Toward an explanation of the power law artifact: Insights from response surface analysis

Abstract

The power law (y =ax −b) has been shown to provide a good description of data collected in a wide range of fields in psychology. R. B. Anderson and Tweney (1997) suggested that the model’s data-fitting success may in part be artifactual, caused by a number of factors, one of which is the use of improper data averaging methods. The present paper follows up on their work and explains causes of the power law artifact. A method for studying the geometric relations among responses generated by mathematical models is introduced that shows the artifact is a result of the combined contributions of three factors: arithmetic averaging of data that are generated from a nonlinear model in the presence of individual differences.

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Correspondence to In Jae Myung.

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This paper is based on a presentation at the thirty-first annual meeting of the Society for Mathematical Psychology in August 1998. This research was partly supported by NIMH Grant MH57472 to I.J.M. and M.A.P.

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Myung, I.J., Kim, C. & Pitt, M.A. Toward an explanation of the power law artifact: Insights from response surface analysis. Memory & Cognition 28, 832–840 (2000). https://doi.org/10.3758/BF03198418

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Keywords

  • Response Surface
  • Response Curve
  • Power Function
  • Retention Interval
  • Exponential Model