the test reliabilities and intercorrelations as well as the actual distribution of 89 ability and achievement scores for the students sampled. The graphs provide a tool for generating hypotheses regarding the numbers of students who will be identified by different methods based upon selected test characteristics and intercorrelations. 90 Om. 00. OO. Om. Om. OO. Om. OO. Om. 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Methods 3 and 4 will include significantly fewer high ability students and significantly more low ability students than either Method 1 or 2 (Objective 3). 93 5. There will be no significant differences in the mean age, grade placement, or sex ratio of identified students across the four methods (Objective 3). Part II Because of the large number of factors (such as test reliability, subtest intercorrelations, floor and ceiling effects, subtest content, and mode of presentation) which can potentially influence obtained discrepancies, as well as the conflicting patterns of test intercorrelation which have been reported in the literature, the following hypotheses regarding the comparison of K—ABC, WISC—R, and PIAT subtests scores are suggested: 1. There will be no significant differences between the proportions of students who demonstrate a severe discrepancy between ability and achievement using K-ABC Mental Processing/Achievement comparisons and WISC-R/ PIAT comparisons across the four methods for calculating a discrepancy (Objective 1). 2. There will be a significant correspondence (percent of agreement and intercorrelation) between the following pairs of test scores for each of the four discrepancy methods: .a. FSIQ-PIAT Arithmetic with MPC-KABC Mathematics b. FSIQ-PIAT Reading Recognition with MPC-KABC Reading Decoding 94 c. FSIQ-PIAT Reading Comprehension with MPC-KABC Reading Understanding d. FSIQ-PIAT General Information with MPC-KABC Faces and Places e. FSIQ-PIAT Total with MPC-KABC Achievement (Objective 2). E. Subjects The sample of students included in this study consists of children in the State of Michigan who had been referred for psychoeducational evaluation during the Fall of 1983 and who were subsequently diagnosed using the WISC-R, the K-ABC, and PIAT. Table 1 shows the descriptive statistics for this group of students. It can be seen that urban students represent 12.8 percent of the sample while the remaining 87.2 percent of the sample is approximately equally divided between rural and suburban students. 1980 Census data indicate that 27.9 percent of the population is urban, while 43.8 percent is suburban and 28.3 percent is rural. Males account for more than twice the number of students as females, a trend which is consistent with other studies of learning disabled students and learning disabilities referrals. White students represent almost 90 percent of the children in the sample, while Blacks and other minorities constituted 10.5 percent of the sample. This contrasts Table 1 Student Characteristics (n = 86) Educational Setting Freq. Pct. 1. Urban 11 12.8 2. Rural 38 44.2 3 Suburban 37 43.0 Sex Freq. Pct. 1. Male 61 70.9 2. Female 25 29.1 Race Freq. Pct. 1. White 77 89.5 2. Black/Other 9 10.5 Grade Placement Freq. Pct. 1. Kindergarten 3 3.5 2. First 14 16.3 3. Second 26 30.2 4. Third 14 16.3 5. Fourth 15 17.4 6. Fifth 6 7.0 7. Sixth 8 9.3 Mean: 2.86 S.D.: 1.6 Chronological Age Mean: 8.83 S.D.: 1.7 Range: 6.0 to 12.3 years Parental Education Freq. Pct. 1. Less than 12 yrs. 23 26.7 2. 12 years 38 44.2 3. 13—15 years 11 12.8 4. 16 or more years 10 11.6 5. Not reported 4 4.7 95 96 with 1980 U.S. Census data which shows that Blacks and other minorities make up 26.9 percent of the total population (Kaufman & Kaufman, 1983b; 1980 Census of Population). The under-representation of minority students is quite likely related to the disproportionately small number of urban students in the sample. Further examination of Table 1 shows that grade placement is concentrated on the second grade level with relatively few students at the kindergarten, fifth, and sixth grade levels. Chronological age statistics also show a concentration of students in the seven to ten year age range. Parental education is 12 years or less in more than 70 percent of the cases. Approximately 24 percent of the parents have some college or advanced training. All of the students in the sample were evaluated by certified school psychologists or supervised school psychology interns. The average years of experience for the school psychologists/interns who contributed data to this study was 7.78 Years (range 0 to 22 years). 32.6 percent were male and 67.4 percent were female. To be included in the study, the following requirements were established: 1. Age at the time of the evaluation between 6 years, 0 months and 12 years, 6 months 2. WISC-R Full Scale IQs ranging from 70 to 125 3. Students referred for learning problems 4. Diagnosis conducted using WISC—R, PIAT, and K-ABC 97 5. Evaluation completed by certified school psychologist or school psychology intern who was supervised by a certified school psychologist 6. English as a primary language 7. Student free of physical/motor handicap Students with complete data sets who met these criteria were selected from a larger sample of 171 _ referrals. Children whose ability estimates fell into the Educable Mentally Impaired Range (I.Q < 70) or who were referred primarily for behavioral or emotional difficulties (suspected Emotionally Impaired) were not included in the study. Gifted referrals were also eliminated. F. Instruments 1. Wechsler Intelligence Scale for Children-Revised The Wechsler Intelligence Scale for Children- Revised (WISC-R) is an individually administered intelligence test developed for children between the ages of 6 and 16. The WISC-R provides estimates of verbal abilities (Verbal IQ), visual-perceptual abilities (Performance IQ), and a measure of general ability (Full Scale IQ). A more complete description of the subtests, standardization group, and application of the WISC-R is included in Appendix A: Description of Tests. 