SECTION 15.1 Summary

• Two-way analysis of variance (ANOVA) is used to compare population means when populations are classified according to two factors. ANOVA assumes that the populations are Normal and that independent SRSs are drawn from each population. The populations may have different means, but they all have the same standard deviation.
• Marginal means are calculated by taking averages of the group means, when organized in a two-way table, either across rows or down columns. These means can be used in an interaction plot to aid in the interpretation of the results.
• ANOVA separates the total variation into parts for the model and error. Pooling is used to estimate the error, or within-group variance. The model variation is separated into parts for each of the main effects and the interaction. We describe main effects by the differences between marginal means. An interaction is present if the main effects provide an incomplete description of the group means.