intra-individual discrepancy in diagnosing specific learning disabilities

Hammill Institute on Disabilities

Intra-Individual Discrepancy in Diagnosing Specific Learning DisabilitiesAuthor(s): Linda E. O' DonnellSource: Learning Disability Quarterly, Vol. 3, No. 1 (Winter, 1980), pp. 10-18Published by: Sage Publications, Inc.Stable URL: http://www.jstor.org/stable/1510421 .

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INTRA-INDIVIDUAL DISCREPANCY IN DIAGNOSING SPECIFIC

LEARNING DISABILITIES

Linda E. O'Donnell

Abstract. The relationship between intra-individual discrepancy and exceptionality is studied in 248 children from grades one through six. Categories of exceptionality include children classified as: gifted/creative; sensorily impaired; behavior disordered; physically handicapped; mentally retarded; and learning disabled. The discrepancy between a child's expected level of functioning and actual level of functioning is computed by nine formulae commonly used in the field of special education. The study revealed a highly statistically significant relationship between discrepancies and exceptionalities, though a relatively low strength of association was found. The results also indicate that the intra-individual discrepancy is questionable when used as the defining characteristic of special learning disabilities; such a discrepancy is equally likely to occur in children classified as sensorily disordered, behaviorally disordered, and learning disabled.

The discrepancy between an individual's level of achievement and capacity is an

important diagnostic characteristic used in

special education to differentiate among types of exceptional children. The achievement level refers to the level at which an individual actually functions in areas such as

reading, arithmetic, language, or spelling. The level of capacity, which refers to an estimate of the level at which the child should be able to function, is often called the expectancy level; it is determined by one of several formulae. The difference between where the child does function and where the child should be able to function is the intra-individual discrepancy. For example, diagnosis might show that a child reads like a second grader (achievement level), but has the capacity to read like a seventh grader (expectancy level) placing the child five years behind in reading (intra-individual discrepancy).

The intra-individual discrepancy initially became important as a diagnostic clue indicating learning difficulties in the research of Monroe (1932). Over the past 40 years numerous other formulae or methods have been presented for measuring intra-individual discrepancies in children who exhibit learning difficulties (Bond & Tinker, 1973; Dechant, 1968; Durrell, 1956; Gallagher, 1966; Harris, 1970; Harris, 1975; Horn, 1941; Kirk, 1966; Myklebust, 1967; Otto & McMenemy, 1966; Salvia & Ysseldyke, 1978; Smith, Smith, & Smith, 1977; Woodbury, 1963; Young, 1976). Recent federal guidelines have formalized the assumption that intra-individual discrepancies

LINDA E. O'DONNELL, Ph.D., is Assistant Professor, Special Education Program, Division of Reading Education, University of Missouri-Kansas City.

10 Learning Disability Quarterly



indicate learning difficulties by requiring diagnosticians to provide evidence of such a discrepancy as the major defining characteristic of learning disabilities (U.S. Government, 1976, p. 52105). As a result, discrepancy analysis is becoming a key part of differential diagnosis for every child suspected of having characteristics of learning disabilities.

The discrepancy hypothesis, which most special educators in the field of learning disabilities assume to be accurate is as follows. If the achievement level is well below the

expectancy level (rather than the reverse), if the discrepancy is wide enough to be statistically significant, and if the extraneous causes of the discrepancy are ruled out, then the intra-individual discrepancy may be interpreted, in effect, as the major defining characteristic of specific learning disabilities. Discrepancy research previously cited supports the assumption that the discrepancy occurs in learning disabled children. However, research has never determined whether intra- individual discrepancies also occur in exceptional children other than those with learning disabilities. The discrepancy is seldom checked in the diagnosis of a child suspected of having problems other than learning disabilities.

Diagnosticians use several formulae inter- changeably to measure intra-individual differences between capacity and achievement. The few studies which evaluate comparability of the most common formulae offer very limited evidence. Yet, they all caution against interchangeable use. Rodenborn (1974) compares Monroe's formula with those proposed by Bond and Tinker, Harris, and Horn; he recommends that several formulae be used simultaneously since their outcomes are not comparable, especially at the lower and higher extremes of intelligence. Harris (1971) concludes that the method and the cutoff point (which varies from formula to formula) make a difference in marginal cases; he provides an illustration in which a child has a learning disability in reading according to Monroe and the Bond and Tinker formulae, while the child does not according to the Myklebust formula. Alspaugh and Burge (1972) compare the Harris formula with the Bond and Tinker formula,

rejecting both methods as inferior to a regression analysis method of determining expectancy. These studies suggest that research, intended to determine the presence or absence of discrepancies in children, should check several of the most commonly used formulae rather than just one discrepancy method.

