Simple rank statistics are used to test that two samples come from the same distribution. Sidak's E-test (Apl. Mat. 22 (1977), 166-175) is based on the number of observations from one sample that exceed all observations from the other sample. A similar test statistic is defined in Ann. Inst. Stat. Math. 52 (1970), 255-266. We study asymptotic behavior of the moments of both statistics.