Form, effect size and power in moderated regression analysis

This paper presents the results of a simulation study designed to show how a moderator variable affects the form of the relationship between two other variables. Particular attention is paid to the relationship of the strength of a moderator to statistical significance and the magnitude of the increment in R2 associated with the moderator. The increment in R2 is viewed as an incomplete measure of the strength of moderator effects. We propose a standardized measure of the strength of moderator effects based on the rate of change in the slope of the regression surface. The relation of sample size and statistical power to this measure is investigated.