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I have data with two biological factors. The first factor has 2 levels (say, Alive vs. Dead) and the second factor has 80 levels (protein of interest). I'm only interested in whether the mean value differs between alive vs dead for each protein. That is, I'm interested in comparing Alive vs Dead for 80 pairwise comparisons.

Since I'm not interested in main effects - I don't care whether the mean differs between Alive and Dead for all proteins, and I don't care if the mean differs between proteins - is it acceptable/valid to run an ANOVA + post-hoc? Or should I just run 80 t-tests followed by multiple comparison correction?

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  • $\begingroup$ Is the experiment run in a way that assures the data are independent from one protein to the next? $\endgroup$
    – whuber
    Commented Jun 10, 2016 at 22:32
  • $\begingroup$ @whuber Yes, the data should be independent between proteins. $\endgroup$ Commented Jun 10, 2016 at 22:40
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    $\begingroup$ That eliminates any need to run ANOVA. In fact, ANOVA makes much more stringent assumptions (it assumes all residuals are homoscedastic) and precludes the ability to account for different variances between each pair of groups. But if you have reasons to believe the residuals should be homoscedastic, then ANOVA effectively "borrows strength" among all the groups to obtain a (much) more precise estimate of the residual variance. Depending on your experiment, your theory, and the results themselves, it's even possible to create some hybrid of the two approaches you suggest. $\endgroup$
    – whuber
    Commented Jun 10, 2016 at 22:46

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That sounds like an acceptable approach as long as you correct for multiple comparisons when running the 80 t-tests. However, a lot of times these conventions differ by area of research, so it might be worthwhile checking with someone in your area on how things are normally done.

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  • $\begingroup$ Since the analyses / relevant data appear to be independent of each other. Running 80 t-tests isn't different from running a single t-test in 80 different experiments (where no one would correct for multiple comparisons). As a result, it isn't clear correcting for multiple comparisons is necessary here, although assessing something like the false discovery rate might be of exploratory interest. $\endgroup$ Commented Apr 8, 2021 at 15:12

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