Type S error rates for classical and Bayesian single and multiple comparison procedures
Type S error rates for classical and Bayesian single and multiple comparison procedures
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DOI：
10.1007/s001800000040
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发表时间：
2000-01-01
影响因子：
1.3
通讯作者：
Tuerlinckx, FA
中科院分区：
文献类型：
--
作者：
Gelman, A;Tuerlinckx, FA
在经典统计学中，比较的显著性（例如，θ（1）-θ（2））是使用类型1误差率校准的，依赖于真实差异为零的假设，这在许多应用中是没有意义的。我们建立了一个更相关的框架，在这个框架中，真实的比较可以是正面的或负面的，并且，基于数据，你可以说“有信心的theta（1）> theta（2）”，“有信心的theta（2）> theta（1）”，或者“没有信心的声明”。“我们关注的是S型（符号）错误，当你声称“theta（1）> theta（2）”时，当theta（2）> theta（1）（反之亦然），就会发生这种错误。我们计算了经典和贝叶斯置信度陈述的S型错误率，发现经典的S型错误率可能非常高（高达50%）。贝叶斯置信度声明是保守的，在这个意义上，基于95%后验区间的声明具有0到2.5%之间的S型错误率。对于多重比较情况，结论是相似的。
Fn classical statistics, the significance of comparisons (e.g., theta(1) - theta(2)) is calibrated using the Type 1 error rate, relying on the assumption that the true difference is zero, which makes no sense in many applications. We set up a more relevant framework in which a true comparison can be positive or negative, and, based on the data, you can state "theta(1) > theta(2) with confidence," "theta(2) > theta(1) with confidence," or "no claim with confidence." We focus on the Type S (for sign) error, which occurs when you claim "theta(1) > theta(2) with confidence" when theta(2) > theta(1) (or vice-versa). We compute the Type S error rates for classical and Bayesian confidence statements and find that classical Type S error rates can be extremely high (up to 50%). Bayesian confidence statements are conservative, in the sense that claims based on 95% posterior intervals have Type S error rates between 0 and 2.5%. For multiple comparison situations, the conclusions are similar.