Why aggregated learning follows the power law of practice when individual learning does not: comment on Rickard (1997, 1999), Delaney et al. (1998), and Palmeri (1999).

Abstract

The power law of practice is often considered a benchmark test for theories of cognitive skill acquisition. Recently, P. F. Delaney, L. M. Reder, J. J. Staszewski, and F. E. Ritter (1998), T. J. Palmeri (1999), and T. C. Rickard (1997, 1999) have challenged its validity by showing that empirical data can systematically deviate from power-function fits. The main purpose of the present article is to extend their explanations in two ways. First, the authors empirically show that abrupt changes in performance are not necessarily based on a shift from algorithm to memory-based processing, but rather and more generally, that they occur whenever a more efficient task strategy is generated. Second, the authors show mathematically and per simulation that power functions can perfectly fit aggregated learning curves even when all underlying individual curves are discontinuous. Therefore, the authors question conclusions drawn from fits to aggregated data.