Carleton University, Ottawa, Ontario, Canada.
Br J Math Stat Psychol. 2011 May;64(Pt 2):233-43. doi: 10.1348/000711010X501671.
The Type I error probability and the power of the independent samples t test, performed directly on the ranks of scores in combined samples in place of the original scores, are known to be the same as those of the non-parametric Wilcoxon-Mann-Whitney (WMW) test. In the present study, simulations revealed that these probabilities remain essentially unchanged when the number of ranks is reduced by assigning the same rank to multiple ordered scores. For example, if 200 ranks are reduced to as few as 20, or 10, or 5 ranks by replacing sequences of consecutive ranks by a single number, the Type I error probability and power stay about the same. Significance tests performed on these modular ranks consistently reproduce familiar findings about the comparative power of the t test and the WMW tests for normal and various non-normal distributions. Similar results are obtained for modular ranks used in comparing the one-sample t test and the Wilcoxon signed ranks test.
当在合并样本的分数等级上直接进行独立样本 t 检验，而不是原始分数时，其Ⅰ类错误概率和功效与非参数 Wilcoxon-Mann-Whitney（WMW）检验相同。在本研究中，模拟结果表明，当通过将相同的等级分配给多个有序分数来减少等级数量时，这些概率基本保持不变。例如，如果通过将连续等级的序列替换为单个数字，将 200 个等级减少到 20、10 或 5 个等级，那么Ⅰ类错误概率和功效几乎保持不变。对这些模块化等级进行的显著性检验始终复制了关于 t 检验和 WMW 检验在正态和各种非正态分布下的比较功效的熟悉发现。在比较单样本 t 检验和 Wilcoxon 符号秩检验时使用的模块化等级也得到了类似的结果。
