We prove the following conjecture of Narayana: there are no nontrivial dominance refinements of the Smirnov two-sample test if and only if the two sample sizes are relatively prime. We also count the number of natural significance levels of the Smirnov two-sample test in terms of the sample sizes and relate this to the Narayana conjecture. In particular, Smirnov tests with relatively prime samp...

We prove the following conjecture of Narayana: there are no nontrivial dominance reene-ments of the Smirnov two-sample test if and only if the two sample sizes are relatively prime. We also count the number of natural signiicance levels of the Smirnov two-sample test in terms of the sample sizes and relate this to the Narayana conjecture. In particular, Smirnov tests with relatively prime sampl...

In statistics, two-sample tests are used to determine whether two samples have been drawn from the same population. A widely used test as such is the Kolmogorov-Smirnov two-sample test. There are other distribution-free tests which might be applied in similar occasions. In this article, we describe a two-sample omnibus test introduced by Epps and Singleton, which has – albeit being distribution...