How Much g Is in the Distractor? Re-Thinking Item-Analysis of Multiple-Choice Items

Abstract

Distractors might display discriminatory power with respect to the construct of interest (e.g., intelligence), which was shown in recent applications of nested logit models to the short-form of Raven’s progressive matrices and other reasoning tests. In this vein, a simulation study was carried out to examine two effect size measures (i.e., a variant of Cohen’s ω and the canonical correlation RCC) for their potential to detect distractors with ability-related discriminatory power. The simulation design was adopted to item selection scenarios relying on rather small sample sizes (e.g., N = 100 or N = 200). Both suggested effect size measures (Cohen’s ω only when based on two ability groups) yielded acceptable to conservative type-I-error rates, whereas, the canonical correlation outperformed Cohen’s ω in terms of empirical power. The simulation results further suggest that an effect size threshold of 0.30 is more appropriate as compared to more lenient (0.10) or stricter thresholds (0.50). The suggested item-analysis procedure is illustrated with an analysis of twelve Raven’s progressive matrices items in a sample of N = 499 participants. Finally, strategies for item selection for cognitive ability tests with the goal of scaling by means of nested logit models are discussed.