Sidak-type tests for the two-sample problem based on precedence and   exceedance statistics
  This paper deals with a class of nonparametric two-sample tests for ordered alternatives. The test statistics proposed are based on the number of observations from one sample that precede or exceed a threshold specified by the other sample, and they are extensions of \v{S}id\'ak's test. We derive their exact null distributions and also discuss a large-sample approximation. We then study their power properties exactly against the Lehmann alternative and make some comparative comments. Finally, we present an example to illustrate the proposed tests. 
Eugenia Stoimenova, N. Balakrishnan
math.ST stat.TH