Calculational short cuts for Kendall's tau and average tau and for Hays' average tau with a criterion ranking (τC) are shown. The short cuts are based mainly on counting “inversions” in the ordering ofnobjects by a given judge, and summing overmjudges, rather than counting agreements for a given object-pair and summing over object-pairs. The sum of the number of inversions thus counted forτChas a limiting normal distribution under the null hypothesis. From this is derived a statistic which approximates the sampling distribution of τC. The approximation is shown to be close even for smallmandn.