Two-way ANOVA

Interpreting the Interaction using Post-Hoc Tests

ANOVA only tells us if the overall influnce of the IV is significant. Not where. We use post hoc tests (after the fact) tests to examine where the differences lie. We will used Tukey's HSD like we did before.

In the ANOVA dialog panel fined the Post hoc label and select it to open the post hoc dialog.

 

In the dialog, move the two main effects (Attractiveness and Commitment) and the interaction (Attractiveness*Commitment) from the box on the left to the box on the right. It should appear like below.

Note that Tukey is selected. Also, since this is a 2x2 Factorial Design you do not need to do the post-hoc on the main effects since there is only two levels, but if you have more than two levels on any IV you will want to do then post hoc on that IV.

We are most concerned with the interaction where the effect of one indendent variable on the dependent varialbe is different dependent on the level of the other indepdent variable. From our graph, we thought we saw the following pattern of effects.

• High-commitment: High = Low Attractive Target
• Low-commitment: High > Low Attractive Target

The Pairwise Comparisons table gives us this information:

Not the easiest table to read, but every possible condition is compared. Then first column indicates then first condition in the compareisin and then the secod column has then second condition. We see the simple effect of attractiveness for low-commitment subjects: high-attractive targets are rated 2.526 points higher than low-attractive targets, which is significant at p < .001 (that’s what the “.000” means under the “Sig.” column). In the top two rows, we see that the simple effect of attractiveness for high-commitment subjects is not significant (p = .131).

Putting it all together, we can write up the results of our analysis like so (new parts in bold font):

Partner ratings were analyzed with a 2 (Attractiveness: Low versus High) x 2 (Commitment: Low versus High) between-subjects ANOVA. The main effect of attractiveness on partner ratings was significant, F(1,196) = 5.74, p = .018. The main effect of commitment on partner ratings was also significant, F(1,196) = 13.19, p <.001. These main effects were qualified by a significant interaction between attractiveness and commitment, F(1,196) = 20.63, p < .001. Tukey post hoc comparisons indicated that, as hypothesized, low-commitment subjects rated the high-attractive partner 2.53 points higher than the low-attractive partner (p < .001, 95% CI of the difference = 1.51 to 3.54). In contrast, ratings of high- and low-attractiveness targets did not significantly differ for high-commitment subjects (p = 0.131).

Some observations on that description:

1. I got the 2.53-point difference from the Pairwise Comparisons results. The 95% confidence interval came from the same table under the "Lower Bound" and "Upper Bound" columns.
2. If a simple effect is significant, you need to report the p-value and describe the pattern of the effect: which mean was higher than which other mean?
3. When you report a difference (e.g., 2.53 points), you should also report the 95% confidence interval so that the reader understands the precision of your estimate.
4. If a simple effect is not significant, you do not need to describe the pattern or report the confidence interval, but you should report the p-value.