Contrasts in two-way ANOVA: A simple approach to formulating contrasts in two-way (and higher-way) ANOVA is first to specify contrasts separately for each set of main effects, obtaining interaction...

Contrasts in two-way ANOVA: A simple approach to formulating contrasts in two-way (and higher-way) ANOVA is first to specify contrasts separately for each set of main effects, obtaining interaction contrasts by forming all pairwise products of the main-effect contrasts. Then, as long as the main-effect contrasts satisfy the rules (on page 193), the interaction contrasts will as well. Imagine, for example, a 3
2 classification arising from an experiment in which the first factor consists of a control group (R₁) and two experimental groups (R2 and R3). The second factor is, say, gender, with categories male (C₁) and female (C₂). A possible set of main-effect contrasts for this experiment is

The following table shows the full set of main-effect and interaction contrasts for all six cells of the design (with the parameter for each contrast in parentheses):