Dominance refinements of the Smirnov two-sample test |
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| Institution: | 1. Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands;2. LaBRI, Université de Bordeaux I, 33405 Talence, France;1. Department of Applied Mathematics III, Universitat Politècnica de Catalunya, Manresa, Spain;2. AU Herning, Aarhus University, Denmark;3. Department of Computer Science, Universitat Politècnica de Catalunya, Barcelona, Spain |
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| Abstract: | 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 sample sizes turn out to have many more natural significance levels than do Smirnov tests whose sample sizes are not relatively prime (for example, equal sample sizes). |
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