Shaffer Juliet Popper
Department of Statistics, University of California, Berkeley 94720-3860, USA.
Psychol Methods. 2002 Sep;7(3):356-69. doi: 10.1037/1082-989x.7.3.356.
L. V. Jones and J. W. Tukey (2000) pointed out that the usual 2-sided, equal-tails null hypothesis test at level alpha can be reinterpreted as simultaneous tests of 2 directional inequality hypotheses, each at level alpha/2, and that the maximum probability of a Type I error is alpha/2 if the truth of the null hypothesis is considered impossible. This article points out that in multiple testing with familywise error rate controlled at alpha, the directional error rate (assuming all null hypotheses are false) is greater than alpha/2 and can be arbitrarily close to alpha. Single-step, step-down, and step-up procedures are analyzed, and other error rates, including the false discovery rate, are discussed. Implications for confidence interval estimation and hypothesis testing practices are considered.
L. V. 琼斯和J. W. 图基（2000年）指出，通常在α水平下进行的双侧、等尾零假设检验可以重新解释为对两个方向不等式假设的同时检验，每个假设的水平为α/2，并且如果认为零假设为真的概率不可能，那么I型错误的最大概率为α/2。本文指出，在将族错误率控制在α的多重检验中，方向错误率（假设所有零假设均为假）大于α/2，并且可以任意接近α。分析了单步、逐步下降和逐步上升程序，并讨论了包括错误发现率在内的其他错误率。考虑了对置信区间估计和假设检验实践的影响。
