A non-parametric test for several independent samples

We introduce a large sample non-parametric test for the hypothesis of equal distributions of three or more independent samples. The test can be considered as a generalisation of the two sample run tests of Wald and Wolfowitz in that it sorts the data and replaces the values with the 'label' of the sample from which they come, thus transforming the problem to a question about the randomness of the resulting pooled sample. The test statistic and its asymptotic null distribution are derived using the central limit theorem of finite Markov chains. Simulation results and comparisons with the standard k-sample Kruskal-Wallis and Kolmogorov-Smirnov tests are given. One particular strength of the test is that it is capable of distinguishing between different distributions having the same mean in a few cases when the Kruskal-Wallis test is completely paralysed.