Distribution-Free Two-Sample Tests For Equivalence

So far, equivalence test, including clinical and biological equivalence test, are widely used. A wide range of use-cases has been seen in industries such as psychology and economics. In this paper, with the distribution-free two-sample tests for equivalence, we compare the equivalence test and significance test, and propose a new approach for equivalence test.This paper firstly introduces the background, development, adoption and current state of equivalence test.There have been a lot of investigation and references about sig-nificance test and equivalence test under the parametric framework, so this paper focuses on distribution-free two-sample tests for equivalence.In chapter 2, based on two-sample t-test and two-one-sided equivalence test under normal distribution, we use two ways to compare the power and sample size and explore the relation laws between distribution-free significance test and equivalence test. On the basis of Monte Carlo experiment, we construct simulation study of Mann-Whitney test for difference and equivalence.In chapter 3, we apply the ranked set sampling in test for equivalence test.From the perspective of asymptotic efficiency, ranked set sampling(RSS) have an advantage over the simple random sampling(SRS) in two-sample tests.With the comparison result ,we propose Mann-Whitney test for equivalence in RSS.In chapter 4, the problem of assessing the similarity of two cumulative distribution function F and G is considered,based on the Kolmogorov-Smirnov distance and Mallows distance,modified Kolmogorov-Smirnov distance is also able to be applied to the nonpara-metric assessment of equivalence.Moreover, we use bootstrap method to conform K-S test and corresponding bootstrapping test.Finally,we consider generalizing the distribution-free test for equivalence when ties occur between observations from different samples.Some concise conclusion is drawn in the end of this paper.