The general research problem of this study is a delineation of the relationship between exceptionality and discrepancy. Two specific research questions are examined. First, is there a statistically significant difference among the categories of exceptional children in the amount of discrepancy between capacity and achievement? Second, are the discrepancies of children who are classified as learning disabled greater than those of other exceptional children, as assumed by diagnosticians? Nine of the most common discrepancy formulae and six types of exceptional children are considered.

METHOD Subjects

A total of 248 subjects were drawn from a population of exceptional children in six' categories. The numbers of subjects in each category include: 36 gifted and creative (GC), 37 sensorily impaired (SI), 35 behaviorally disordered (BD), 17 physically handicapped (PH), 37 mentally retarded (MR), and 78 learning disabled (LD) children. Excluded from the statistical analysis were 8 subjects who fit no category of exceptionality.

Demographic characteristics of grade, age, sex, and culture-race were recorded for all subjects. Children ranged in grade level from one to six if placed by chronological age without consideration for their handicapping conditions. The chronological age ranged from a low of 6 to a high of 13. Within the total sample of 240 subjects, 19% were 6 years old, 15% were 7 years old, 14% were 8 years old, 12% were 9 years old, 17% were 10 years old, 17% were 11 years old, and 5% were 12 and 13 years old. There were 62% males and 38% females. The cultural-racial characteristics included 5% black, 1% Hispanic, 89% non- Hispanic white, and 5% unknown. Socio- economic indicators were not available on 65% of the subjects; the remainder consisted

Volume 3, Winter 1980 11



of 11% lower class, 21% middle class, and 4% upper class according to diagnostic reports in institutional records.

The sites from which data were gathered include five locations in Kansas and Missouri. Information was not available on each subject for rural, suburban, or city representation. A rough estimate is possible by comparing the percentages of subjects from each site: less than 1 % from the Kansas State School for the Blind, 14% from the Kansas State School for the Deaf, 31% from Shawnee Mission Public Schools, 7% from Kansas City, Missouri Public Schools, and 48% from Blue Springs Public Schools. The Kansas City Missouri Public School District is best described as a central-city district while the Shawnee Mission Public Schools and the Blue Springs Public Schools serve predom- inantly suburban areas. The two state schools draw students from city, suburban, and rural populations. Therefore, a great majority of the subjects represent a suburban location with a few students coming from rural and city areas.

The major criterion for inclusion in each of the six categories of exceptionality was the label designated by the institution serving the child. Each institution claims to adhere to the federal guidelines for assignment. For example, in learning disabilities the school-labeled criteria for inclusion were: no obvious intellectual retardation, presence of severe academic deficits, absence of visual and hearing acuity handicaps, and parental consent. Based on a case-by-case evaluation of potential subjects' diagnostic records, the remaining criteria for inclusion of subjects in the study were availability of a reading score, arithmetic score, and intelligence score; all three tests had to be normative rather than criterion referenced, individually rather than group administered, and had to yield a global score. Excluded from the research population were students who were unable to complete the necessary tests (e.g., behavior-disordered students who refused to cooperate according to the diagnostician's protocol notes) and subjects whose records described multihandicapping conditions (e.g., blind, deaf, behavior disordered, physically handicapped, and learning disabled students who had in-

telligence quotients and adaptive behavior levels in the mentally retarded range).

A quota form of nonprobability sampling was used to select subjects from the population of exceptional children. Nonprob- ability sampling does not involve random sampling methods. The quota form refers to a procedure according to which strata of the population-exceptionality and age in this case-are used to select sample members that are representative and suitable for certain research purposes. Nonprobability samples "are often necessary and unavoidable. Their weakness can to some extent be mitigated by using knowledge, expertise, and care in selecting samples and by replicating studies with different samples" (Kerlinger, 1973, p. 129).

