14.32 Ideology by gender and race Refer to Example 12, the sample means from which are shown again below (for 2008 data).

a. Explain how to obtain the following interpretation for the interaction from the sample means: “For females there is no race effect on ideology. For males, whites are more conservative by about half an ideology category, on the average.”

b. Suppose that instead of the two-way ANOVA, you performed a one-way ANOVA with gender as the predictor and a separate one-way ANOVA with race as the predictor. Suppose the ANOVA for gender does not show a significant effect. Explain how this could happen, even though the two-way ANOVA showed a gender effect for each race. (Hint: Will the overall sample means for females and males be more similar than they are for each race?)

c. Refer to part

b. Summarize what you would learn about the gender effect from a two-way ANOVA that you would fail to learn from a one-way ANOVA.

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Mean political Ideology Race Gender Black White Female 4.164 4.2675 Male 3.819 4.4443