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Abstract
Various non-parametric methods have been used to perform hypothesis test on multiple regression coefficients. In this article, at first the most important methods which has been introduced from other statisticians as proper methods, such as Kennedy, Freedman and Lane, and modified Kennedy, are explained and then, Freedman and Lane (Huh-John) method will be modified in the form of Kennedy method; finally, all aforementioned methods will be compared as simulating. At last, we look for a method that done best. So, Huh-John (2001) modify the method of Kennedy which was proposed in 1995 and showed by simulation that is called modified Huh-John method; and it has less type I error. On the other hand, Anderson as simulation (1991) and Schadrekh as theory (2011) had shown that Freedman& Lane method has lower type I error in comparison with Kennedy method. We did some modification on Freedman and Lane method that Huh-John had done on Kennedy method and compared this modified method with Freedman and Lane and Huh-John method. We conclude that Freedman and Lane modified method often has lower type I error estimation and higher power than Freedman& Lane and Huh-John method.
Highlights
When fundamental hypotheses to perform hypothesis test are not true on linear models regression coefficients, doing classic tests on regression coefficients will not give a reliable answer, so we should use non-parametric methods
There is an agreement among statisticians about linear simple regression for hypothesis test, but different methods have been proposed for multiple regression
Important methods that are based on Permutability principle include: Freedman and Lane (1983), Kennedy (1995), Manly (1991), Ter Bruak (1992)
Summary
When fundamental hypotheses to perform hypothesis test are not true on linear models regression coefficients, doing classic tests on regression coefficients will not give a reliable answer, so we should use non-parametric methods. One group of these tests is re-sampling tests including Jacknife, Botstape, and permutation tests. In 1999, Anderson and Legendr investigated four above methods by doing extensive simulation and showed that Freedman and Lane method and Kennedy method perform better than other. Schaderch in 2010 showed that Freedman and Lane method is better than Huh and John. Our goal is to modify the method of Freedman& Lane as the way that Huh and John has modified Kennedy method, as well as compare it by Freedman and Lane and Kennedy method as simulation
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