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

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.