  The random variate m is, in combinatorics, a basis for comparing
permutations, as well as the solution to a centuries-old riddle involving the
mishandling of hats. In statistics, m is the test statistic for a disused null
hypothesis statistical test (NHST) of association, the matching method. In this
paper, I show that the matching method has an absolute and relatively low limit
on its statistical power. I do so first by reinterpreting Rae's theorem, which
describes the joint distributions of m with several rank correlation statistics
under a true null. I then derive this property solely from m's unconditional
sampling distribution, on which basis I develop the concept of a deficient
statistic: a statistic that is insufficient and inconsistent and inefficient
with respect to its parameter. Finally, I demonstrate an application for m that
makes use of its deficiency to qualify the sampling error in a jointly
estimated sample correlation.