2. Kaufman Assessment Battery for Children The K-ABC has been described in detail in the literature review (see Review of Literature: B. Description 98 and Background of the K-ABC; C. K-ABC Validity Studies; D. Critique of the K-ABC). The reader is referred to those sections for a more complete discussion of the K-ABC. 3. Peabody Individual Achievement Test The PIAT is an individually administered achievement test designed for children between the ages of 5 years, 8 months and 18 years, 3 months. It includes five subtests: Mathematics, Reading Recognition, Reading Comprehension, Spelling, and General Information. The battery is based largely on a multiple-choice format where the student is presented with a test plate (page) and must select a correct response from among four possible answers. A more complete description of the subtests is included in Appendix A: Description of Tests. G. Procedures The data for this study were submitted by school psychologists who participated in a course on the Kaufman Assessment Battery for Children which was offered through Michigan State University and the Michigan Association of School Psychologists in Fall of 1983. Each school psychologist was requested to administer the three selected instruments to five referred students as well as collect behavioral ratings and personal data for each child. The data collection instruments appear in Appendix B. Also included were reason for referral and order of test administration. Complete protocols were returned by 86.5 "~_ ...~—-—* — 99 percent of the course participants. H. Data Analysis In order to test the hypotheses which have been generated, the following statistical techniques will be used. 1. Kappa Statistic: The Kappa statistic described by Cohen (1960) for measuring nominal agreement among raters will be used to measure the agreement between pairs of formulas in identifying the same students as exhibiting a severe discrepancy between ability and achievement. (See Appendix F for the formula for calculating kappa). This procedure will be used to test Hypothesis 2, Part 1 and Hypothesis 2, Part 2. The percent overlap of students identified by the various pairs of methods and tests will also be reported. The overlap statistic will provide descriptive evidence regarding the agreement of the four methods for determining a discrepancy (Part I) and the agreement between the K-ABC MPC/Achievement and WISC-R FSIQ/PIAT subtest discrepancies (Part II) in identifying students. 2. Spearman Rank Order Correlation Coefficient: Spearman's rho will also be used to measure the agreement between formulas in calculating discrepancy. The rank order based on the magnitude of the discrepancy calculated for each student using a particular method or pair of tests 100 will be correlated with the rank order of discrepancies obtained using other methods or tests. This procedure will also be used to test Hypothesis 2, Part I and Hypothesis 2, Part 2. 3. Analysis of Variance: Analysis of variance procedures will be used to compare mean ability estimates, mean chronological age, and mean grade placement differences across methods. Planned comparisons will be used to compare the hypothesized differences proposed in Hypothesis 3, Part 1 while post hoc comparisons will be used to compare means for hypotheses which propose no significant differences (Hypotheses 3, Part 2). 4. Friedman two-way analysis of variance by ranks/ chi-square: The Friedman two-way analysis of variance will be used to test hypotheses which involve the comparison of the proportions of students identified by different methods (Hypothesis 1, Part 1). Chi—square will be applied when comparing the proportions of students who demonstrate a severe discrepancy across tests. When analyzing proportions which are correlated (Hypothesis 1, Part 2), McNemar's test for correlated proportions will be used to estimate chi- square (see Appendix F for a description of procedures). I. Limitations Perhaps the most significant limitation of the proposed study is the non-random nature of the sample of students who are being investigated. Although students 101 represent diverse educational settings, the generalization of many of the results of this study to areas outside the State of Michigan is questionable. The generalization is especially limited in terms of the actual numbers of referred students who exhibit a discrepancy using various methods. Certainly substantial differences exist between states, and even between school districts, in the number and type of students who are referred for evaluation. Less variable are the results obtained from investigating the characteristics and relative proportions of students identified using the selected discrepancy procedures and selected test comparisons. A second limitation of this research involves the procedure which was used by each psychologist in selecting subjects to be evaluated using the three instruments and submitted once the evaluations were complete. Although students were evaluated within a circumscribed period of time, the cases received from each psychologist may have been selected on a non-random basis. Cases with missing data were also eliminated from consideration, which may have biased the final data set in some additional manner. Third, it was not possible to consider discrepancies in the areas of oral expression, listening comprehension, and written