Illuminating Statistical Analysis Using Scenarios and Simulations

35Two-Way Means and Variance Ratios: ANOVA

The previous chapter dealt with one-way ANOVA, also called single-factor ANOVA. Two-way ANOVA is a powerful extension that allows you to assess scaled data across two factors (two nominal variables). Further, as we'll see, it detects possible interactions between the two factors. The two factors can have any number of categories, but we'll look at the simplest case where each factor has only two categories. The basic layout is shown in Table 35.1. The inner four cells give the sample means for the subgroups of DM, DF, RM and RF.

Table 35.1 Scenario layout.

Males	Females
Democrat	DM mean	DF mean	Overall D mean
Republican	RM mean	RF mean	Overall R mean
Overall M mean	Overall F mean	Grand mean

Say, that a survey was conducted and respondents indicated how closely they follow politics on a 1–7 scale. Overall differences across political affiliations (D&R) can be assessed using the rightmost column and the overall differences across sexes (M&F) can be assessed using the bottom row. These are called the two main effects. Further, we can detect possible interaction effects between the two factors by looking for patterns in the inner cells. In particular, we can look to see whether DM mean minus DF mean is different from RM mean minus RF mean.

Study Tables 35.2–35.7, which are hypothetical scenarios to clearly show you the various types of statistical situations. Assume the sample sizes are large enough and the sample variances ...