# Factor Levels in a Two-Way ANOVA

I'm trying to figure out the explanations of the Effect Plots below. I believe I have figures out Figure 9a, but the explanation for Figures b, c, and d given in the textbook I do not comprehend.

Any further detail would be greatly appreciated. Figure 9(a) shows that the means for Factor $$A$$ are equal (because the three dots are on the same horizontal line), but the response differs for the two levels of Factor $$B$$ (because the lines are one above the other). Thus, there is no effect of Factor $$A$$ on the response, but a Factor $$B$$ main effect is present. In Figure 9(b), the Factor $$A$$ means differ, but the Factor $$B$$ means are equal at each level of Factor $$A$$ (WHY?????). Here a Factor $$A$$ main effect is present, but no effect of Factor $$B$$ is present. Figure 9(c) and Figure 9(d) illustrate cases in which both factors affect the response. In Figure 9(c), the mean response between levels of Factor $$A$$ does not change for the three levels, so the effect of Factor $$A$$ on the response is independent of Factor $$B$$. That is, the two factors do not interact. In contrast, Figure 9(d) shows that the differences between mean distances between levels of Factor $$B$$ varies with the levels of Factor $$A$$. Thus, the effect of Factor $$A$$ on the response depends on the levels of Factor $$B$$, and the two factors do interact.