Podgor M J, Gastwirth J L
Division of Biometry and Epidemiology, National Eye Institute, National Institutes of Health, Bethesda, Maryland 20892.
Stat Med. 1994;13(5-7):747-58. doi: 10.1002/sim.4780130535.
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.
当备择假设比位置上的简单偏移更一般时，针对双样本问题已经提出了各种检验方法：非参数检验；奥布赖恩广义t检验和秩和检验；以及其他与t检验相关的检验。我们表明，这些广义检验与勒佩奇提出的非参数检验直接相关。因此，我们得到了一类更广泛、更灵活的奥布赖恩型程序，它们继承了非参数检验的水平稳健性。我们还计算了在几种模型下这些检验的经验大小和功效。在所研究的设置中，非参数程序和相关的奥布赖恩型检验是有效的，并且具有良好的功效。对于偏态和长尾分布，它们比t检验及相关程序更可取，因为后者的I型错误与名义大小有明显差异。