expression, three academic areas which are also used to qualify students as learning disabled. Since no standard scores were available in the three areas, it was impossible to indicate the additional number of students 102 who would have shown a severe discrepancy in these achievement areas. Additionally, when examining the criteria for qualifying students as learning disabled, it becomes apparent that a severe discrepancy is a necessary but not sufficient condition in classification decisions. In addition to demonstrating a discrepancy, it must be shown that the student's learning difficulties are not a result of visual, hearing, or motor handicaps, of mental retardation, or of environmental, cultural or economic disadvantage (P.L. 94-142,121a.5 b(9)). Because it was not possible to control for all of these factors, the direct translation of the observed discrepancies into "learning disabilities" is strongly cautioned against. Another important distinction which should be made when interpreting the discrepancies which result from various methods is the difference between statistical significance and educational significance of obtained test scores. While a small raw score difference between two highly reliable instruments might result in a statistically significant discrepancy at the .05 level, the difference may not constitute an educationally meaningful difference. Since the data obtained for this study were collected as part of a training course in the K-ABC, it is expected that the protocols which were received represented some of the first experiences of psychologists with this new instrument. While all psychologists are required to have familiarity with individually administered, 103 standardized tests, it is difficult to asses the impact that lack of experience may have had on the resultant K-ABC test scores. Finally, the test data which were collected for this study consisted principally of face sheets from the K-ABC, PIAT, and WISC-R. Therefore, it was impossible to perform a random check to determine the accuracy with which the various tests were scored. The examination of eight complete protocols indicated that proper determination of basal and ceiling had occurred. Calculations and table consultation were also accurate for this limited sample of protocols. Again, this does not insure against improper administration or scoring of tests for the larger sample of students. IV. RESULTS AND DISCUSSION Before testing the hypotheses which were set forth in the previous section, it is useful to examine the statistics which describe the test scores of the students included in this study. Table 2 illustrates the means and standard deviations of the scale scores and standard scores of the K-ABC, WISC-R, and PIAT. Of interest is the consistent tendency of the K-ABC Achievement subtest scores to be lower than the respective PIAT subtest scores. The mean K-ABC Reading Decoding subtest score is 6.52 standard score points below the mean PIAT Reading Recognition subtest score, while the mean K-ABC Reading Understanding subtest score is 6.10 standard score points below the mean PIAT Reading Comprehension subtest. It will be recalled that Naglieri (1985b), in a study of normal children, found an average PIAT Reading Comprehension standard score of 117.7 and an average K-ABC Reading/Understanding standard score of 104.5. The disparity in scores, therefore, appears to have some substantiation in previous comparative studies. This trend may have a substantial impact on the number of students who exhibit a severe discrepancy between ability 104 Table 2 Means and Standard Deviations of WISC-R, K-ABC, and PIAT Subtests and Score Composites 105 K-ABC Subtests Mean S.D. 1. Hand Movements 9.14 2.4 2. Gestalt Closure 9.71 3.0 3. Number Recall 9.13 3.0 4. Triangles 9.52 3.2 5. Word Order 9.11 3.1 6. Matrix Analogies 9.67 2.3 7. Spatial Memory 9.01 2.7 8. Photo Series 9.80 2.5 9. Faces & Places 87.65 12.7 10. Arithmetic 89.14 11.7 11. Riddles 95.94 11.3 12. Reading Decoding 84.75 12.5 13. Reading Understanding 85.22 12.3 14. Sequential 95.23 14.9 15. Simultaneous 97.30 11.9 16. Mental Processing 95.83 12.8 17. Achievement 87.42 11.1 WISC-R Subtests Mean S.D. 1. Information 7.97 2.7 2. Similarities 9.97 3.0 3. Arithmetic 7.94 2.4 4. Vocabulary 9.42 2.9 5. Comprehension 10.04 2.8 6. Digit Span 7.52 2.8 7. Picture Completion 10.20 2.5 8. Picture Arrangement 9.99 2.6 9. Block Design 9.29 2.5 10. Object Assembly 9.86 2.6 11. Coding 8.44 2.8 12. Verbal IQ 94.11 12.7 13. Performance IQ 96.86 12.3 14. Full Scale IQ 94.94 11. PIAT Subtests Mean S.D. 1. Mathematics 92.93 10.6 2. Reading Recognition 91.27 9.1 3. Reading Comprehension 91.32 10.3 4. Spelling 90.20 10.0 5. General Information 94.84 11.8 6. Total 89.74 10.0 106 and reading achievement. A higher average PIAT standard score also was achieved in the area of arithmetic, although the disparity is less pronounced than in reading achievement. The difference between the average PIAT Total standard score and the average K-ABC Achievement Scale score is the smallest (2.32 standard score points favoring the PIAT). It might be anticipated that the average standard score difference will be larger with MPC/K-ABC Achievement comparisons than with WISC-R/PIAT subtest comparisons, particularly in the area of reading. It is interesting to note that the K-ABC Mental Processing subtests show very little variability, with the average scale scores ranging from 9.01 on the Spatial Memory subtest to 9.80 on the Photo Series subtest. This flat profile of average subtest scores contrasts with previous studies which suggest that learning disabled students, learning disabilities referrals, and dyslexic students perform more poorly on Hand Movements, Word