The power law repealed: The case for an exponential law of practice

Abstract

The power function is treated as the law relating response time to practice trials. However, the evidence for a power law is flawed, because it is based on averaged data. We report a survey that assessed the form of the practice function for individual learners and learning conditions in paradigms that have shaped theories of skill acquisition. We fit power and exponential functions to 40 sets of data representing 7,910 learning series from 475 subjects in 24 experiments. The exponential function fit better than the power function in all the unaveraged data sets. Averaging produced a bias in favor of the power function. A new practice function based on the exponential, the APEX function, fit better than a power function with an extra, preexperimental practice parameter. Clearly, the best candidate for the law of practice is the exponential or APEX function, not the generally accepted power function. The theoretical implications are discussed.

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Correspondence to Andrew Heathcote.

Additional information

We acknowledge financial assistance from Australian Research Council Grant 42/280/022 to R. Heath and A.H., a University of Newcastle Research Management Committee grant to A.H., and grants from the Natural Science and Engineering Research Council of Canada to D.J.K.M. Thanks to everyone who contributed data to the survey and to reviewers of a previous version of this paper, including J. R. Anderson, W. Estes, G. Logan, R. D. Luce, T. Rickard, and J. Wixted.

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Heathcote, A., Brown, S. & Mewhort, D.J.K. The power law repealed: The case for an exponential law of practice. Psychonomic Bulletin & Review 7, 185–207 (2000). https://doi.org/10.3758/BF03212979

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Keywords

  • Exponential Function
  • Power Function
  • Learning Rate
  • Journal ofExperimental Psychology
  • Mental Rotation