Hilton J F
Department of Epidemiology and Biostatistics, University of California at San Francisco 94143-0560, USA.
Stat Med. 1996 Mar 30;15(6):631-45. doi: 10.1002/(SICI)1097-0258(19960330)15:6<631::AID-SIM206>3.0.CO;2-6.
In two-sample studies with ordinal responses, the Wilcoxon rank-sum test is generally chosen to test equality of the distributions, in spite of it being a specific test of location shift. I compared the power of the exact tests based on the Wilcoxon statistic, O'Brien's generalized Wilcoxon statistic, and the omnibus Smirnov statistic in the presence of location shift and scale alternatives. All three tests can gain power as a function of the scale parameter, depending on its magnitude relative to the shift parameter. As the relative influence of the scale parameter grows, the O'Brien test is the most powerful. I also compared the power of the asymptotic Wilcoxon test with its exact version, and found that it either inflates or deflates power if there are scale changes present. I present results of a simulation study.
在具有有序响应的双样本研究中，尽管Wilcoxon秩和检验是位置偏移的特定检验，但通常仍选择它来检验分布的相等性。我比较了在存在位置偏移和尺度替代的情况下，基于Wilcoxon统计量、奥布赖恩广义Wilcoxon统计量和综合斯米尔诺夫统计量的精确检验的功效。所有这三种检验都可以根据尺度参数获得功效，这取决于它相对于偏移参数的大小。随着尺度参数的相对影响增加，奥布赖恩检验是最有效的。我还比较了渐近Wilcoxon检验与其精确版本的功效，发现如果存在尺度变化，它要么夸大要么降低功效。我展示了一项模拟研究的结果。
