Sources of Artifacts in SLODR Detection

Abstract

Background

Spearman’s law of diminishing returns (SLODR) states that intercorrelations between scores on tests of intellectual abilities were higher when the data set was comprised of subjects with lower intellectual abilities and vice versa. After almost a hundred years of research, this trend has only been detected on average.

Objective

To determine whether the very different results were obtained due to variations in scaling and the selection of subjects.

Design

We used three methods for SLODR detection based on moderated factor analysis (MFCA) to test real data and three sets of simulated data. Of the latter group, the first one simulated a real SLODR effect. The second one simulated the case of a different density of tasks of varying difficulty; it did not have a real SLODR effect. The third one simulated a skewed selection of respondents with different abilities and also did not have a real SLODR effect. We selected the simulation parameters so that the correlation matrix of the simulated data was similar to the matrix created from the real data, and all distributions had similar skewness parameters (about –0.3).

Results

The results of MFCA are contradictory and we cannot clearly distinguish by this method the dataset with real SLODR from datasets with similar correlation structure and skewness, but without a real SLODR effect. The results allow us to conclude that when effects like SLODR are very subtle and can be identified only with a large sample, then features of the psychometric scale become very important, because small variations of scale metrics may lead either to masking of real SLODR or to false identification of SLODR.