Paired Sample t-tests do not link up with the Repeated-Measures ANOVA


I'm currently writing up my results section for my dissertation that's looking at the nocebo effect. I'm using a repeated-measures ANOVA that has three factors each with two levels, synchronicity (synchronous vs. asynchronous), phase (pre-conditioning vs. post-conditioning), and treatment (hyperalgesic vs. control). The dependent variable I'm looking at is Unpleasantness, and I found a significant synchronicity by phase interaction, with the asynchronous condition having a higher unpleasantness ratings than synchronous on the pre-conditioning phase, with this falling drastically on the post-conditioning phase, where as it rises slightly on the synchronous condition. I decided to conduct a paired-samples t-test on this using syncronous pre-conditioning vs. asynchronous pre-conditioning/synchronous post-conditioning vs. asynchronous post-conditioning and synchronous pre-conditioning vs. synchronous post-conditioning/ asynchronous pre-conditioning vs. asynchronous post-conditioning. However, none of these results are significant, and while I know this is possible, I don't exactly know what it means.

I'm currently trying to work out why there is a significant interaction if the t-tests show that there is nothing going on. I've attempted to factor in the treatment in the tests and found that it is the pre-conditioning control site for asynchronous that is significant only, this would also mean that I had a three-way interaction right? What I've been thinking is that the reason these t-tests don't support the interaction is because treatment is also necessary to cause a difference, but once more I just keep thinking that this would also mean that I would get a three-way interaction.

Could anyone help explain possibilities as to how this can happen? I hope I've explained it properly. Just let me know if you need more information.

Thanks a lot!!
Hi Znahouli1, I think you explained it pretty clearly -- although I'm not sure I understand the part where you explain which t-tests you performed, that part gets a little confusing

Sometimes, tests disagree

For example -- many PROCs in SAS give Wald-test confidence intervals and LRT p-values as defaults, and I've seen these disagree when significance is close to borderline

In your case, based on what you've said, I think I'd stick with the ANOVA results since that accounts for more information. If I'm understanding things here correctly, I think you've run into a common predicament -- you're now faced with trying to explain why two statistical tests gave different results, which isn't necessarily easy at all. Best never to let yourself get into that situation, i think.


TS Contributor
There is actually a fairly simple explanation. See the attached files for an extreme example using created data.

This example shows a strong interaction between two factors with no main effect. Obviously, from the interaction plot both A and B have an actual effect. But, when calculating the means for each level for each factor, we find the the means are equal. This may occur for one or the other factor or both.

This is why the main factors involved in an interaction should be retained in the model.

It also why Ellis Ott said "Plot the data!"