Prior to data gathering, five research assistants were trained to identify 40 items of information on each subject from special education records. All research assistants were graduate students in a special education program, and all had completed training in methods of diagnosis for learning disabilities, principles of measurement, and individual intelligence testing. The training program for this project included directions about pro- tection of privacy, human experimentation guidelines, and a system of numerical coding of data.

Data gathering was conducted on location at the five institutional sites. No new tests were administered to subjects. Rather, existing tests and information were taken from the files of the participating institutions. One file was available for each of the 240 subjects. Research assistants needed approx- imately 20 minutes per folder to extract the information necessary to compute nine discrepancy scores for each subject. In actual clinical diagnosis, special educators use several kinds of skills for discrepancies; in this study the discrepancies were limited to reading and arithmetic skills.

The analysis of data involved 10 variables: exceptionality and nine different discrepancy variables. Exceptionality was an independent variable consisting of nominal measurement. It had six categories: gifted, sensorily impaired, behaviorally disordered, physically handicapped, mentally retarded, and learn-




TABLE 1 Discrepancy Formulae for Learning Disabilities

Source Variables Discrepancy Formula

Bond & Tinker Years in school = YIS IQ (1973) Intelligence quotient = IQ YIS x + 1. - RG

Actual reading grade = RG 100

Harris Mental age = MA MA - RA (1970) Actual reading age = RA

Harris Mental age = MA (2xMA) +CA (1975) Chronological age = CA - RA

Actual reading age = RA 3

Horn Mental age = MA For CA of 6-0 to 8-5 (1941) Chronological age = CA MA + CA

Actual reading age = RA L - RA 2

For CA of 8-8 to 9-11

-RA 3(MA) +

2(CA) 5

For 10-0 to 11-11 2(MA) + CA

3 IRA Monroe Actual reading grade = RG RG

(1932) Chronological grade = CG CG + MG + AG Mental grade = MG 3 Arithmetic grade = AG

Myklebust Actual achievement age = AA AA (1967) Mental age = MA MA + CA + GA

Chronological age = CA 3 Grade age = GA

Smith Chronological age = CA IQ +.17 (1977) Intelligence quotient = IQ CA+ .17 -2.5

300




ing disabled. The discrepancy variables consisted of the following interval measurements: the Bond and Tinker (1973) discrepancy formula; the original Harris (1970) discrepancy formula; the revised Harris (1975) discrepancy formula; the Monroe (1932) discrepancy formula; the Myklebust (1967) discrepancy formula for reading; the Mykle- bust (1967) formula for arithmetic; the federal guidelines based on the Smith et al. (1977) discrepancy formula for arithmetic. The discrepancy formulae are presented in Table 1.

A computer program was designed to figure nine discrepancy formulae for each of the 240 subjects. The program also transposed the raw data into transformed scores appropriate for statistical analysis. Two illustrations demonstrate adaptations made to make formulae comparable. First, the formulae's final outcomes would not be similar if used as directed by original sources. The Myklebust formula yields a learning quotient to be evaluated against an unvarying mean of 100 and a lower cutoff of 90. The Smith formula provides a variable, individual, cutoff point as a grade level below which an actual achievement score (such as reading) would be considered indicative of a learning disability. The Bond and Tinker formula results in an expected level of functioning, not an

upper or lower limit for normal or abnormal functioning. To make the formulae in Table 1 comparable for research purposes, it was necessary to enter each formula to locate the points at which the expectancy, the discrepancy, and the actual level of functioning were figured; since every formula had all three components--computed with different variables and by different methods-this solution did not modify the original intent of the formulae.

Second, some formulae (e.g., Harris) rec- ommend months or twelfths of a year while others (e.g., Myklebust) require tenths of a year. Some formulae are determined with age scores (e.g., Horn) while others are completed with grade scores (e.g., Bond and Tinker). Thus, the authors' original formulae might report the identical expectancy information in four ways: 1-6 (grade in months), 1.5 (grade in tenths of year), 6-6 (age in months), or 6.5 (age in tenths of a year). For research purposes, all subjects' scores were changed to grade scores reported in tenths of a year before statistical comparison.

