# In mixed three-way ANOVA, how to interpret the 2-way interaction when there is no 3-way interaction?

I'm doing a mixed three-way repeated measures ANOVA. I have a significant two-way interaction A:B (with no significant three-way interaction).

My between factor is A (3 levels) and within factors are B (2 levels) and C (2 levels).

  Effect DFn DFd     F    p  p<.05     ges
1 A       2  31 3.975 0.029     * 0.108000
2 C       1  31 1.824 0.187       0.011000
3 B       1  31 7.297 0.011     * 0.017000
4 A:C     2  31 0.926 0.407       0.011000
5 A:B     2  31 3.800 0.033     * 0.018000
6 C:B     1  31 0.039 0.845       0.000332
7 A:C:B   2  31 0.624 0.542       0.011000


So C doesn't matter for the AxB effect, right?

My first question is what's the next step.

If the next step is to run a two-way ANOVA with factor A and factor B, what's the response variable? Since I have both values in C1 and C2. Which should I choose? Run them both or use the mean of values in C1 and C2?

I tried to use the mean value of C1 and C2 and it gave me the same P-value and it looks nice.

 Effect DFn DFd   F     p p<.05 ges
1 A     2  31 3.979 0.029     * 0.181
2 B     1  31 7.289 0.011     * 0.031
3 A:B   2  31 3.799 0.033     * 0.033


But is this the right way?

I appreciate it if you can share your own experience with interpreting 3-way ANOVA. Thanks!