APA Dictionary of Psychology

in a three-way analysis of variance, the joint effect of all three independent variables, a, b, and c, on a dependent variable. A statistically significant three-way interaction indicates that one or more of the three possible two-way interactions (a × b, a × c, and b × c) differ across the levels of a third variable. For example, the a × b interaction may differ for one level of c compared to another level of c. A three-way interaction is a type of higher order interaction.