Moderation (interaction, simple slopes)

A moderation asks whether the relationship between X and Y depends on a third variable W (the moderator). Statable centers X and W at the mean, forms the product X·W and runs a regression with this interaction term. If it is significant, the slope of X depends on W. The simple slopes show it at low (mean − 1 SD), medium and high W (mean + 1 SD); ΔR² is the gain in explained variance due to the interaction. Johnson-Neyman gives the values of W from which the slope becomes significant.

Example: Interaction: B = 1.73, 95% CI [1.19, 2.28], p < .001, ΔR² = .17: under low strain, more support is barely related to higher scores (b = 0.01); under high strain, clearly (b = 4.20).

Caution: Because of the centering, the coefficients of X and W are conditional effects at the mean of the other variable; the interaction itself does not change. Simple slopes outside the observed range of W are extrapolation. Interactions need many people to be detected.