Uses of Rasch scaling in the measurement of cognitive development and growth

This report describes two types of findings: (a) the consistency between two major cognitive tests in terms of their developmental scales based on item-response theory, and (b) the initial development of ideas and methods for the revival of the classic concept of ratio IQ. The ratio IQ (e.g., Stanford-Binet, 1937) was formed by the division of mental age (derived from test performance) by chronological age multiplied by 100. Following a multitude of criticisms about the scaling qualities of the ratio IQ, it was mostly abandoned by the major intelligence batteries, beginning with the Wechsler scales in the 1940's, in favor of standard scores. This study presents a new approach to age equivalence scores as a basis for mental age, and the calculation of ratio IQ, based on Rasch-model item response theory. The new ratio IQ was compared statistically with standard-score IQ (mean 100, SD 15) from the Leiter International Performance Scale--Revised (Leiter-R) and from the Woodcock-Johnson Psychoeducational Battery--Revised (WJ-R). The essential element of the new ratio IQ is the W-scale, a Rasch-based score employed in the WJ-R and in the Leiter-R. Mental age was estimated from the W-scale estimate of ability and chronological age from a W-scale age equivalence for each month of age. Statistical results showed a highly similar growth curve for the W-scale scores on the Leiter-R and the WJ-R, even though the two scales have different content and standardization samples. Also, high correlations were found between the new ratio IQ and standard-score IQ (e.g., correlations ranging from .87 to .95 depending on age range). Criterion-related evidence of validity was found in the correlation of .82 between the new ratio IQ and the Wechsler Intelligence Scale for Children--Third Edition (WISC-III) standard-score IQ and in correlations with achievement-test scores. Finally, the ratio IQ showed predictable mean differences between groups of children with typical cognitive ability, cognitive delay levels of performance and giftedness. The standard deviation of the new ratio IQ was somewhat variable across age groups, however, so new interpretive guidelines would be needed if the new index is to employed in published tests. Implications of the scaling methods are discussed.