Refer to Example 12, the sample means from which are shown again below.

a. Explain how to obtain the following interpretation for the interaction from the sample means: €œFor 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.
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