Assessing bimodality to detect the presence of a dual cognitive process

Researchers have long sought to distinguish between single-process and dual-process cognitive phenomena, using responses such as reaction times and, more recently, hand movements. Analysis of a response distribution's modality has been crucial in detecting the presence of dual processes, because they tend to introduce bimodal features. Rarely, however, have bimodality measures been systematically evaluated. We carried out tests of readily available bimodality measures that any researcher may easily employ: the bimodality coefficient (BC), Hartigan's dip statistic (HDS), and the difference in Akaike's information criterion between one-component and two-component distribution models (AIC(diff)). We simulated distributions containing two response populations and examined the influences of (1) the distances between populations, (2) proportions of responses, (3) the amount of positive skew present, and (4) sample size. Distance always had a stronger effect than did proportion, and the effects of proportion greatly differed across the measures. Skew biased the measures by increasing bimodality detection, in some cases leading to anomalous interactive effects. BC and HDS were generally convergent, but a number of important discrepancies were found. AIC(diff) was extremely sensitive to bimodality and identified nearly all distributions as bimodal. However, all measures served to detect the presence of bimodality in comparison to unimodal simulations. We provide a validation with experimental data, discuss methodological and theoretical implications, and make recommendations regarding the choice of analysis.