Power Law of Practice

The Power Law of Practice states that the logarithm of the reaction time for a particular task decreases linearly with the logarithm of the number of practice trials taken. It is an example of the learning curve effect on performance. It was first proposed as a psychological law by Newell & Rosenbloom (1981). Delaney et al. (1998) showed that the power law fit better than an exponential if the analysis was performed across strategies, for a mental arithmetic task.

However, subsequent research by Heathcote, Brown, and Mewhort (2000) suggests that the power function observed in learning curves that are averaged across participants is an artifact of aggregation. Heathcote et al. suggest that individual-level data is better fit by an exponential function and the authors demonstrate that the multiple exponential curves will average to produce a curve that is misleadingly well fit by a power function.

Power function:

RT = aP^-b + c

Exponential function:

RT = ae^-b(P-1) + c

Where

RT = Trial Completion Time

P = Trial Number, starting from 1 (for exponential functions the P-1 argument is used)

a, b, and c, are constants

References

Newell, A., & Rosenbloom, P. S. (1981). Mechanisms of skill acquisition and the law of practice. In J. R. Anderson (Ed.), Cognitive skills and their acquisition (pp. 1-55). Hillsdale, NJ: Erlbaum. ISBN 0898590930

Delaney, P. F., Reder, L. M., Staszewski, J. J., & Ritter, F. E. (1998). The strategy specific nature of improvement: The power law applies by strategy within task. Psychological Science, 9(1), 1-8.

Heathcote, A., Brown, S., & Mewhort, D. J. K. (2000). The power law repealed: The case for an exponential law of practice. Psychonomic Bulletin & Review, 7(2), 185-207.