Do Normal Children Have “Flat” Ability ProJiles? 285

The data presented here provide a basal level of scatter. Before roncluding that an exceptional child, or a group of exceptional children, exhibits marked scatter on the McCarthy, the clinician must first consider the basal level of “normal scatter.”

REFERENCES KAUFMAN, A. S. A note on interpreting profiles of McCarthy scale indexes. Perceptual and Motor

Skills, 1975, 41, 262. MCCARTHY, D.

Note: Thanks are due The Psychological Corporation for providing the data source.

Manual for the McCarlhy Scales of Children’s Abilities. New York: Psychological Corporation, 1972.

RELATION BETWEEN ITPA AVERAGE DEVIATION AND STANFORD-BINET INTELLIGENCE SCORES

EDWARD BURNS

State University of New York at Binghamlon

The relation between average deviation, as determined using the Illinois Test of Psycholinguistic Abilities, and Stanford-Binet intelligence scores was ex- amined using a preschool sample. The results revealed a curvilinear (quadratic) relation between total average deviation and Stanford-Binet intelligence scores. The use of average deviation as an index of “learning disabilitieh” was discussed.

Overall indices of intratest variability have been associated with groups ranging from the mentally retarded (Satter, 1955) to patients diagnosed as schizo- phrenic (Wechsler, 1958; Wechsler & Jaros, 1965). Kirk and Elkins (1975) have proposed that average deviation be used to screen children for learning disabilities. Rapaport, Gill and Schafer (1968) have reported a direct relation between the degree of scatter and IQ. Paraskevopoulos and Kirk (1969) have suggested that average deviation can be used as an index of learning difficulties. Using the Illinois Test of Psycholinguistic Abilities (ITPA) (Kirk, h9cCarthy and Kirk, 1968), Paraskevopoulos and Kirk state that, “Normal children probably exhibit a rela- tively flat profile, that is, little deviation from the mean scaled score. The smaller the deviation, the less discrepant the child’s growth. The larger the deviation, the more discrepant the child’s growth, and the more likely i t is that the child will have learning disabilities.” (p. 142) I n contrast to this interpretation, Burns (1976) has suggested that the relation between I& and average deviation using ITI’A scaled scores may be nonlinear.

Since I& has been hypothesized to be an important factor in understanding discrepant learning growth, the association between average deviation and I& should be thoroughly understood. The purpose of the present paper was to evaluate the relation between average deviation, as determined using the ITPA, and Stanford- Binet (Terman & Mcrrill, 1960) intelligence scores.

Requests for reprints should be sent to Edward Burns, Programs in Professional Education, State University of New York, Uinghamton, N.Y. 13901.

286 Psychology in the Schools, July, 1976, "01. 13, No. 3.

M E T H O D

Xubjects Tcst scores for 75 prcschool children, 43 males and 32 females, were cxamined.

Each child had becn administcrcd thc ITPA and Stanford-Binet by trained per- sonnel over a five-month period. The mcan CA of this group was 4.47 years (SD = .86), and the mcan Stanford-Binct IQ was 99.6 (SD = 12.41).

Procedure Avcragc deviation was calculated for each individual by finding the sum of the

absolute deviations of each subtcst score subtracted from an individual's mcan subtest score and then dividing by 10 (the number of subtests). Each ITPA sub- test has a scaled mcan of 36 and a standard dcviation of 6.

RESULTS AND DISCUSSION The relation betwccn averagc dcviation and I& was assessed using the fol-

lowing model : Average Deviation = bl (I&) + bz + c

The results revealed that the linear component accounted for 12% ( R = .345 and R2 = .119) of the variance of average deviation scores, F (1,73) = 9.86, p < .01, while the quadratic term accounted for an additional 20y0 of the variance, F (1,72) = 21.23, p < .01. Overall thc quadratic model accounted for 32y0 of average deviation scorc variance, F (2, 72) = 16.92, p < .01. So as to give an idea of the relation between averagc dcviation and Stanford-Bjnet IQs, average deviation scores were calculated for ZQ points of 80, 100, and 120, where predicted average deviation was found by the following formula: -0.63475 (I&) + 0.00335 -+33.67874. For these selected I& points the respective predicted average devia- tion scores were 4.34, 3.70, and 5.75.

