# How to confirm a two-way interaction in a three-way ANOVA model using SPSS

I have two groups of subjects, both undergoing two experimental conditions, and data are collected at two time points: pre- and post- condition.

I run a 3-way ANOVA, with one between subject factor (group) and two within subject factors (condition and time). The analysis does not find a three-way interaction, but there is a group x condition interaction.

My question is: How to run a two-way ANOVA for the group x condition interaction? If the interaction is condition x time, then I can pool all the subjects into one group and run a two-way ANOVA (condition, time). But for a group x condition interaction, I don't know how to do that because time is a within group factor.

(I am using SPSS)

In your 3-way ANOVA with one between-subjects factor (group) and two within-subject factors (condition and time), you have already shown that the interaction of group x condition is statistically significant. I don't understand why you would want to run a separate two-way ANOVA again because such an analysis would essentially give you exactly the same result.

To confirm such an equivalence yourself, you may try the following two approaches:

1) Obtain for each subject the average value between the two time points for each condition, and then run 2 x 2 mixed ANOVA (one between- and one within-subject factor).

2) With a 2 x 2 mixed ANOVA, the group x condition interaction is basically a Student t-test. You can get the difference between the two average values above in 1) (one for each condition) for each subject, and then run a two-sample t-test on the condition difference. In other words, the group x condition interaction shows the group difference of the condition difference.

Furthermore, to tease apart the specifics of the interaction, you can do the following:

(a) Run 2 two-sample t-tests, one on the average value for each condition; Or perform 2 paired t-tests for each group on the average values for the two conditions.

(b) Run 4 one-sample t-tests, one on the average value for each condition within each group.

With these tests you can use plots as shown on this page to understand the interaction.