Chapter 5 Moderation with Analysis of Variance (ANOVA)
Key concepts: eta-squared, between-groups variance, within-groups variance, F test on analysis of variance model, pairwise comparisons, post-hoc tests, one-way analysis of variance, two-way analysis of variance, balanced design, main effects, moderation, interaction effect.
Watch this micro lecture on moderation with analysis of variance for an overview of the chapter.
Summary
Imagine an experiment in which participants watch a video promoting a charity. They see George Clooney, Angelina Jolie, or no celebrity endorse the charity’s fund-raiser. Afterwards, their willingness to donate to the charity is measured. Which campaign works best, that is, produces highest average willingness to donate? Or does one campaign work better for a specific gender? This study only compares the genders ‘male’ and ‘female’.
In this example, we want to compare the outcome scores (average willingness to donate) across more than two groups (participants who saw Clooney, Jolie, or no celebrity). To this end, we use analysis of variance. The null hypothesis tested in analysis of variance states that all groups have the same average outcome score in the population.
This null hypothesis is similar to the one we test in an independent-samples t test for two groups. With three or more groups, we must use the variance of the group means (between-groups variance) to test the null hypothesis. If the between-groups variance is zero, all group means are equal.
In addition to between-groups variance, we have to take into account the variance of outcome scores within groups (within-groups variance). Within-groups variance is related to the fact that we may obtain different group means even if we draw random samples from populations with the same means. The ratio of between-groups variance over within-groups variance gives us the F test statistic, which has an F distribution.
Differences in average outcome scores for groups on one independent variable (usually called factor in analysis of variance) are called a main effect. A main effect represents an overall or average effect of a factor. If we have only one factor in our model, for instance, the endorser of the fund-raiser, we apply a one-way analysis of variance. With two factors, we have a two-way analysis of variance, and so on.
With two or more factors, we can have interaction effects in addition to main effects. An interaction effect is the joint effect of two or more factors on the dependent variable. An interaction effect is best understood as different effects of one factor across different groups on another factor. For example, Clooney may increase willingness to donate among females but Jolie works best for males.
The phenomenon that a variable can have different effects for different groups on another variable is called moderation. We usually think of one factor as the predictor (or independent variable) and the other factor as the moderator. The moderator (e.g., sex) changes the effect of the predictor (e.g., celebrity endorser) on the dependent variable (e.g., willingness to donate).