Chapter 11 Factorial ANOVA Interaction

Chapter 11 Factorial ANOVA

Interaction

What is an Interaction Effect?  In factorial ANOVAs the total variance is partitioned into main effects, interaction effects, and error.  The main effects are associated with the levels of the independent variables.  The interaction effects are associated with any changes that occur to the dependent variable due to differential effects of combinations of the independent variables.

Factorial ANOVA  In a two-way ANOVA • • • •

Main effect for variable A, Main effect for variable B, Interaction, and Error Female

 Three F tests available: • Factor A, • Factor B, • Interaction

Male

Placebo

Drug

Interactions in Factorial ANOVAs  Increasingly complex as the number of main effects and interaction effects become more numerous.  For example, in a four-way ANOVA there may be 15 F-tests available: • • • •

Main effects for variable A, B, C, D, Double interactions for AB, AC, AD, BC, BD, and CD, Triple interactions for ABC, ABD, BCD, and ACD Quadruple interaction for ABCD

 Interpretation of results becomes increasing difficult?

Example of Interaction The mood enhancing drug worked significantly better for females than for males. There is a significant interaction effect.

Mood Scale

Females

Males

Placebo

Drug