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.