TL;DR If you do a statistical test before a dimensional reduction method like PCA, the highest source of variance is likely to be whatever you tested statistically.
Wait, Why?? Let me describe the situation. You’ve done an -omics level analysis on your system of interest. You run a t-test (or ANOVA, etc) on each of the features in your data (gene, protein, metabolite, etc). Filter down to those things that were statistically significant, and then finally, you decide to look at the data using a dimensionality reduction method such as principal components analysis (PCA) so you can see what is going on.