Reynolds & Keith. A test of Spearman’s law of diminishing returns in the Kauffman Assessment Battery for Children, Second Edition.
From Program Abstract
- According to Spearman’s “law of diminishing returns,” positive correlations among cognitive ability tests are higher in low ability groups versus high ability groups. Raw data from the Kaufman Assessment Battery for Children, Second Edition standardization sample were studied to determine if the phenomenon is present in this intelligence battery. The sample used in this study included 2175 participants ranging from 7 to 18 years in age. The sample was split into two groups: One group included individuals who had a Fluid-Crystallized Index (FCI) of 100 or below (low IQ group) and a second group included those who had a FCI of above 100 (high IQ group). The FCI is comparable to a Full Scale IQ score.
- Principal component analyses were used to replicate a previous study of the Wechsler Intelligence Scale for Children, Revised (Jensen, 2003). Confirmatory factor analyses using nested factor models were used to answer questions related to the changes in factor variances, subtest loadings on the g factor, and intercorrelations among broad ability factors. Results from the PCAs indicated that the law of diminishing returns was present in the KABC-II, although it was not produced uniformly across the subtests. Results from the CFAs indicated that higher g is associated with lower g variance, a depression of subtests’ g loadings, and lower intercorrelations between the broad ability factors. The law of diminishing returns was present in the KABC-II: g appears less general and more differentiated in a high IQ group compared to a low IQ group. This phenomenon was not produced uniformly across subtests, but it was also not produced only by the subtests with the weakest g loadings.
A small note on CHC and Flynn effect.
ReplyDeleteI have just read your co-authored 2000 book (The Wechsler Intelligence Scales and Gf Gc Theory, followed by a Flynn 2000 paper, "IQ gains, WISC subtests and fluid g: g theory and the relevance of Spearman's hypothesis to race" in The Nature of Intelligence.
Flynn looked at post-WW2 gains on 10 WISC subtests. Gains were generally higher on tests correlating with Raven's matrices, which he interpreted as an indicator of Gf, suggesting that since WW2, people have put more mental effort into developing Gf abilities than Gc abilities (whereas gains were across-the board pre-WW2).
The correlation between gains and his Gf indicator (namely, correlation with Raven's) is not very strong (he claims .4, I got .3, probably using a different measure), and it's influenced a lot by the scores for Block Design. But I wondered what it looked like on CHC. Using your Table 3.2, I took his results and found (hopefully this formats OK, it didn't allow the "pre" tag).
Subtest IQ Gain Raven's CHC broad
(WISC) (Avg) corr (avg) (Table 3.2)
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Similarities 19.75 .466 Gc
Block Design 14.70 .645 Gv
Picture Arr. 14.33 .515 (Gv, Gc)
Coding 11.30 .390 Gs
Object Assembly 10.32 .529 Gv
Picture Completion 9.75 .499 (Gv, Gc)
Comprehension 9.74 .418 Gc
Vocabulary 5.89 .551 Gc
Information 2.42 .389 Gc
Arithmetic -1.52 .443 Gq
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So, there it is.