Order, Number Recall, and Matrix Analogies subtests (Kaufman & Kaufman, 1983b). It is consistent, however, with the Kaufman & McLean (1986) study of learning disability referrals and children with diagnosed learning disabilities which showed little variability among the K-ABC Mental Processing subtest scores. Sequential Processing scores were slightly lower (2 points) than Simultaneous Processing scores, a finding which is consistent with the standardization studies with 107 learning disabled students (#17 and #19) which showed Sequential Processing standard scores to be 2 to 5 points below Simultaneous Processing standard scores. The average WISC-R subtest scores, however, reflected a characteristic "ACID" profile with depressed Arithmetic, Coding, Information, and Digit Span scores. This pattern of scores has been identified with learning disabled students in previous literature (Kaufman & McLean, 1986), although its utility and generalizability has been seriously questioned by other authors (Clarizio & Veres, 1983). The WISC-R Verbal IQ is 2.75 points lower than the average Performance IQ, while there is less than a point difference between the average K-ABC MPC (95.83) and the WISC-R Full Scale IQ (94.94). This finding is somewhat inconsistent with the K-ABC standardization studies with learning disabilities referrals which showed a lower K-ABC MPC (90.8) than WISC-R FSIQ (94.7) (Study #17). The average scores are more consistent, however, with the scores from Naglieri's (1985a) sample of learning disabled students (FSIQ: 96.8; MPC: 96.1). B. Testing of Hypotheses: Part I The first hypothesis in Part I states: "There will be no significant differences between the proportions of students who demonstrate a severe discrepancy between ability and achievement using the four proposed methods for calculating a discrepancy." 108 In order to test this hypothesis, zdif was calculated for each student using the four methods described in the previous section: Method 1, Z-score differences; Method 2, Estimated true score differences; Method 3, Regression analysis I; Method 4, Regression analysis II. If zdif exceeded 1.65 for Methods 1, 2, or 3, the student was considered to have a severe discrepancy between ability and achievement for that method. If zdif exceeded zmod for Method 4, the student was determined to have a severe discrepancy for that Method. (Recall that zmod adjusted za for unreliability of the ability and achievement tests). The proportion of students demonstrating a discrepancy for each method across each WISC-R/PIAT and K—ABC MPC/Achievement comparison appears in Table 3. A Friedman two—way analysis of variance by ranks was conducted to determine if significant differences existed between proportions of students identified by each method. For purposes of this analysis, sz was calculated and compared to critical values of chi-square for 3 degrees of freedom (see Appendix F for the formula for calculating sz and justification for using the chi-square approximation). It can be seen that‘Xr2 is significant, suggesting that the methods for determining a severe discrepancy do, in fact, tend to select different proportions of students. A closer examination of Table 3 reveals that Methods 1 and 2 select similar proportions of students while Method 3 generally identifies smaller numbers of students than Table 3 Proportion of Students Showing a Severe Discrepancy Between Ability and Achievement Using Four Methods METHOD TEST METHl METHZ METH3 METH4 PIAT MATH 8.1 10.5 2.3 31.4 PIAT RREC 27.9 24.4 4.7 23.3 PIAT RCOMP 16.9 16.9 7.0 62.0 PIAT TOT 32.1 29.6 3.7 33.3 KABC ARITH 46.5 40.7 17.4 53.5 KABC RDEC 53.5 53.5 24.4 52.3 KABC RUND 57.8 57.8 28.9 57.9 KABC ACHIEV 53.5 52.3 31.4 44.2 XrZ = 15.19 df = 3 p<.01 109 110 Methods 1 or 2. Method 4 selects similar proportions of students as Methods 1 and 2 for PIAT Reading Recognition, PIAT Total Achievement, and each of the K-ABC subtest comparisons. In two instances (PIAT Mathematics and PIAT Reading Comprehension), Method 4 selects considerably more students that the other three methods (more than three times as many students as Methods 1 or 2). The reliabilities are low for both the PIAT Mathematics and the PIAT Reading Comprehension (.74 and .64, respectively), suggesting that, when using tests with low reliabilities, Method 4 will tend to select more students than other methods. The analysis presented in Table 3 does not support the first hypothesis. There are significant differences between the proportion of students who demonstrate a severe discrepancy across the selected methods. Therefore, it can be anticipated that, in a group of referred children, the method chosen will have a significant impact on the numbers of students who are qualified as learning disabled. 2. The second hypothesis in Part I states: "The agreement in identification of students who demonstrate a discrepancy will be significantly higher when comparing Method 1 with Method 2 than when comparing Methods 1 or 2 with Methods 3 or 4." Two approaches were taken to the testing of this hypothesis. First, the percent overlap between methods was lll calculated (number of students who are identified by two methods divided by the total number of students identified by both methods). The percent overlap indicates the extent of agreement among the pool of eligible students identified by two methods. Secondly, kappa, the extent of nominal agreement among methods, was calculated. Kappa reflects the consistency of decisions made across two methods after the effects of chance have been removed (see Appendix F). The results of these comparisons appear in Tables 4 through 7. Table 4 shows a high degree of correspondence between Method 1 and Method 2 