为什么我们（通常）不必担心多重比较
Why we (usually) don't have to worry about multiple comparisons
摘要：
应用研究人员经常发现自己在似乎需要多重比较调整的环境中进行统计推断。我们挑战这些修正背后的第一类错误范式。此外，我们认为，多重比较的问题可以完全消失时，从分层贝叶斯的角度来看。我们建议在多重比较出现的情况下建立多级模型。多水平模型执行部分合并（将估计值相互偏移），而经典过程通常保持区间中心不变，通过使区间变宽来调整多重比较（或者，等效地，调整与固定宽度区间对应的$p$值）。因此，多水平模型解决了多重比较问题，也产生了更有效估计，特别是在组水平变异较低的情况下，这是多重比较特别关注的地方。
英文摘要：
Applied researchers often find themselves making statistical inferences in settings that would seem to require multiple comparisons adjustments. We challenge the Type I error paradigm that underlies these corrections. Moreover we posit that the problem of multiple comparisons can disappear entirely when viewed from a hierarchical Bayesian perspective. We propose building multilevel models in the settings where multiple comparisons arise. Multilevel models perform partial pooling (shifting estimates toward each other), whereas classical procedures typically keep the centers of intervals stationary, adjusting for multiple comparisons by making the intervals wider (or, equivalently, adjusting the $p$-values corresponding to intervals of fixed width). Thus, multilevel models address the multiple comparisons problem and also yield more efficient estimates, especially in settings with low group-level variation, which is where multiple comparisons are a particular concern.
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