In this study we aim to place PCA as applied to genetic data on a solid statistical footing. We develop a technique to test whether eigenvectors from the analysis are reflecting real structure in the data or are more probably merely noise. Other papers will explore applications to medical genetics [14] and to the uncovering of demographic history. In this paper, our main purpose is to describe and to validate the method, rather than to make novel inferences based on application to real data, which we leave to future work. We show that statistically significant structure is real and interpretable, and also that our methods are not failing to recover real structure that is found by other techniques.
