Abstract.
We consider the uniformly most powerful unbiased (UMPU) one-sided test for the comparison of two proportions based on sample sizes m and n, i.e., the randomized version of Fisher's exact one-sided test. It will be shown that the power function of the one-sided UMPU-test based on sample sizes m and n can coincide with the power function of the UMPU-test based on sample sizes m+1 and n for certain levels on the entire parameter space. A characterization of all such cases with identical power functions is derived. Finally, this characterization is closely related to number theoretical problems concerning Fermat-like binomial equations. Some consequences for Fisher's original exact test will be discussed, too.
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Finner, H., Strassburger, K. Increasing sample sizes do not always increase the power of UMPU-tests for 2×2 tables. Metrika 54, 77–91 (2001). https://doi.org/10.1007/s001840100117
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DOI: https://doi.org/10.1007/s001840100117