according to both percent overlap and kappa. The lowest agreement occurred with the WISC-R/PIAT Mathematics comparison (k=.587). Examination of the zdif s for discrepant cases (see Appendix E for a listing of zdif's for each comparison) shows that lack of agreement occurred on cases for which the zdif for one method was slightly below 1.65 (e.g., 1.58) while the zdif for the other method was slightly above 1.65 (e.g., 1.68). Only seven students were identified with Method 1 while nine were identified with Method 2. It is possible that the relatively low reliability of the PIAT Mathematics subtest, (r =.74), coupled with the highest mean achievement score xx (92.93) of the subtests in the study resulted in a very low number of students identified (and, consequently, the lower degree of agreement between methods). It should be noted, however, that nearly perfect agreement was achieved TEST Table 4 Agreement between Method 1 and Method 2 in the Selection of Students Number with Discrepancy Method 1 Method 2 %Overlap Kappa Sig PIAT MATH 7 9 45.5 .587 p<.01 PIAT RREC 24 21 87.5 .910 p<.001 PIAT RCOMP 12 12 92.3 .949 p<.001 PIAT TOTAL 26 24 92.3 .947 p<.001 KABC ARITH 40 35 87.5 .882 p<.001 KABC RDEC 46 46 100.0 1.00 p<.001 KABC RUND 44 44 100.0 1.00 p<.001 KABC ACHIEV 46 45 97.8 .977 p<.001 112 113 between Methods 1 and 2 for PIAT Reading Comprehension, which had the lowest subtest reliability (.64) and a high average standard score score (91.32). In general, the close correspondence revealed through these analyses (kappa is greater than .87 in seven of the eight comparisons) indicates that Method 1 and Method 2 are highly comparable. When using achievement tests with high reliabilities, the methods are nearly interchangeable. Method 1 (Z-score differences) and Method 3 (Regression analysis 1) are compared in Table 5. It is apparent that the percent overlap between these methods is considerably lower than achieved between Methods 1 and 2. Method 1 identifies six times the number of students for the PIAT Reading Recognition subtest and nearly nine times the number of students for the PIAT Total comparisons. In each case, all students identified by Method 3 are also identified by Method 1. The percent overlap ranges from 11.5 percent for comparisons involving the PIAT Total standard scores to 58.7 percent for comparisons involving the K-ABC Achievement Composite. Kappa is significant in all K-ABC subtest comparisons, but in only one of the PIAT comparisons. The low agreement appears to be attributable to the limited number of students identified by Method 3, particularly for the PIAT subtests for which the average standard scores are higher. Table 5 Agreement between Method 1 and Method 3 in the Selection of Students Number with Discrepancy TEST Method 1 Method 3 %Overlap Kappa Sig PIAT MATH 7 2 28.6 .423 N.S. PIAT RREC 24 4 16.7 .224 N.S. PIAT RCOMP 12 5 41.7 .543 p<.01 PIAT TOTAL 26 3 11.5 .150 N.S. KABC ARITH 40 15 37.5 .391 p<.001 KABC RDEC 46 21 45.7 .439 p<.001 KABC RUND 44 22 50.0 .466 p<.001 KABC ACHIEV 46 27 58.7 .569 p<.001 114 115 Table 6 shows the relationship between Method 1 (Z- score discrepancy) and Method 4 (Regression analysis 2) The percent overlap varies from 25.9 percent for comparisons involving the PIAT Mathematics subtest to 91.3 percent for comparisons involving the K-ABC Reading Understanding subtest. Kappa is significant at the .05 level for comparisons involving the PIAT Mathematics and the PIAT Reading Comprehension scores. Significance at the .001 level was achieved for each of the remaining comparisons. Similar numbers of students were identified by the two methods in six out of eight comparisons (PIAT Reading Recognition, PIAT Total, and the K-ABC subtest comparisons). For the two comparisons involving subtests with lower reliabilities (PIAT Mathematics and PIAT Reading Comprehension), Method 4 identified nearly four times as many students as Method 1. A high degree of consistency (kappa=.79 to .89) was achieved for each of the comparisons involving the K-ABC subtests, while moderate kappas (.57 to .58) were achieved for comparisons involving the PIAT Mathematics and PIAT Reading Comprehension subtests. Method 2 (Estimated true score differences) and Method 3 (Regression analysis 1) are compared in Table 7. The percent overlap ranges from 10 percent for PIAT Mathematics comparisons to 60 percent for K-ABC Achievement Composite comparisons. Kappa is significant for all K-ABC subtest comparisons but is consistently lower for the PIAT subtests. This trend is due, again, to the very limited Table 6 the Selection of Students Number with Discrepancy Agreement between Method 1 and Method 4 in TEST Method 1 Method 4 %Over1ap Kappa Sig PIAT MATH 7 27 25.9 .324 p<.05 PIAT RREC 24 20 51.7 .574 p<.001 PIAT RCOMP 12 44 27.3 .222 p<.05 PIAT TOTAL 26 27 55.9 .579 p<.001 KABC ARITH 4o 46 87.0 .861 p<.001 KABC RDEC 46 45 82.0 .790 p<.001 KABC RUND 44 44 91.3 .892 p<.001 KABC ACHIEV 46 38 82.6 .815 p<.001 116 Table 7 Agreement between Method 2 and Method 3 in the Selection of Students Number with Discrepancy TEST Method 2 Method 3 %Overlap Kappa Sig PIAT MATH 9 2 10.0 149 N.S. PIAT RREC 21 4 19.0 .262 N.S. PIAT RCOMP 12 5 31.0 .412 p<.05 PIAT TOTAL 24 3 12.5 .167 N.S. KABC ARITH 35 15 42.9 .471 p<.001 KABC RDEC 46 21 45.7 .439 p<.001 KABC RUND 44 22 50.0 .466 p<.001 KABC ACHIEV 45 27 60.0 .588 p<.001 117 118 number of students identified by Method 3, particularly using the PIAT subtests. The comparisons involving the K-ABC subtests, however, reflect more consistency, with all students identified by Method 3 also identified by Method 2 and overlap ranging from 42.9% to 60.0%. Table 8 illustrates the comparison of Method 2 (Estimated true score