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I want to compare multivariate gene expression data (1000s of genes) from two different conditions. I have three samples from each condition and the samples were collected in pairs on three different occasions. Although the "paired" samples are from different individuals, PCA shows that there is a strong batch effect (stronger than the experimental effect, which corresponds to PC2) and so I believe paired t-tests (with a false discovery rate correction) are preferable in this case. However, I've been queried twice on this by other biologists and so want to get a statistician's opinion. Should/could I be doing an ANOVA or batch effect correction instead?

(In regards to the small sample size, the aim of this type of experiment is not so much to determine whether there is a difference between the two conditions overall - there certainly is, even if we don't detect it - but to identify which, if any, of the genes are differentially expressed between conditions and merit further investigation in targeted experiments.)

Edit - A related question: if the paired t-test is appropriate, is this sufficient correction for batch effects or should/could the data be adjusted prior to testing? Sometimes gene expression data is adjusted for unwanted variation using methods based on factor analysis prior to hypothesis testing, but I'm not sure it's appropriate here. Perhaps only if there are more experimental variables in play?

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  • $\begingroup$ With "paired" you actually mean that different biological samples were processed in the same batch? Then I agree that paired t-test if defensible. You measured differences in expression three times and test if on average the difference is different from zero $\endgroup$ – Knarpie Dec 20 '18 at 12:46
  • $\begingroup$ Yes, on 3 separate occasions, one sample was collected for the experimental condition from one individual and another sample was collected for the control condition from an independent individual. The two samples were processed together, which greatly affects the data, but are otherwise unrelated. Glad that you agree, thanks. $\endgroup$ – Jess Dec 20 '18 at 12:57
  • $\begingroup$ Given your goal of seeing which genes are differentially expressed, I'm not sure you want any statistical test. Just look. Which genes are different? Never mind statistical significance, what are the effect sizes? $\endgroup$ – Peter Flom Dec 20 '18 at 13:16
  • $\begingroup$ Hi Peter. We've already looked at the fold changes but wanted to take into account the variance and the consistency of the direction of change. Stats are also preferred for publication. I've just calculated the effect sizes using Cohen's d and they're normally distributed around 0, with 17.5% having "very large" effect sizes of >1.2. $\endgroup$ – Jess Dec 20 '18 at 14:29

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