Draw the ANOVA interactive cases listed below (Figure 16.4 in the text). Name your dependent variable Y and assume that there are two factors, X1 with three levels (X11, X12, and X13 ), and X2 with two levels (X21 and X22 )

Briefly discuss/describe the interaction shown in each of your drawings.
1. no interaction
2. ordinal interaction
3. disordinal interaction (noncrossover)
4. disordinal interaction (crossover)

Refer to Figure 16.4 in the text for a picture of what the students should draw in response to this question and to follow the illustrative discussion given.

Case 1 depicts no interaction. The effects of X1 on Y are parallel over the two levels of X2. Although there is some departure from parallelism, this is not beyond what might be expected from chance. Parallelism implies that the net effect of X22 over X21 is the same across the three levels of X1. In the absence of interaction, the joint effect of X1 and X2 is simply the sum of their individual main effects.

Case 2 depicts an ordinal interaction. The line segments depicting the effects of X1 and X2 are not parallel. The difference between X22 and X21 increases as we move from X11 to X12 and from X12 to X13, but the rank order of the effects of X1 is the same over the two levels of X2.

Case 3 depicts disordinal interaction of a noncrossover type. The lowest effect of X1 at level X21 occurs at X11, and the rank order of effects is X11, X12, and X13. However, at level X22, the lowest effect of X1 occurs at X12, and the rank order is changed to X12, X11, X13. Because it involves a change in rank order, disordinal interaction is stronger than ordinal interaction.

Case 4 depicts disordinal interactions of a crossover type - the line segments cross each other. In this case, the relative effect of the levels of one factor changes with the levels of the other. Note that X22 has a greater effect than X21 when the levels of X1 are X11 and X12. When the level of X1 is X13, the situation is reversed, and X21 has a greater effect than X22. (Note that in cases 1, 2, and 3, X22 had a greater impact than X21 across all three levels of X1.) Hence, disordinal interactions of a crossover type represent the strongest interactions.