differences) with Method 4 (Regression analysis 2). It can be seen that percent overlap ranges from 27.3 percent for PIAT Reading Comprehension comparisons to 89.1 percent for K-ABC Reading Understanding comparisons. Kappa is significant at the .05 level for the PIAT Mathematics, and Reading Comprehension subtest comparisons. The .01 level of significance was achieved with the other PIAT subtest comparisons (Reading Recognition and Total), while the remainder of the kappas were significant at the .001 level. Again, a higher degree of correspondence was found between methods for subtests with higher reliabilities. The two regression procedures, Method 3 and Method 4, are compared in Table 9. Percent overlap varies from 7.4 percent for the PIAT Mathematics subtest to 71.1 percent for the K—ABC Achievement comparisons. Kappa was nonsignificant for all of the PIAT subtests, with Method 4 identifying from five to nine times as many students as Method 3. Significance at the .01 level was achieved for comparisons involving the K—ABC Arithmetic subtest, while significance at the .001 level was obtained for the Table 8 Agreement between Method 2 and Method 4 in the Selection of Students Number with Discrepancy TEST Method 2 Method 4 %Overlap Kappa Sig PIAT MATH 9 27 28.6 .341 p<.05 PIAT RREC 21 20 44.4 .456 p<.01 PIAT RCOMP 12 44 27.3 .222 p<.05 PIAT TOTAL 24 27 41.7 .400 p<.01 KABC ARITH 35 46 76.1 .747 p<.001 KABC RDEC 46 45 85.7 .837 p<.001 KABC RUND 44 44 89.1 .892 p<.001 KABC ACHIEV 45 38 84.4 .838 p<.001 119 Table 9 Agreement between Method 3 and Method 4 in the Selection of Students Number with Discrepancy TEST Method 3 Method 4 %Overlap Kappa Sig PIAT MATH 2 27 7.4 .099 N.S PIAT RREC 4 20 20.0 .277 N.S. PIAT RCOMP 5 44 11.4 .089 N.S. PIAT TOTAL 3 27 11.1 .143 N.S. KABC ARITH 15 46 32.6 .310 p<.01 KABC RDEC 21 45 46.7 .455 p<.001 KABC RUND 22 44 50.0 .457 p<.001 KABC ACHIEV 27 38 71.1 .733 p<.001 120 121 remaining K-ABC subtest comparisons. While kappa reached significance in many of the above comparisons, the statistic should be interpreted in light of the corresponding percent overlap, particularly when the placement of students is being considered based upon the resulting severe discrepancies. It is not unlikely, for example, to achieve a highly significant kappa with less than fifty percent of the same students being identified using two methods. Consequently, in many comparisons, quite a different population of students would show severe discrepancies depending on the method selected. In discussing the testing of kappa for significance, Cohen (1960) indicates, "...it is generally of as little value to test kappa for significance as it is for any other reliability coefficient-to know merely that kappa is beyond chance is trivial since one usually expects much more than this in the way of reliability in psychological measurement. It may, however, serve as a minimum demand in some applications" (p. 44). With this in mind, the greatest agreement appears to be achieved between Method 1 and Method 2, with perfect agreement resulting in two of the eight comparisons and kappa greater than .87 in seven of the eight comparisons. Method 4 corresponds closely with Methods 1 and 2 when comparing the K-ABC subtests. With subtests with lower reliabilities (PIAT Mathematics and PIAT Reading Comprehension), however, Method 4 tends to identify 122 considerably more students than Methods 1 and 2. The lowest agreement appears between comparisons involving Method 3 (Regression analysis 1), primarily because of the very limited number of students identified using this approach. The agreement, when using the PIAT subtests, tends to be lower than agreement obtained with K—ABC subtests across methods. (Figures 3 through 10 graphically illustrate the relationship between the discrepancy methods. The symbols below each line represent students who were selected by the respective methods. The number of students falling into the selection area corresponds to the entries in the preceding tables. WISC-R/PIAT Mathematics comparisons appear in Figure 3. The test reliabilities and intercorrelations are listed at the top of the graph. It can be seen that Method 3, Regression analysis I, is the most restrictive of the Methods, selecting only two students. The regression procedure cutoff lines have equal slopes (rxy) and vary only in the intercepts. Because of the substantial correction for subtest unreliability, the intercept for Method 4 is larger than the intercept for Method 3. Consequently, more students are identified with Method 4 than with Method 3. The low percent overlap between Methods 1 and 2 is explained both by the diverging lines (resulting from the 1J23 Om OO. Om. OO. Om. Om. OO. Om. OO. Om. .Nu momumEonumz 94Hm\muumH3 “mocmamuom.p 0L0>om m mcwc.ELoump L00 moonuoe L00w mo comwumaeoo < .m 0L30.m Om.u OO.N Om.. 00.. Om. O Om.- OO..- Om..- OO.N- Om.w- +-uu-+-c--+-u-n+nonn+-an-+uca-+u-um+-a:-+--on+uun-+--a-+---u+-uu-+u---+--n-+-x--+uuan+uunu+----+----+. + A N m_m>_mcm co_mmoLoo¢ ”a vague: _ _ m_m>_mcm co_mmoLmo¢ "m oozuo: ; oLoum uzLu voume_umu “N vogue: . oLOUmnN up posuoz ‘ll-OO-I-Oh-Ir-l“‘ :- ‘ ‘ ... . . . . . . a _ + + ~ _ . . . . . . + + . . . . . . . . + + . . . . . . . . . L + H + . . L H 4 ~. 4 u u 4 u _ m .4 ~ + a + . . . . . . . L . . . . .. . 