I have a multivariate dataset representing multiple locations, each of which has a set of reference observations and a single test observation. For each location, I would like to measure how anomalous the test observation is relative to the reference distribution, using the Mahalanobis distance. Then I would like to compare these Mahalanobis distances to evaluate which locations have the most abnormal test observations.

My question is: is it valid to compare Mahalanobis distances that were generated using different reference distributions? I have only ever seen it used to compare test observations relative to a single common reference distribution. The data for each of my locations is structurally identical (same variables and number of observations) but the values and covariances differ, which would make the principal components different for each location.

I have a good intuitive understanding of how Mahalanobis distance works by combining PCA and SED, but am not a statistician so would appreciate answers on the less technical end of the spectrum.