5.7 Take-Home Points

• In analysis of variance, we test the null hypothesis that all groups have the same population means. Behind the scenes, we actually test the ratio of between-groups variance to within-groups variance.

• The overall differences in average outcome scores between groups on one factor (independent variable) are a main effect in an analysis of variance.

• The differences in average outcome scores between subgroups, that is, groups that combine a level on one factor (predictor) and a level on another factor (moderator), represent an interaction effect. Note that we are dealing with the differences between subgroup scores that remain after the main effects have been removed.

• Moderation is the phenomenon that an effect is different in different contexts. The effect can be stronger or it can have a different direction. In analysis of variance, interaction effects represent moderation.

• Eta-squared measures the size of a main or interaction effect in analysis of variance. It tells us the proportion of variance in the dependent variable that is accounted for by the effect.

• A means plot is very helpful for interpreting and communicating results of an analysis of variance.

• The F tests in analysis of variance do not tell us which groups have different average scores on the dependent variable. To this end, we use independent-samples t tests as post-hoc tests with a (Bonferroni) correction for capitalization on chance.

• To apply analysis of variance, we need a numeric dependent variable that has equal population variance in each group of a factor or each subgroup in case of an interaction effect. However, equality of population variances is not important if all groups on a factor or all subgroups in an interaction are more or less of equal size (the largest count is at most 10% of the largest count larger than the smallest count.)