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The high degree of agreement between Methods 1 and 2 results from the high reliabilities of the Full Scale IQ (.96) and the PIAT Reading Recognition subtest (.89). It can be seen that Methods 1, 2, and 4 include all of the students who are selected by Method 3. Once again, the correction for unreliability creates a higher intercept for Method 4 than for Method 3. The correction is somewhat less than on Figure 3, however. The WISC-R/PIAT Reading Comprehension comparisons appear in Figure 5. The relationship between Method 1 and Method 2 is more discrepant than in Figure 4, and the disparity can be attributed directly to the lower PIAT Reading Comprehension subtest reliability (ryy = .64). Because of the distribution of scores, however, the agreement between the two methods is still relatively high (overlap = 92.3 %). The lines representing the two regression methods are again parallel, with all of the students selected by Method 3 also identified by Method 4. 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H H . >x A\\ w w :m u L N H.913: 1 1 R. u :1 1 1 XX H H . I H H :m I L H H H H H H +u---+----+----+----+u:--+u---+---u+----+----+----+---u+uuuu+--u-+nu--+----+-u:-+----+u---+--u-+----+. mN.N m>.. mu.. mp. mu. mn.- mp.- mu..- mp..- mu.u- ooaaHZH: om4x N hHN H moaomeu< om .85), when 168 extrapolated to poor quality tests, the results are difficult to interpret. The two regression approaches to the calculation of a discrepancy are perfectly correlated but result in the selection of different populations of students. Method 4 corrects for lack of subtest reliability, making it much easier to establish a severe discrepancy. The less reliable the subtest, the larger the difference between the numbers of students identified with Method 3 and Method 4. The most extreme cases were illustrated with the PIAT Mathematics subtest (rxx = .74) and the PIAT Reading Understanding subtest (rxx = .64). For the comparisons involving the PIAT Mathematics, Method 3 identified 2 students, while Method 4 identified 27 students. For the PIAT Reading Comprehension, Method 3 identified 5 students, while Method 4 identified 44 students. It would appear that the correction for unreliability, which is included in Reynold's regression analysis procedure, is an appropriate adjustment. When this adjustment is not made, it is very difficult to obtain a significant score difference, even at the .05 level. In looking at Figures 3 through 10, it becomes apparent that Methods 1 and 2 are generally functioning quite differently than Methods 3 and 4. One then might ask, which set of procedures is preferred? The correlations of discrepancies obtained by each method with teacher ratings of the severity of a child's problem in the 169 academic area of concern revealed that the regression procedures correlated somewhat better with the ratings than the z-score difference or the estimated true score difference. A regression procedure, therefore may be a more valid approach to the determination of a discrepancy. The question of which intercept to use with the regression cutoff line may be a point of debate, however. Figure 11 illustrates how several approaches to regression analysis compare. Several school districts have recommended the use of a straight regressed score difference (e.g. a 1.0 or 1.5 z-score difference) which takes the form: 2 - z > 1.0 (or 1.5) x (rxy) Y These lines are plotted along with the cutoff lines for Reynolds' regression analysis (Method 4) to demonstrate the impact of selecting one procedure over another. It is clear that the choice of an alpha level (or more simply, the magnitude of the regressed score-observed score difference) will have an influence on the size of the population which will qualify as learning disabled. It would seem appropriate for an individual school district to determine the means and standard deviations of the ability and achievement scores of the general population of students, determine the percentage of that population which can effectively be served in programs for learning disabled, and, then set a cutoff which corresponds to that 170 Om. OO. Om. OO. Om. Om. OO. Om. OO. Om. NI Hucmampome mpm>mm m mchHEHmump OH :umOHQdm mHmHHmcm conmOHmoH on: .HOH mHH0uso mob: Ho :OmHHmQEOO 4 “HH 0.50: Om.w OO.N Om.. OO.— Om. 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I.Q...OCOOCOO l OOOOOOOOOOOOOOOO.....OOOOOOOOOOOOOOO0.00.00 APPENDIX D TEST INTERCORRELATIONS 204 PIATB PIAT9 PIAT1O PIAT11 PIAT12 PIAT? «IA- UN'O 10 (DA.- IOAO rune ID (WAA vouw ouno II VQ [slav- V50 m C II VQ c—A- CMDO ouno v u vQ QA— cwoo vaKD v II V0. WISCR1 QACD mm 11 VQ mav- ah-O rune m 0 ~22; .001 WISCRZ VAC- WISCR3 “A- Q'fl3 ‘0 II V0. 0A1- VAC OGHD ID a VQ v-Ac— NOI <30 v [DAV- QA- r490 OCH) LO fiAP GHOO 11 V0. WISCRd VAC- '%00 vcoo V II VQ WISCRS “A? “00 (”AID “A- quD 000 ('3 WA? cuno ‘D . II we: mav- Nv-O OPWD II v0. PIATQ 0A1- uvah (Two mp4: N VCL 05A? v00 m . II V0. 0A.— moKD rwno m 0 II V0. PIATIO NA.- w~w~ PIAT11 VA.- (Dav- v-Au- 0*C> I~m0 (V) . II VCL ans!- PIATIQ C 0 E F F I C I E N T S C 0 R R E L A T I 0 N P E A R S 0 N KA8C28 KABC29 KABC30 KABC27 VA.- v-Afs KABC17 KABC18 .662 86 .001 (Dr-Av- aMOO VGKD Q o n v0. mAv- KABC19 [\Av- (00 mm «A- V0 mm ('3 hrww v-QO II V0. .249 86 .01 II VCL KA8C2O 209 M'- ('30 V5 (9 V0. (WAQ 00" VFC) N II VG. ”A? VAL!) 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"P m II m NF mm .— —mvl m vaw m I—NI m: I m P vm' mwm— I I Fhmth*OOhFNNOOMQFWQNVwammOOOOOOFO’FOFMmmfimO’mNFVWDOONNFV0NO*®bm0vmbmv mvmnmmmmmummv—m050vmmmvaOm—hbomohmBGOvmmovaw—wvomoOOvmhvmmOhmmm—NNmmn mvohmmommh—mmoomm—m—mmvmomwom—oNovm>vo—mouvmouhmwmomoowmhvmmowmmmmvomoo wNm N m ~NMNNmmmvaINmmm VIMIGMOQOOPGNNWFN msm—wv—mvaMVImm—m I I I mmmv—vammmmObvcmOOmmmmvavNmOObOOmNOOmmwhhmomNm—VFONOFNGVOMOvamOvOmom mmmmvm00vmvvov>mmoommmmvmomvv ovommmvovmmmmmomvmmmvmvomvmvmmomvmmowommm abhmvmoomovPOV*omOOhmoOmmOmwb OvOmbhooomovv*O*vammwmommwmooomhmNOmO>00 m 0"” m? lemmvlw m or I—mmn ummmmu' I I l va—wwmm?