Jeffries Neal O
National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD 20892, USA.
Biostatistics. 2007 Apr;8(2):500-4. doi: 10.1093/biostatistics/kxl025. Epub 2006 Sep 12.
In experiments involving many variables, investigators typically use multiple comparisons procedures to determine differences that are unlikely to be the result of chance. However, investigators rarely consider how the magnitude of the greatest observed effect sizes may have been subject to bias resulting from multiple testing. These questions of bias become important to the extent investigators focus on the magnitude of the observed effects. As an example, such bias can lead to problems in attempting to validate results, if a biased effect size is used to power a follow-up study. An associated important consequence is that confidence intervals constructed using standard distributions may be badly biased. A bootstrap approach is used to estimate and adjust for the bias in the effect sizes of those variables showing strongest differences. This bias is not always present; some principles showing what factors may lead to greater bias are given and a proof of the convergence of the bootstrap distribution is provided.
在涉及多个变量的实验中，研究人员通常使用多重比较程序来确定不太可能是偶然结果的差异。然而，研究人员很少考虑最大观察效应量的大小可能如何受到多重检验导致的偏差影响。对于关注观察到的效应大小的研究人员来说，这些偏差问题变得很重要。例如，如果使用有偏差的效应量为后续研究提供效力，这种偏差可能会在试图验证结果时导致问题。一个相关的重要后果是，使用标准分布构建的置信区间可能会有严重偏差。对于显示出最显著差异的那些变量的效应量偏差，采用自助法进行估计和调整。这种偏差并非总是存在；给出了一些表明哪些因素可能导致更大偏差的原则，并提供了自助分布收敛性的证明。
