Spurious Power Laws of Learning and Forgetting: Mathematical and Computational Analyses of Averaging Artifacts


It has frequently been claimed that learning performance improves with practice according to the so-called “Power Law of Learning”. Similarly, forgetting may follow a Power Law. It has been shown on the basis of extensive simulations that such Power Laws may emerge as artifacts through averaging functions with other shapes. Here, we present a mathematical analysis that power functions will indeed emerge as a result of averaging over exponential functions, if the distribution of learning rates follows a gamma distribution. Power Laws may, thus, arise as a result of data aggregation over subjects or items. Through a number of simulations we further investigate to what extent these findings may affect empirical results in practice. We conclude that spurious Power Laws will be more likely with large numbers of subjects and shorter time scales and with gamma distributions with much probability mass close to zero and with a not too low variance.

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