平衡假设检验和等尾置信区间的情况
The case for balanced hypothesis tests and equal-tailed confidence intervals
摘要：
简介：关于双侧假设检验的方向推断存在持续的争论，对此，一些作者认为拒绝$θ= θ_0$并不能得出$θ> θ_0$或$θ< θ_0$的结论，而只能得出$θ\neq θ_0$的结论，而其他人认为这是没有实际后果的小错误。讨论：新的因素被带到辩论中。结果表明，一些非方向性的假设检验的受试者工作特征（ROC）和生存曲线的方向性解释可能会导致膨胀的第三类错误率的概率得出结论，差异存在于实际差异的相对侧，可以达到50%，在最坏的情况下。方向检验的一些问题也适用于双侧置信区间（CI）。它表明，等尾CI应首选最短的CI。提出了新的双侧CI和假设检验的评估标准，以提供可靠的方向性解释：假设检验的部分左侧和右侧$α$错误率，高估和低估$α_L$和$α_U$的概率和双侧CI的区间半宽。结论：双侧CI和双侧检验得到了方向性解释。这意味着在制定和评价置信区间和检验时应考虑方向解释。
英文摘要：
Introduction: there is an ongoing debate about directional inference of two-sided hypothesis tests for which some authors argue that rejecting $θ= θ_0$ does not allow to conclude that $θ> θ_0$ or $θ< θ_0$ but only that $θ\neq θ_0$, while others argue that this is a minor error without practical consequence. Discussion: new elements are brought to the debate. It is shown that the directional interpretation of some non-directional hypothesis tests about Receiver Operating Characteristic (ROC) and survival curves may lead to inflated type III error rates with a probability of concluding that a difference exists in the opposite side of the actual difference that can reach 50% in the worst case. Some of the issues of directional tests also apply to two-sided confidence intervals (CIs). It is shown that equal-tailed CIs should be preferred to shortest CIs. New assessment criteria of two-sided CIs and hypothesis tests are proposed to provide a reliable directional interpretation: partial left-sided and right-sided $α$ error rates for hypothesis tests, probabilities of overestimation and underestimation $α_L$ and $α_U$ and interval half-widths for two-sided CIs. Conclusion: two-sided CIs and two-sided tests are interpreted directionally. This implies that directional interpretation be taken in account in the development and evaluation of confidence intervals and tests.
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