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  • 标题:Normal Approximations to the Distributions of the Wilcoxon Statistics: Accurate to What N? Graphical Insights
  • 本地全文:下载
  • 作者:Carine A. Bellera ; Marilyse Julien ; James A. Hanley
  • 期刊名称:Journal of Statistics Education
  • 电子版ISSN:1069-1898
  • 出版年度:2010
  • 卷号:18
  • 期号:2
  • 出版社:American Statistical Association
  • 摘要:

    The Wilcoxon statistics are usually taught as nonparametric alternatives for the 1- and 2- sample Student-t statistics in situations where the data appear to arise from non-normal distributions, or where sample sizes are so small that we cannot check whether they do. In the past, critical values, based on exact tail areas, were presented in tables, often laid out in a way that saves space but makes them confusing to look up. Recently, a number of textbooks have bypassed the tables altogether, and suggested using normal approximations to these distributions, but these texts are inconsistent as to the sample size n at which the standard normal distribution becomes more accurate as an approximation. In the context of non-normal data, students can find the use of this approximation confusing. This is unfortunate given that the reasoning behind梐nd even the derivation of梩he exact distributions can be so easy to teach but also help students understand the logic behind rank tests. This note describes a heuristic approach to the Wilcoxon statistics. Going back to first principles, we represent graphically their exact distributions. To our knowledge (and surprise) these pictorial representations have not been shown earlier. These plots illustrate very well the approximate normality of the statistics with increasing sample sizes, and importantly, their remarkably fast convergence.

  • 关键词:Graphics; Mann-Whitney U statistic; Nonparametrics; Normal approximation; ;Ranking methods; Sampling distribution; Wilcoxon rank-sum statistic; Wilcoxon ;signed-rank statistic
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