  We present analytical expressions for the means and covariances of the sample
distribution of the cross-validated Mahalanobis distance. This measure has
proven to be especially useful in the context of representational similarity
analysis (RSA) of neural activity patterns as measured by means of functional
magnetic resonance imaging (fMRI). These expressions allow us to construct a
normal approximation to the estimated distances, which in turn enables powerful
inference on the measured statistics. Using the results, the difference between
two distances can be statistically assessed, and the measured structure of the
distances can be efficiently compared to predictions from computational models.
