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?