Gómez Herazo, Cristian J.

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    Un estudio de diferentes pruebas para el problema general de dos muestras
    (2018-05) Gómez Herazo, Cristian J.; Rolke, Wolfgang A.; College of Arts and Sciences - Sciences; González, Edgardo Lorenzo; Santana Morant, Dámaris; Ocasio González, Víctor; Department of Mathematics; Coutin Rodicio, Sandra
    In its most general form the two-sample problem is concerned with the question whether two independent samples come from the same probability distribution. There are a wide variety of methods to test this hypothesis. We will study some of the most well known: the Permutation, Wilcoxon, Wald-Wolfowitz Runs, Kolmogorov Smirnov, Anderson-Darling and Chi-Square test. We also develop an extension to the Q-Q plot by adding a confidence band to test specifically whether the two samples come from a uniform distribution. These methods are based on the statistics of order, rank, and empirical distribution function. We will compare the different tests, studying their power for different distributions, varying parameters and using different sample sizes. The power of each test will be calculated by simulation, for which we created an interactive online web application (shinyapps) programmed in R, which is available at: https://server-cristian.shinyapps.io/two sample problem/. The results show that there is no uniformly best test for the general problem of two samples. This is because the powers are affected to a large extent by the definition of the alternate distributions, we can however give some guidelines to use the tests more appropriate in a number of standard cases.