Abstract
Some rank tests can be proposed for the null hypothesis of equality of all sampling distribution functions versus ordered location-scale alternatives in k-sample problem (k_??_2). The asymptotic distributions of the proposed test statistics and of rank test statistics against ordered location alternatives and against non-ordered alternatives are drawn under a contiguous sequence of the location-scale alternatives. The tests are numerically compared each other by asymptotic local power. As a result, it is seen that the tests based on the sum of two rank analogues of Bartholomew's likelihood ratio test statistic against ordered location alternatives assuming normality have reasonably high asymptotic power.
