Test for differences between groups of samples

Question

Sorry if the answer to this should be obvious.

I have RNA-expression results from 24 samples which can be divided into 6 groups, (wildtype and two different mutants at two different ages) with a total of 24 samples. I have made a PCA plot and when describing it in my thesis said separation between samples is minimal. One of my examiners has said

You state that the separation between samples in the principal component analysis is minimal, this needs to be quantified to differentiate between minimal but statistically significant, and not significantly different.

I have no idea how he expects me to test for significance. I know how to test for significant differences between individual samples, and for differences per gene/principle component. I don't know how to group samples together while testing for significance against multiple things or if I should use genes or principle components (probably the latter).

I'm writing it in R so if anyone knows which R function can do the kinds of statistical tests I need that would be a huge help. Alternatively is this something which I shouldn't really do and I should push back on?

I'm already performing significance testing using DESeq2. To the best of my knowledge that only tests for whether a single gene is significant. It doesn't test for whether the samples are significantly different as a whole which is what I'm after.

Answer 1

PCA does not do any testing and has no p-values. You may state that a separation of less than m units in PC > i is not significant while a separation of greater than n units in PC < i is significant as PCs < i explain X% of the variation (i being 2 or 3). That's how you can back your statement on the separation being minimal.

That is, in this sample plot:

PC2 distance of < 0.05 might be called trivial compared to PC1 distance > 0.5 if PC1 explains 80% of the variance. This is just 2 PCs though, so your actual case will need to be more robust.