Two-Way ANOVA

Factorial ANOVAs (also called multifactorial ANOVAs), those with more than one independent variable (or factor), permit us to test more than one hypothesis in a single study. They also allow us to examine interactions between independent variables. Factorial ANOVAs are often named by referring to the levels of their independent variables (e.g., 2 × 2) rather than the number of independent variables (e.g., two-way). With a two-way ANOVA, we can examine two main effects (one for each independent variable) and one interaction (the way in which the two variables might work together to influence the dependent variable). Because we are examining three hypotheses, we calculate three sets of statistics for a two-way ANOVA.

Understanding Interactions in ANOVA

Researchers typically interpret interactions by examining the overall pattern of cell means. A cell is one condition in a study. We typically write the mean of a group in its cell. We write the marginal means for each row to the right of the cells and the marginal means for each column below the cells. If the main effect of one independent variable is stronger under certain conditions of the second independent variable, there is a quantitative interaction. If the direction of the main effect actually reverses under certain conditions of the second independent variable, there is a qualitative interaction.

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Conducting a Two-Way Between-Groups ANOVA

A two-way between-groups ANOVA uses the same six steps of hypothesis testing that we used previously, with minor changes. Because we test for two main effects and one interaction, each step is broken down into three parts. Specifically, we have three sets of hypotheses, three comparison distributions, three critical F values, three F statistics, and three conclusions. We use an expanded source table to aid in the calculations of the F statistics. We also calculate a measure of effect size, R², for each of the main effects and for the interaction.