On non-parametric and generalized tests for the two-sample problem with location and scale change alternatives.
Various tests have been proposed for the two-sample problem when the alternative is more general than a simple shift in location: non-parametric tests; O'Brien's generalized t and rank sum tests; and other tests related to the t. We show that the generalized tests are directly related to non-parametric tests proposed by Lepage. As a result, we obtain a wider, more flexible class of O'Brien-type procedures which inherit the level robustness property of non-parametric tests. We have also computed the tests' empirical sizes and powers under several models. The non-parametric procedures and the related O'Brien-type tests are valid and yield good power in the settings investigated. They are preferable to the t-test and related procedures whose type I errors differ noticeably from nominal size for skewed and long-tailed distributions.
Division of Biometry and Epidemiology, National Eye Institute, National Institutes of Health, Bethesda, Maryland 20892.
M J
MJ
Podgor
J L
JL
Gastwirth
D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D003929:Diabetic Neuropathies / Q000628:therapy; D006801:Humans; D015233:Models, Statistical; D016011:Normal Distribution; D010147:Pain Measurement / Q000706:statistics & numerical data; D012044:Regression Analysis; D016896:Treatment Outcome