Theories of automaticity and the power law of practice

In a recent reanalysis of numerosity judgment data from T. J. Palmeri (1997 ), T. C. Rickard (1999) found that mean response times did not decrease as a pure power law of practice and standard deviations systematically increas ed and then decreased with practice in some conditions. Rickard argued that these results were consistent with the component power laws (CMPL) theory of strategy shifting (Rickard, 1997), but were inconsistent with instance t heory (G. D. Logan, 1988) and the exemplar-based random walk (EBRW) model ( R. M. Nosofsky & Palmeri, 1997). In this article, the author demonstrates h ow a slightly more complex power function fitted the numerosity data nearly as well as the CMPL function, and how race models, such as instance theory and the EBRW, can predict deviations from a pure power law of practice and can predict nonmonotonic changes in standard deviations with practice. Pot ential limitations of CMPL are also discussed.