Spearman’s Law of Diminishing Returns (SLODR): Examining Effects at the Level of Prediction

Abstract

The current study presents the results of an incremental validity investigation using a hierarchical multiple regression design, examining standard score data from the standardization sample (N = 4,722) of the Woodcock-Johnson III Tests of Cognitive Abilities (WJ-III COG) and Achievement (WJ-III ACH). Specifically, this study examined whether or not the differentiation hypothesis known as Spearman's law of diminishing returns (SLODR) impacts the incremental predictive validity of the Cattell-Horn-Carroll (CHC) broad cluster scores on the WJ-III COG. Consistent with the SLODR hypothesis, differential patterns of prediction were observed across ability classes (e.g., Below Average, Average, Above Average). Specifically, the general factor score (GIA) accounted for significantly less portions of achievement variance in the Above Average group (R² = .11 to .20) when compared to estimates for the Below Average group (R² = .24 to .32). Secondary chi-square goodness of fit tests provided additional evidence of predictive variance across ability classes. The results of this study indicate that the effects of SLODR must be accounted for when interpreting the results of the contemporary cognitive ability tests in clinical settings.

Temporal stability of lower order ability scores and intelligence profiles in high ability students

“…The findings on SLODR have informed different kinds of analyses of ability-dependent differences in intelligence structure and ability profiles. While there is initial evidence supporting the increased incremental validity of specific ability scores McGill, 2015) and compelling evidence for an increased prevalence of highly diversified intelligence profiles (Lohman et al, 2008) with increased cognitive ability, the present study marks the first indication of greater profile stability in high ability individuals. The current investigation focused on adolescents.…”

“…Intelligence profiles were also found to be associated with stable academic interest profiles (Lubinski et al, 2001). Moreover, there is some evidence for greater incremental validity of specific ability scores beyond general intelligence for the explanation of academic achievement in high ability students than for average or low ability students McGill, 2015).…”

“…This finding implies that at least for the top 15% of the intelligence distribution, the interpretation of intelligence profiles may not be hindered by insufficient temporal stability of the scores. Evidence for the validity of intelligence profiles for individuals in this section of the ability distribution was provided by analyses of the incremental validity of specific ability scores McGill, 2015). Interpreting the ability profiles goes along with a modified use of the general intelligence score, as this score is no longer the only criteria for diagnostic decisions.…”

Spearman’s Law of Diminishing Returns: Investigation on Large-Scales Russian Samples

“…Продолжительность выполнения всех тестов ограничивалась, причем жесткость ограничения в ряде случаев превышала оптимальную для тестов такого уровня (van der Linden, 2011; Kyllonen, 2016); данный факт мог приводить к искусственному завышению коэффициентов ОМН для некоторых тестов. Разделение выборки пополам не позволяет установить характер связи между выраженностью эффектов SLODR и уровнем ОКС; она может быть как линейной, так и нелинейной (Lynn, 1992;McGill, 2015;Canali, 2016). Для получения ответов на эти вопросы необходимы дополнительные исследования.…”

Sources of Artifacts in SLODR Detection

“…As the SLODR e ect is not strong, it can be statistically con rmed only when large data samples are used. We have seen such very large samples in SLODR studies (for instance, Arden & Plomin, 2007;Breit, Brunner, & Preckel, 2020;Dombrowski, Canivez, & Watkins, 2018;Hartmann & Reuter, 2006;Hartung et al, 2018;McGill, 2015). Using large samples not only allows the researcher to obtain more statistically reliable results, but it also enhances the probability of the appearance of artifacts ( Korneev, Krichevets, & Ushakov, 2019).…”