RESULTS The results of nine separate one-way

analyses of variance support the conclusion that a relationship exists between the in-

TABLE 2 Statistical Significance and Strength of Association Between

Type of Exceptionality and Nine Discrepancy Measures

Dependent Variable F Ratio F Probability Eta Eta2

Bond & Tinker 18.50 <.001 .570 .325 Harris I 3.19 <.005 .275 .076 Harris 11 7.18 <.001 .396 .157 Horn 9.43 <.001 .444 .197 Monroe 14.70 <.001 .526 .276 Myklebust Rdg. 30.47 <.001 .731 .535 Myklebust Arith. 18.31 <.001 .639 .409 Smith Rdg. 11.76 <.001 .554 .307 Smith Arith. 6.13 <.001 .433 .188




dependent variable of exceptionality and the dependent variables of discrepancy. In each one-way analysis of variance, the independent variable consisted of six groups of exceptional children with one of the discrepancy formulae as the dependent variable. The comparison of within-group variance (estimating the random error or chance fluctuation) and the between-group variance (estimating the influence of exceptionality on the discrepancy fluctuation) is shown in the F ratios provided in Table 2. Since the F ratios were all highly statistically significant at the p <.01 level, the results support rejection of the null hypothesis that samples of exceptional children are drawn from populations having the same mean discrepancy.

To determine the strength of the association between the discrepancy variable and the categories of exceptional children, eta2 was figured for each analysis of variance (Table 2). As a brief rationale for selecting this method, the F test of statistical significance unfortunately does not indicate the magnitude or strength of the relationship; an F test which is statistically significant simply says that a relationship exists. The eta2,

a measure of the strength of the relationship between each independent and dependent variable, indicates whether the differences in variability are to be considered trivial or substantial. Results in Table 2 indicate a relatively low strength of association on the Harris I, Harris II, and Smith arithmetic, while there is a relatively high strength of association on the Bond and Tinker, Mykle- bust arithmetic, and Myklebust reading discrepancies.

Since the F test was highly statistically significant, a Scheffe test of all the differences between the means was completed to determine the main sources of differences between the subgroups. This a posteriori contrast test is appropriate for use with unequal group sizes. The pairs of groups of exceptional children, with differences between means which contributed most to the significance of the F ratios, are presented in Table 3.

To clarify the differences between the learning disabled subjects and other groups, the differences between means were studied using t contrasts on data from the analysis of variance. Each set of six t contrasts was examined. The Monroe discrepancy formula

TABLE 3 Pairs of Exceptionalities Significant on Scheffe Test*

3Q -

c:c

.e. Gro o u

Group1 c,

Learning Disabilities 7 1 2 Gifted/Creative 7 5 7 8 8 Sensory Impairment 5 1 1 Behavior Disorders 7 1 1 Physical Handicaps 1 8 1 Mental Retardation 2 8 1

Note. The numbers represent how many of the nine discrepancy formulae yielded pairs of exceptionalities which were significant.

'p<.05




TABLE 4 Differences Between Learning Disabilities and Other Groups

on t Contrasts with Separate Variance Estimates

Contrast

Group X SD Contrast Value t df p

Monroe Discrepancy Formula

LD 0.16 0.9 GC -1.47 1.5 -1.63 -6.10 47 .000' SI 0.47 1.7 0.31 1.08 46 .286 BD 0.51 1.1 0.35 1.66 55 .103 PH 1.14 0.9 0.98 4.02 23 .001* MR 0.67 0.9 0.51 2.75 68 .008*

'p<.05.

in Table 4, for instance, shows the contrast between the means of the learning disabled group (X = 0.16) and the physically handicapped group (X = 1.14) to be 0.98; this yields a t value of 4.02 which is significant at the p<.05 level (p = .001). Supple- mentary statistical tables reporting all 54 t contrasts are available on request.2 The total results of the t contrasts and the results of the Scheffe contrasts both support the conclusion that the category of learning disabilities differs significantly from the categories of the gifted, the mentally retarded, and the physically handicapped on discrepancy characteristics.

DISCUSSION Among institution-labeled groups of ele-

mentary-level, exceptional children, the results indicate a relationship of high significance and low strength of association between category-of-exceptionality and degree-of-discrepancy. The study supports the conclusion that discrepancies of the magnitude found in learning disabled students are found equally often among children who are classified as sensorily impaired and behavior disordered; in other words, these measures do not differentiate between learning disabilities, on the one hand, and visual or hearing impairment and behavior disorders on the other. The outcome con-

tradicts the existing premise that the intra- individual discrepancy is found only in learning disabilities and that it is the major characteristic differentiating learning disabilities from all other types of exceptionality.

