CHAPTER 13 SUMMARY

• • Two-way analysis of variance (ANOVA) is used to compare population means when populations are classified according to two factors.

• • We assume that independent SRSs are drawn from each population and that the responses from each population are Normal with possibly different means but the same standard deviation.

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• • As with one-way ANOVA, these assumptions should be assessed. Preliminary analysis includes examination of means, standard deviations, residual plots, and Normal quantile plots.

• • Marginal means are calculated by taking averages of the cell means, either across rows or down columns. These means can be used in an interaction plot to aid in the interpretation of results.

• • Similar to one-way ANOVA, the total variation is separated into parts for the model and error. Pooling is also used to estimate the error, or within-group variance. However, given that there are now two factors, the model variation is separated into parts for each of the main effects and the interaction.

• • The calculations are organized into an ANOVA table. F statistics and P-values are used to test hypotheses about the main effects and the interaction.

• • Careful inspection of the means is necessary to interpret significant main effects and interactions. Plots are a useful aid.