Principal component analysis and statistical significance I've been drawn into a discussion at work on interpretation of principal component analyses. My "adversary" claims that the PCA score plot shows "statistically significant" differences (separation) and/or similarities (clustering).
From my understanding, statistical sigificance is something that can be inferred from statistical tests. PCA is not a statistical test and tells us nothing about statistical significance. It really only tells us how our samples/points may correlate to each other. Am I wrong?

I think you are right. PCA can be thought as a rotation of the axes done in such way that the first axis captures more variation than the second axis, the second more than the third etc and all axes are orthogonal to each other and the origin is centered on the mean of the datapoints. Here variation is the sum of square distances between the points projected on an axis and the origin.
There is no statistics involved since you are not trying to infer anything about the population that generated the given data. (I'm pretty sure I'm not getting things 100% right myself).
