Hello all,
I am trying to do analyses of gene expression microarray data and have a result that I don't understand. I'm hoping someone here might be able to shed light on the problem. The experiment is a 2x2 factorial (say factors A and B). When I analyze the data to identify those genes that show differences based on the analysis of a 2x2 factorial ANOVA (with or without shrinkage), I find only factor A has any genes that are significant after adjusting for multiple comparisons using the FDR. I looked at the histograms of the three tests (page 1 of attachment) and was surprised to see that distribution of the p-value for the interaction was shifted towards large p-values. I have checked my code and had others check my code with no mistakes found. I have checked for potential problems with normalization and did not find anything. I then looked at the p-value histograms by comparing treatments pairwise and excluding the arrays not of "interest" (attachment page2) When I do this, I get a result that seems to contradict the results from the ANOVA. The comparison of A1 vs A2, given either B1 or B2 shows evidence for a large number of differences. The comparison of B1 vs B2 only shows evidence for differences given A2. While multiple testing and problems in variance estimation will make the latter analysis not exactly correct, the second analysis seems to me to suggest that there are interactions here. How can these results be reconciled? Are there interaction effects here or not? Why is there an apparent contradiction? Any help will be greatly appreciated
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Robert Podolsky
Georgia Health Sciences University
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