I want to analyze the results of an experiment that was conducted as a 3 X 3 balanced, repeated measures study. There are two factors in my design--let's call them Factor A and Factor B. Both factors have three levels.
Factor A is the central factor being investigated in the study, and I am most interested in testing whether there are significant differences between the three levels in Factor A.
The main reason that I am including Factor B in my experimental design is because it is known (from previous studies) to have a significant effect on my response variable--for this reason, it wouldn't make sense to run a repeated measures study without including it as a factor. While we'd like to consider and report on the effects of Factor B, it isn't the central factor that we're investigating.
I decided to run a two-way repeated measures ANOVA on my data, and determined the following:
- There was no significant interaction effect between Factor A and Factor B.
- Factor B had a significant effect on my response variable (as expected, and indeed, this is why we bothered to include it as a factor in the first place).
- Factor A did not have a significant effect on my response variable.
Since there were no interaction effects between the two factors, I'm under the impression that I could proceed to run one-way ANOVAs on Factor B to better understand its simple main effects. However, this isn't the central focus of our study (and, again, has already been done in other studies).
The question that I have, is whether I can proceed to do any additional statistical analysis on Factor A, the factor that our investigation is most interested in? The two-way ANOVA has shown it to be insignificant--is that all I can report about it?
The idea that I had was to decompose the two-way repeated measures ANOVA into three separate one-way repeated measures ANOVA that would test the effect of Factor A within each level of Factor B. However, I don't know whether this is allowed or even valuable/meaningful.
If anyone has any insights into how to tackle this analysis, that would be helpful. Thanks!