Some do and some don't? Accounting for variability of individual difference structures.

A prevailing notion in experimental psychology is that individuals' performance in a task varies gradually in a continuous fashion. In a Stroop task, for example, the true average effect may be 50 ms with a standard deviation of say 30 ms. In this case, some individuals will have greater effects than 50 ms, some will have smaller, and some are forecasted to have negative effects in sign-they respond faster to incongruent items than to congruent ones! But are there people who have a true negative effect in Stroop or any other task? We highlight three qualitatively different effects: negative effects, null effects, and positive effects. The main goal of this paper is to develop models that allow researchers to explore whether all three are present in a task: Do all individuals show a positive effect? Are there individuals with truly no effect? Are there any individuals with negative effects? We develop a family of Bayesian hierarchical models that capture a variety of these constraints. We apply this approach to Stroop interference experiments and a near-liminal priming experiment where the prime may be below and above threshold for different people. We show that most tasks people are quite alike-for example everyone has positive Stroop effects and nobody fails to Stroop or Stroops negatively. We also show a case that under very specific circumstances, we could entice some people to not Stroop at all.