If one adheres to the position of the federal guidelines for identifying learning disabilities, the implications of the study confirm the need for careful screening and diagnosis of visual acuity, hearing acuity, and behavior disorders in every child suspected of having learning disabilities. This approach to assessment ex- cludes false, positive identification of children- those who display the misleading discrepancy but who are not really learning disabled. The intra-individual discrepancy is necessary but not sufficient for recognition of learning disabilities.

One could take a different position. Among single handicapping conditions the intra- individual discrepancy might be as legitimate a diagnostic characteristic for deafness, blind- ness, and behavior disorders as it is for learning disabilities. It may be the identifying characteristic in learning disabilities, while the discrepancy is one of several diagnostic characteristics of sensory or behavior disorders. Such an approach would not mean the blind child is learning disabled; rather, it would mean that the discrepancy is characteristic of visual impairment just as it is characteristic of learning




disabilities. The implications of this interpretation suggest the importance of careful assessment of intraindividual discrepancies in students suspected of having sensory impairment and behavior disorders.

Still another position may be implied about multihandicapping conditions. Perhaps there are actually pervasive, genuine learning disorders among most children who are classified as blind, deaf, and behaviorally disordered. By maintaining the current diagnostic strategy of ruling out a diagnosis of learning disabilities if discrepancies are found concomitant with sensory acuity impairments and behavioral problems, diagnosticians may be excluding the numerous multihandicapped students who should be eligible for special education services in learning disabilities. Advances in differential diagnosis of LD-deaf, LD-blind, and LD- behaviorally disordered children would be important, if such an interpretation of this study's results were made.

Overall results are best understood in a broad context. The discrepancy hypothesis has become increasingly central to the identification of learning disabilities. Since its origin in the 1930's, several methods have emerged as alternative ways to implement the discrepancy hypothesis in diagnosis. They can be categorized as: discrepancy-formula methods, regression-equation methods, and profile- analysis methods.

The discrepancy-formula methods considered in this study are controversial. The formulae have questionable validity; the dangers of implementing two or more complex ratios, such as a mental age or an intelligence quotient, within still another index, such as those of discrepancy formulae, are discussed by Hammill (1976), Kerlinger (1973), Macy, Baker, and Kosinski (1976), and Thorndike (1963). Furthermore, the reliability has never been established. Discrepancy formulae usually disregard the reliability of the several measures plugged into the formula, the intercorrelation between tests being compared, and the reliability of the differences scores. Since the reliability of the composite expectancy score(yielded by discrepancy formulae) has never been established, and since many of the scores used to determine actual level of functioning lack reliability scores, the reliability of the difference

between the expected and actual levels of functioning cannot be computed.

Profile-analysis and regression-equation methods are considered by many authorities to be superior in both validity and reliability to the discrepancy-formula methods (Alspaugh & Burge, 1972; Salvia & Ysseldyke, 1978; Thorndike, 1963; Woodbury, 1963). How- ever, profile-analysis and regression-equation approaches are seldom implemented in clinical settings. The reason could be their diffi- culty in computation and application. Another reason may be that clinical data are frequently insufficient to enter these two more sophisti- cated methods. Perhaps the formulae continue to be used because the federal guidelines support the procedure or because of the formulae's long history in remedial and special education.

The popularity of the discrepancy-formula method is probably assured in the future in spite of the serious weaknesses in both validity and reliability. Therefore, it is essential to clarify the assets and limitations of discrepancy- formula methods; this study adds one piece to the existing information about the nature of discrepancy formulae and their use in special education.

REFERENCES Alspaugh, J., & Burge, P. Determination of reading

expectancy. The Journal of Experimental Edu- cation, 1972, 40(4), 1-5.

Bond, G., & Tinker, M. Reading difficulties: Their diagnosis and correction (3rd ed.). New York: Appleton-Century-Crofts, 1973.

Dechant, E.V. Diagnosis and remediation of reading disability. West Nyack, NY: Parker, 1968.

Durrell, D.D. Improving reading instruction. New York: Harcourt, Brace, & World, 1956.

Gallagher, J. Children with developmental im- balances: A psychoeducational definition. In W. Cruickshank (Ed.), The teacher of brain-injured children: A discussion of the basis for com- petency. Syracuse, NY: Syracuse University, 1966.

