Mean Centering is Not Necessary in Regression Analyses, and Probably Increases the Risk of Incorrectly Interpreting Coefficients

Lee H. Wurm^*Miles Reitan

• Gonzaga University, Spokane, United States

Scholars trained in the use of factorial ANOVAs have increasingly begun using linear modelling techniques. When models contain interactions between continuous variables (or powers of them), it has long been argued that it is necessary to mean center prior to conducting the analysis. A review of the recommendations offered in statistical textbooks shows considerable disagreement, with some authors maintaining that centering is necessary, and others arguing that it is more trouble than it is worth. We also find errors in people's beliefs about how to interpret first-order regression coefficients in moderated regression. These coefficients do not index main effects, whether data have been centered or not, but mischaracterizing them is probably more likely after centering. In this study we review the recommendations, and then provide two demonstrations using ordinary least squares (OLS) regression models with continuous predictors. We show that mean centering has no effect on the numeric estimate, the confidence intervals, or the t-or p-values for main effects, interactions, or quadratic terms, provided one knows how to properly assess them. We also highlight some shortcomings of the standardized regression coefficient (beta), and note some advantages of the semipartial correlation coefficient (sr). We demonstrate that some aspects of conventional wisdom were probably never correct; other concerns have been removed by advances in computer precision. In OLS models with continuous predictors, mean centering might or might not aid interpretation, but it is not necessary. We close with practical recommendations.