Section 12.4 Summary

1. In two-way ANOVA, we are interested in testing for the significance of two factors. There is interaction between the two factors of a two-way ANOVA if the effect of one factor depends on the level of the other factor. If the two factors have substantial interaction, then we will not be able to safely draw conclusions regarding either of the factors. An interaction plot is a graphical representation of the cell means for each cell in the contingency table.
2. Two-way ANOVA actually involves a series of three hypothesis tests: (a) test for interaction between the factors, (b) test for Factor A effect, and (c) test for Factor B effect. If interaction exists between the factors, then it becomes problematical to try to draw conclusions about the main effects. Therefore, if the test for interaction concludes that interaction is present, then we do not proceed to perform the test for either Factor A or Factor B.