In modern individual-difference studies, researchers often correlate performance on various tasks to uncover common latent processes. Yet, in some sense, the results have been disappointing as correlations among tasks that seemingly have processes in common are often low. A pressing question then is whether these attenuated correlations reflect statistical considerations, such as a lack of individual variability on tasks, or substantive considerations, such as that inhibition in different tasks is not a unified concept. One problem in addressing this question is that researchers aggregate performance across trials to tally individual-by-task scores. It is tempting to think that aggregation is fine and that everything comes out in the wash. But as shown here, this aggregation may greatly attenuate measures of effect size and correlation. We propose an alternative analysis of task performance that is based on accounting for trial-by-trial variability along with the covariation of individuals' performance across tasks. The implementation is through common hierarchical models, and this treatment rescues classical concepts of effect size, reliability, and correlation for studying individual differences with experimental tasks. Using recent data from Hedge et al. Behavioral Research Methods, 50(3), 1166-1186, 2018 we show that there is Bayes-factor support for a lack of correlation between the Stroop and flanker task. This support for a lack of correlation indicates a psychologically relevant result-Stroop and flanker inhibition are seemingly unrelated, contradicting unified concepts of inhibition.
Keywords: Bayesian inference; Hierarchical models; Individual differences; Inhibition; Reliability.