Individual differences on speeded cognitive tasks: Comment on Chen,Hale, and Myerson (2007)

Chen, Hale, and Myerson (2007) recently reported a test of the difference engine model (Myerson, Hale, Zheng, Jenkins, & Widaman, 2003). This test evaluated whether the standard deviation (SD) is proportional to the amount of processing—that is, mean reaction time (RT)—in a speeded cognitive task. We show that this evaluation is not a test of the model because its finding is a consequence of relationships in the data. We argue any model structure that produces increasing values of RT as a function of difficulty, with different slopes for different individuals, necessarily produces a correlation between SD and mean RT. We illustrate this with a different model structure—that is, the diffusion model proposed by Ratcliff (1978)—showing that it produces a fan out between fast- and slow-group means and produces the correlation between SD and mean RT that matches the empirical result.