Tests of Moderation Effects: Difference in Simple Slopes versus the Interaction Term

TLDR

In regression models, the difference between the slopes of X for two groups equals the interaction coefficient b₃, which appears in Equation 1. After detecting a significant interaction, the researcher splits the data by group and fits separate regressions of Y on X to assess group‑specific slopes. A significant interaction coefficient b₃ indicates that the slopes of X differ between groups, confirming a moderated relationship between X and Y.

Abstract

(3b) Within Equations 2b and 3b, the slopes of X for Groups 1 and 2 are b1 and (b1 + b3), respectively. The difference in the two slopes is (b1 + b3) - b1 = b3; the coefficient of the interaction term XZ in Equation 1. Therefore, if the results of the regression model in Equation 1 indicate that the interaction term, b3, is significant, then the slopes of X for Groups 1 and 2 (Z) are statistically different from each other, indicating a statistically significant moderated relationship between X and Y. Once a significant moderated relationship has been identified, a researcher can examine the strength of relationships between X and Y within the individual groups of Z. To accomplish this, data are separated by group and then individual regression equations are estimated with X regressed on Y. These are termed the M