Some distribution-free k-sample rank tests of homogeneity against ordered alternatives

Abstract

A problem which occurs frequently in statistical analysis is that of deciding whether several samples should be regarded as coming from the same population. This problem, usually referred to as the k-sample problem, when expressed formally is stated as follows: Let $X_{ii} , j = 1, · · · , m_i, i = 1, · · · , k,$ be a set of independent random variables and let $F_i(x)$ be the probability distribution function of $X_{ii}$ . The set of admissible hypotheses designates that each $F_i$ belongs to some class of distribution functions $\Omega$.