Dictionaries of Paradoxes for Statistical Tests on k Samples
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多样本统计检验的悖论字典
- 研究问题
- 对多个样本进行排序或逐步筛选时，限制到不同样本子集为何会产生反直觉排序，筛选路径又如何改变最终选择？
- 方法与思路
- 作者建立Kruskal–Wallis检验与Borda投票法的联系，用可能排序的字典分析子集悖论，并研究其他检验类别。
- 材料陈述的贡献
- 摘要称使用秩可减少所研究的投影悖论，并说明同一数据采用不同递归筛选方法，可能得到不同的最佳样本。
- 阅读关注点
- 应核对字典、投影悖论与最优样本的定义，秩权重比较的范围，以及递归筛选结果依赖路径的具体构造。
- 阅读边界
- 材料为版本未注明的OpenAlex索引摘要；比较权重的条件及字典计算细节未说明，减少悖论不等于全面提高检验性能。
原文摘要
A relationship between the Kruskal–Wallis nonparametric statistical test on k samples and the Borda positional method for voting is established and then exploited to gain a complete analysis of the counterintuitive results and statistical orderings that arise when a set of data is restricted to various subsets of the k samples. This is done by introducing and examining the “dictionary” of possible orderings of the samples occurring with the Kruskal-Wallis procedure. It is shown that using ranks, as opposed to any other weights, minimizes the number and kinds of paradoxes that can arise from examining subsets of the data—projection paradoxes. The idea of a dictionary for a statistical procedure is discussed. The dictionaries for the Deshpandé class ℒ of statistical procedures (including Bhapkar's V test and Deshpandé's L test) are computed. An estimate for the relative sizes of the number of paradoxes for the Kruskal-Wallis test and any other such test—by comparing relative sizes of their dictionaries—is given in a few cases. An analysis is given of the method of selecting the “best” of several samples by recursively narrowing down the size of the set of samples one is “reasonably certain” must contain the optimal choice. It is shown that the best sample may be dependent on which recursive method is chosen: For the same data, different recursive methods can yield different outcomes.