higher order interaction
in an analysis of variance, the joint effect of three or more independent variables on the dependent variable. For example, a researcher could conduct a study to assess the effect of a particular treatment (e.g., treatment vs. no treatment) as well as the effect of education level and socioeconomic status on cognitive functioning. This design would allow an examination of the main effects for treatment, education, and socioeconomic status individually; the two-way interactions between treatment and education, education and socioeconomic status, and treatment and socioeconomic status; and the higher order three-way interaction between treatment, education, and socioeconomic status.