I n order to determine whether this quadratic trend was specific to certain components of the ITPA, averagc deviation scores were calculated for the 5 auditory subtests and for the 5 visual subtests. The mean average deviation score for the auditory subtests was 3.92 (SD = 1.88), and the mean average deviation score for the visual subtests was 3.95 ( S D = 1.72). The mean average deviation for all 10 subtests was 4.24 (SD = 1.24). For the auditory subtests the linear component was not significant (R2 = .04). The quadratic term, on the other hand, accounted for 29% of the variance of average deviation scores, F (1, 72) = 30.61, p < .01. The complete quadratic model explained %Yo of auditory subtest average deviation score variance. The analysis of average deviation of the visual subtests revealed a significant linear term, R2 = .06, F (1, 73) = 4.35, p < .05, while the complete quadratic model was not significant.

The results of the present study do not support the hypothesis that average deviation is inversely related to I&. Rather, the results indicated that ITPA average deviation is related to Stanford-Binet I& following a quadratic trend. The trend becomes especially prominent when only auditory subtests are considered. The quadratic model used to describe the relation between average deviation and Stanford-Binet I& is presented as nothing more than a reasonable hypothesis; further research may determine the actuality of this relationship. Indeed, the

I T P A Average Deviation and Stanford-Binet Intelligence Scores 287

curvilinear trend may have resulted from one or more causes. First, the use of norms based on an “average sample” may have contributed to the nonlinear rela- tion between average deviation and I& (see Burns, 1976). Second, varying subtest means and standard deviations may have affected the relation between average deviation and I&. In the present study, subtest means ranged from 33.35 (auditory association) to 36.77 (auditory memory), and standard deviations ranged from 5.83 (visual memory) to 8.45 (verbal expression). Third, asymmetrical score distributions may have contributed to the quadratic trend. For the 10 subtcsts the median low z scorc was -2.16 and the median high x score was 3.00. If the score distributions of several subtests were asymmetrical (viz., positively skewed) this would explain why average deviation increases more rapidly for high IQs than for low IQs. The reason for this is that persons with higher scores would likely exhibit greater variability between subtcsts, thus resulting in higher average deviation scores.

When one considers the information (discrepant learning growth) which average deviation is purported to yield, the rclation between average deviation and I& should be carefully cxamined. In this respect, Kirk and Elkins’ (1975) suggestion that avcrage deviation can bc used to detect learning disabilities in preschool children would seem premature. Quite obviously, if the quadratic trend noted in the prcsent study docs cxist on a morc gcncral basis, comparing a retarded sample to a normal sample (I’araskcvopoulos and Kirk, 1969) would result in the false inference that average deviation and I& were inversely related. Now assuming that thc learning growth of retarded children is “more discrepant” t,han that of normal children, the inference might be made that average deviation is an indicant of “learning disabilities.” This argument would, however, ignore the upper end of the intkllectual continuum. In other words, although children of lower intellectual ability may exhibit greater average deviation than normal children, their average deviation may be less than that of intellectually brighter children. When assessing the relation bctwecn average deviation and intelligcncc, and when using avcrage deviation as an index of “discrepant learning growth,” this possibility should be given serious Consideration.

REFERENCES BURNS, E. The effects of .ricted sampling on ITPA scaled scores. Americaji Journal of ,Ifental

KIRK, S., & ELKINS, J. Journal

KIRK, S., MCCARTHY, J., & KIRK, W. (Rev. ed.)

P.\n.zsrcevoPouLos, J., & KIRK, S. Tile decelopnie/tt atrd psychometric characteristics of the Rez,iaed Urbana: University of Illinois Press, 1969.

RAP.~PORT, I)., GILL, M., & SCHI\FI,:R, It. Diagnostic psychological teslijig. (Rev. ed.) New York:

Deficiency, 1976, in p

of IJeartiitrg Disabilities, 1975, 8, 18-20.

Urbana: Universit,y of Illinois Press, 1968.

Illiiiois Tesl of Psycholinguistic Abililies.

International Universities Press, 1968.

Ident,ifying developmental discrepancies a t the preschool level.

The Illiiiois ‘I’est of Psycholinguistic Abilities.

SATTNR, G. Traitiittg School

TI~RMAN, L., & MKRRILL, M. Boston: Honghton Mifnin, ISGO. WIXHSLI~X~, I>. The measuremcnt and appraisal of adult intelligeiice. (4th ed.) Baltimore: 1Villiams &

WICCHSLI~:R, I). , & JAROS, E. Schziophrenic patterns on the WISC. Journal oJ Cli,iical Psychology,

Psychometric scatter among mentally retarded and normal children.

Staiiford-Riiret Iirtelligeiice Scale. Wulfetitt, 19.55, 52, 63-68.

Wilkins, 19.58.

1965, 21, 288-291.