Form, effect size and power in moderated regression analysis

TLDR

The study focuses on how moderator strength relates to statistical significance and the increase in R², noting that R² alone inadequately captures moderator effects. The paper simulates how a moderator alters the form of a relationship and proposes a standardized measure of moderator strength based on slope change. The authors develop a standardized moderator strength metric from slope change and examine how sample size and power affect it. Simulation results show that a moderator changes the relationship form between two variables.

Abstract

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 R 2 associated with the moderator. The increment in R 2 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.