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Abstract:
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Conover's Rank Transformation (e.g. Conover and Iman 1981) is a general method for using Normal Theory methods with possibly non-normal data. To use the method to test the hypothesis that the ratio of two population medians, say Med(X)/Med(Y), is less than (or greater than) a non-zero constant C, a possible approach is to multiply the Y observations (i.e. the denominator observations) by C, and then test the hypothesis of no difference in medians using this modified data. A possible problem is that the multiplication by C changes the scale of the modified Y observations - how does this affect the validity of the test? Previous work (Schuirmann 2014) suggested that the test remains valid if the underlying distribution is symmetric, but may be conservative or anticonservative for skewed distributions, depending on the direction of the null hypothesis and on the direction of the skewness. The current work continues to explore this question, particularly for underlying distributions that are a mixture of two normals.
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