Spearman’s “Law of Diminishing Returns” and the role of test reliability investigated in a large sample of Danish military draftees

Abstract

The present article investigates Spearman’s “Law of Diminishing Returns” (SLODR), which hypothesizes that the g saturation for cognitive tests is lower for high ability subjects than for low ability subjects. This hypothesis was tested in a large sample of Danish military draftees ( N = 6757) who were representative of the young adult male population, aged 18–19, and tested with a group-administered intelligence test comprised of four subtests. The aim of the study was twofold. The first was to reproduce previous SLODR findings by the present authors. This was done by replicating the methodology applied in the previous study and generally applied in the study of SLODR, i.e. by dividing the subjects into High and Low ability groups while ensuring equal SDs for the four subtests. For both groups independently, the average inter-correlation and the total eigenvalue of the first principal component (PC1) were calculated as an estimate for g saturation. Support was again found for the opposite effect of Spearman’s “Law of Diminishing Returns”, a higher g saturation was found for the High ability group than for the Low ability group. The second aim was to investigate whether differences in reliability could account for the difference in g saturation across ability groups. The results showed that the reliability was larger for the High ability group, thereby not explaining the present findings.