Many investigations have shown considerable advantage of nonparametric rank procedure over the one based on the normal theory for slippage alternatives in the two sample problem. For example, Hodges-Lehmann [4] and [5] gave the values of lower limit 0.864 and 1 of the asymptotic efficiency of Wilcoxon and the Normal scores tests with regard to the classical t-test, respectively. Any tests have not unfortunately ever been found for scale alternatives with such properties as the tests above. On the other hand, construction of optimum rank tests or modification of well-known rank tests have been successfully tried by Capon [2], Dwass [3] and Tamura [8], [9].
We now feel keenly that nonparametric two sample procedure shoud be developed following the line along which the normal theory has been done, that is to say the c-sample problem, multivariate analysis, successive process and etc.
We shall in this paper deal with tests against some alternatives considered in the c-sample problem.