When small effect sizes become huge: Synaesthesia is linked to very large differences in cognition.

Abstract

The replication crisis has taught us to expect small-to-medium effects in psychological research. But this is based on effect sizes calculated over single variables. Mahalanobis D, the multivariate equivalent of Cohen's d, can enable very large group differences to emerge from a collection of small-to-medium effects (here, reanalysing multivariate datasets from synaesthetes and controls). The use of multivariate effect sizes is not a slight of hand but may instead be a truer reflection of the degree of psychological differences between people that has been largely underappreciated.