—mmmm0*wmm0v00mmvwwmwOPOvmhmOmNmevovmmmmmeOOm—mmhowmmmmvmm—o Comma—mama mmomwnOm v-vowwmv—>ONOVmmvommm0m00vm—v>om O FNOOFOVQQFFV*®N@ mmwmmmOOmhmmmOONwmw mvvmwmvmmvONOmmhmONmOvOmOmmomvON O whammowmmwvmwmhm va N mw wmmwwmmmvm Immmm vvmnmmmwmm—mNNMFNIm Imvvwm m owvvvmvmwmv-mm—m I I I vvwwhmmOmmmbowvvoooohmm®v0mmm—O'vamwOmmv—mmohvonhvmo—vmvm—OVGm—Omcvow W"*FGO'ONVMNONQNFOO N50?*OOmv—O*OOmM*OOOmv®NOmm NVNvNOPmmmFFO*—vvooc——— OmmvmvabmhmOvmvaO mVVMNOmeNONovoomovvOvaOoO VQDNVONOFOMNONOONOCCNOO *N F" m II m mmvmm IF wau m mwww m: "N? m** I N ml? * mm: mmom I I I I I I I —mmmhmmhMQFhmvwhmomvmmwwmhwhbwmmmmvmhv-Ov~—mommwmm—©mmo—OmmvmmvooN©~vmm mmmehmmOmmmmOvOOmmmOmmOOm*mmmOOmmmNOmm—mommmmOthOhOhhmmmmbmvmomhmc—mm —NOhom®mNmmmmmmvmmwhmmmwhNONwoo—mvhmmmmmOmhm—mmmOmmNm-Omwm0mhmmmmmmc55m hmOmohommmmommwoohohmmOmommeOOONomomwmoom—mmmmmmwohmmmmmmowmwomOmm—Omc Fw—v— '- v— v- v—v— '- v—v- ~— v-'- v- V- F v- v- v-v-v- v— v-v-v-v- 1— v—v- ~mwhm—NmmommwwhmmmmohmmOFNmmwwONmmwbmmmmmwhmevmohw—wabmmo—mvmhm—MVmno —w—v—wmewmmmmvvvvmmmmmmmomwwwwwwhhhhhmmmmmmmmmmmmmmmooooooo—**—*N v—v—v—v—v-v—v—v—v-O- ...-V— mevmwbmmOFvamwhmmOFvammhmm0?vamwhwmo'wmvmohmmO-vamm —Fv—vwv—vwmmmmmmmmmmmmmmmmmmmmvvvvvvvvwvmmmmmmm n—fl 216 00v.. 00. 000 000 0.5.. 0V0 .05.. 0.0 50. .NO. .50. 000.I 0.0.0 N0... 005 000..I new 0V0..I 00h 00 ..0 ..0. 000.0 000.0 000.0 000 0 000.0 000 0 000.0 000.0 >0 .00 .00. ..0..I 0.0..I 000..I now I .00.NI 0vw I 0N0.NI NNv.I 00. .>0 .0v. 000.0 000.0 000.0 000 0 000.0 000 0 000.0 000.0 00 .vn .0v. .00. 00v..I 5.0. 500 I 000. 000.I vvm. NNv.I .00. .00. .vv. 0.0.0 000.0 00? . .05. N00.v Nvm.. 000.0 00... .00. .h.. .mv. 000.0 ..0.0 .50 . 00. . 000.0 v0m.N 000.0 000.0 .v.. .mm. .Nv. 000.I 000.0 .mv I 000. 5.0..I 0v... 000..I 0V0. .00. .00 .00. V0...I 0N... 0V0 I hmw. >00.I 0v>. 000..I >00 .00. .v0. .00. 000.0 0V0. 000 0 .0.. 000.0 0V0. 000.0 500. .50. .00. .00. 000.0 000.. 000 0 000. 000.0 .0v..I 000.0 500.- .00 .00 .00. 000. 000.. 000 00?. 5N0 bvv. .00. 500. .00 .00 .vw. v.0 I 000.. vvm I 0.v. >00 .I 000. 0V0..- 0.0. 00 .00 .mm. 000 000.0 .Nm 0v... 0.0.. 000.. 000.. 500-. .00. .00. ..N. ..Oma>wa mOmm>wm ..mmawma mmeme ..uHOhN muHOHN ..u.3~ mu.DN 0.30m.3 0000wm 000m>0m N.0m&00m 000m00a N.L.O5N 0uHO5N N.0.0N 0u~DN 0.a00~3 0N00‘<4(4+ 1) This result for df= 4 - l = 3 falls between the .05 and .01 levels of signifi- cance. Actually it is a little above the 2 percent level. if this level of con- fidence is acceptable, we may conclude that the samples are not drawn from the same population and that a difference in the experimental condi- tions is exerting an effect. in this example S = 126. If this is referred to a table of exact critical values of S, as given in Bradley (1968), the associated probability is found to fall between .01 and .05, not far from the .02 level. The chi-square approximation is in close agreement with the more exact test. The asymptotic relative efficiency of the Friedman test relative to the F test resulting from a two-way analysis of variance with one observation The efficiency of the test increases as k increases, and extends from .637 for k = 2 to a maximum of .955 for k = on. For k = 2 this test is the same as the sign test for correlated samples. (142+ 202+ 292+ 17") -\ 3 X 8(4,+ l) = 9.45 Ferguson, G.A. (1976). Statistical analysis in psychology and education. New York: McGraw—HTTl Book Company, pp. 394-396. 223 17.10 A TEST FOR CORRELATED Paoroa'rrons IN A TWO-BY-TWO TABLE A problem that often arises in psychological research is somewhat different from the problem of association between attributes. As an illustration of this problem, suppose that some N individual subjects are each Observed by two independent judges. Each judge places each subject into one of two mutually exclusive and exhaustive categories, such as “high leadership potential”, versus‘ “low leadership potential.” It is assumed that a judge’s ratings of difi'erent indi- viduals are independent. Let us call these categories simply “H ” and “L” for the moment. We would like to ask if these two judges, given all possible subjects in the population, would show the same true proportion of individuals rated in category “H.” In other words, in the population of all subjects to.be‘rated, does p1(H) = p;(H), where p101) is the proportion rated in category H by judge I, and p3(H) is the proportion rated in that category by judge 2? This is a problem of correlated proportions, since each of the two sample proportions will be based in part on the same individuals. A test due to McNemar (1955) applies to this situation. Suppose that the sample of N indi- viduals were arranged into the following 2 X 2 table: J ones 1 I! L H a b JUDGE 2 L c d An exact test of the hypothesis that p1(H) = p201) is possible using binomial distribution. Under this hypothesis, the probability of a given sample result, showing a particular pair of cell frequencies b and c, is just (b ‘1';- °) (.5)... [17.10.1‘] To carry out the exact test, let 9 equal the smaller of the two frequencies, (3 or c. Then one takes the sum of probabilities 2 i (b 1' c) (.5)b+c. (17.10.?) h-O If this number is less than or equal to the value chosen for a, then the null hy- pothesis may be rejected (two-tailed). . When N is relatively large, the exact probability may be approxi- mated by use of x’, where _ (lb - 6| - l)z _ b + c 2 {17.10.31} with one degree of freedom. For our example, a significant result would let one conclude that the true distributions of judgments for the two judges differ. Be sure to notice that this is not an ordinary test of association for a contingency table, but rather a test of the equality of two proportions where each sample proportion involves some of the sameobservations, making the two sample proportions dependent. From Hays, W.L. (1973). Statistics for the social sciences. Chicago: Holt, Rinehart and W' pp. 740:741. 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