Spearmen's law of diminishing returns: the impact of the distribution asymmetry in artefact producing

Spearmen's law of diminishing returns (SLODR) is the hypothesis formulated in 1927 by Ch. Spearmen. It states that intercorrelations between intellectual tests are higher when the dataset contains subjects with less intellectual abilities (factor g score) and vice versa. After almost hundred years of researches only the trend in average was detected. Several works had shown also that test distribution asymmetry may lead to the artefactual appearance of SLODR effect but no systematic analysis of different sources of asymmetry was provided. The aim of our work is to check and to compare the real data set and two simulated sets with different sources of the asymmetry both of which does not present the real SLODR effect but only asymmetry, and the simulation set with SLODR effect. We used three methods of SLODR detection to test whether they can differentiate real and artefactual SLODR effect. The first simulates the asymmetrical choice of respondents with different ability test results. The second one simulates the case of different density of the tasks with different difficulty. We select the simulation parameters so that the simulated data correlation matrixes to be similar to one of the real data, and at the same time all distributions to have similar asymmetry parameters. The SLODR testing methods use the dividing a data sample into two subsamples by g factor median. Then we used so called traditional method comparing the g deviation in subsamples, the structural models comparing, the invariance testing in nested structural models (Reynolds et al, 2010), and the original method of 'Running Variance Estimate'. This method gives the one point estimate of the (1-r) for every 'participant' and so allows getting estimates of 1-r for any subsets of data set, not only for subset having got by median or any other dichotomy. So we can detect not only monotonic change of subtests intercorrelation, but also the nonmonotonic ones. We test the ability of such a detection simulating the dataset with such a property. The results in general demonstrate that all methods used can't differentiate real and artificial SLODR effect having got alone. The summary of all methods gives better result but it is also not complete. We think that this non-completeness is indispensable until sufficient psychometric properties (interval scales in terms of Stevens' typology) be provided. We think that the method of moderated factor analysis that had appeared in some more recent works (Molenaar et al, 2010) as a mean to avoid the problem can't give the essential effect and we hope to test the hypothesis in following research.

Keywords

Authors

References