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 b e artifactual, caused by a number of factors, one of which is the use of im proper data averaging methods. The present paper follows up on their work a nd explains causes of the power law artifact. A method for studying the geo metric relations among responses generated by mathematical models is introd uced that shows the artifact is a result of the combined contributions of t hree factors: arithmetic averaging of data that are generated from a nonlin ear model in the presence of individual differences.