On the Standard Error of the Difference between Two Independent Regression Coefficients in Moderation Analysis: A Commentary on Robinson, Tomek, and Schumacker (2013)

Abstract

In this journal, Robinson, Tomek, and Schumacker (2013) argued that researchers interested in whether the regression coefficient for X in a model estimating Y from X differs between two groups should conduct two separate regressions rather than rely on moderated multiple regression (MMR). They advocate a standard error of the difference between coefficients they claim results in a more powerful test of moderation than MMR without affecting Type I error rate. We show analytically and demonstrate through simulation that, consistent with prior research, their standard error estimator results in substantial underestimation of the standard error and should not be used.