1
$\begingroup$

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!

$\endgroup$
0
1
$\begingroup$

Maybe you could get some information by 'collapsing' the design, but there are disadvantages:

  • You are not analyzing the experiment you actually performed. In any report of findings you'd have to admit and justify collapsing the design.

  • It could be that interaction and A effect are 'explaining' some of the variability---even if not significant. In that case error variance in the original full model might be smaller than error variance in the collapsed one, giving you a bit more power to detect any real differences among levels of factor B.

  • What now appear to be 'replications' within levels of factor B are not necessarily anything like iid. If you do use a collapsed design, you'd have to take a careful look at its residuals.

My preference: Do ad hoc exploration of the original model via contrasts.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.