Discussion on permutation tests andnonparametric tests

• Main Authors: Shun-Jie Ke, 柯舜傑
• Other Authors: Wei-Hou Cheng
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/87493415470340130218

碩士 === 淡江大學 === 數學學系碩士班 === 94 === For most parametric and nonparametric tests，there is a permutation counterpart，and permutation test can be applied to all kinds of data，including continuous、ordered and categorical data，and the resulting permutation test is often as powerful as or more powerful than alternative approaches．Good[1] made a interesting statement in his book：ninety-nine percent of common nonparametric tests are permutation tests in which the original observations have been replaced by ranks，but he did not elaborate．We want to check out this statement．In this thesis，we discuss the connection between nonparametric tests and permutation tests by the property of permutation test (equally likely) and the nonparametric tests we consider are those in Conover''s book[2]. After comparing the two type of tests，we came to some conclusions．The tests based on binomial test can be regarded as some kind of permutation tests under certain definition of "permutaton"．If the tests are related to statistics，then whether they can be viewed as permutation tests depends on if the value of the probability，p，is known where p is the population parameter in the null hypothesis．For tests like Kolmogorov goodness-of-fit test，since the statistics is calculated based on empirical distribution function，hence no matter how we repermutate the observations，the order statistics is the same．This kind of tests can''t be regarded as permutation tests. To sum up，we find that most of nonparametric tests can be regarded as permutation tests，and the key point is to find a appropriate definition of "permutation"．