Detecting Interaction Effects in Moderated Multiple Regression With Continuous Variables Power and Sample Size Considerations

TLDR

Detecting interactions among continuous variables in moderated multiple regression is notoriously difficult, so this article stresses careful consideration of moderator strength, error variation, and variable distribution when computing power and sample size for significance tests of moderating effects. The study aims to provide feasible solutions for power calculation and sample size determination in testing moderating effects in continuous‑variable regression. The authors present a unified framework that integrates moderator strength, error variation, and predictor/moderator distribution, and evaluate it alongside a simplified method through detailed numerical studies. Simulation results show that the recommended method achieves acceptable accuracy in assessing moderated relationships.

Abstract

In view of the long-recognized difficulties in detecting interactions among continuous variables in moderated multiple regression analysis, this article aims to address the problem by providing feasible solutions to power calculation and sample size determination for significance test of moderating effects. The proposed approach incorporates the essential factors of strength of moderator effect, magnitude of error variation, and distributional property of predictor and moderator variables into a unified framework. Accordingly, careful consideration across different plausible and practical configurations of the prescribed factors is an important aspect of power and sample size computations in planning moderated multiple regression research. The performance of the suggested procedure and an alternative simplified method is illustrated with detailed numerical studies. The simulation results demonstrate that an acceptable degree of accuracy can be obtained using the recommended method in assessing moderated relationships.