In the application of Bross' covast test [1] for detecting differences between two treatments with dichotomous response variable in the presence of a covariable, pairwise comparisons are made between subjects receiving different treatments. In the process, the set of all such comparisons is partitioned into two subsets potentially favoring one or the other treatment. Under random allocation of the treatments (with respect to the covariable), the expected proportion of each of these subsets,E(r) andE(1 —r), will be 0.5; in actual experimental situations, however,rwill not usually be equal to 0.5. Approximations are given for the expected value of the test statistic conditional on the ordering with respect to the covariable, both under the “Grand Null Hypothesis” of [1] and under the hypothesis of no treatment differences. Some procedures are suggested for dealing with the caser≠ 0.5.