Hammill, D.D. Defining "LD" for programmatic purposes. Academic Therapy, 1976, 12(1), 29-37.

Harris, A. How to increase reading ability: A guide to developmental and remedial methods (5th ed.). New York: David McKay, 1970.

Harris, A. A comparison of formulas for measuring degree of reading disability. In R.E. Leibert (Ed.), Diagnostic viewpoints in reading. Newark,




Del: International Reading Association, 1971. Harris, A. How to increase reading ability: A

guide to developmental and remedial methods (6th ed.). New York: David McKay, 1975.

Horn, A. The uneven distribution of the effects of special factors. Southern California Education Monographs, 1941, No. 12.

Kerlinger, F.N. Foundations of behavioral research (2nd ed.). New York: Holt, Rinehart, & Winston, 1973.

Kirk, S. The diagnosis and remediation of psycho- linguistic disabilities. Urbana, IL: University of Illinois, 1966.

Macy, D.J., Baker, J.A., & Kosinski, S.C. An empirical study of the Myklebust learning quotient: Unabridged report. National Institute of Education, 1976. (ERIC Document Re- production Service No. ED 130 468).

Monroe, M. Children who cannot read: The analysis of reading disabilities and the use of diagnostic tests in the instruction of retarded readers. Chicago: University of Chicago, 1932.

Myklebust, H. Learning disabilities: Definition and overview. In H. Myklebust (Ed.), Progress in learning disabilities (Vol. 1). New York: Grune & Stratton, 1967.

Otto, W., & McMenemy, R.A. Correction and remedial teaching: Principles and practices. Boston, MA: Houghton Mifflin, 1966.

Rodenborn, L.V. Determining and using expectancy formulas. Reading Teacher, 1974, 28(3), 286-291.

Salvia, J., & Ysseldyke, J.E. Assessment in special and remedial education. Boston, MA: Houghton Mifflin, 1978.

Smith, R.T., Smith, W.J., & Smith, L.M. 50% SLD: Severe learning disability discrepancy. VI-G Percepts: Special Issue, 1977, No. 6.

Thorndike, R.L. The concepts of over- and under- achievement. New York: Teachers College Press of Columbia University, 1963.

U.S. Government. Education of handicapped children. Federal Register, 29 November 1976, 41 (230), 52105-52107.

Woodbury, C. The identification of underachieving readers. The Reading Teacher, 1963, 16(4), 218-223.

Young, B.S. A simple formula for predicting reading potential. The Reading Teacher, 1976, 29(7), 659-661.

FOOTNOTES The research was supported by the University

of Missouri-Kansas City through a Faculty Re- search Grant. 'Two changes in an initially intended eight groups were made following completion of data gathering to yield these six groups. First, two samples of learning disabled children, 38 subjects in self-contained settings and 45 subjects in resource room settings, were combined into a single sample of 78. (Although it originally was believed that the self-contained subjects would be much more severely disabled and, therefore, exhibit wider discrepancies than the resource room subjects with milder learning disabilities, the anticipated difference between the two subgroups in learning disabilities was not found. This decision was made after t-tests contrasting the self-contained and resource room learning disabled subjects showed that they were not significantly different at the .05 level according to the Scheffe procedure).

The second change was the forming of a group called sensorily impaired. It was formed by combining hearing impaired (deaf and hard-of- hearing) subjects with visually impaired (blind and partially sighted) subjects. This was necessary because too few children met the study's re- quirements in the visually impaired group to merit maintaining a separate group. Research assistants documented both variations in testing method and questionable identifying data which resulted in excluding a number of blind subjects from the sample. For example, some children were mentally retarded in addition to being blind; the study requires discrete categorical assignment and does not allow for multihandicapping conditions such as blind-retarded. Several blind children had been given only a partial test making the composite test score, intended for the entire test, invalid. Other blind children had been given tests with so many variations in adminis- tration procedures-such as no time limits on timed tests-that the test scores were judged invalid.

2Supplementary tables are available from the National Auxiliary Publications Service of the American Society for Information Science (ASIS/ NAPS), c/o Microfiche Publications, 305 East 46th Street, New York, New York 10017.




intra-individual discrepancy in diagnosing specific learning disabilities

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