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Knowing the signs: a direct and generalizable motivation of two‐sided tests
The Journal of the Royal Statistical Society, Series A (Statistics in Society) ( IF 2 ) Pub Date : 2019-12-26 , DOI: 10.1111/rssa.12496
Kenneth Rice 1 , Tyler Bonnett 2 , Chloe Krakauer 1
Affiliation  

Many well‐known problems with two‐sided p‐values are due to their use in hypothesis tests, with ‘reject–accept’ conclusions about point null hypotheses. We present an alternative motivation for p‐value‐based tests, viewing them as assessments of only the sign of an underlying parameter, where we can conclude that the parameter is positive or negative, or simply say nothing either way. Our approach is decision theoretic, but—unusually—we consider the whole set of possible utility functions available. Doing this we show how, in a specific sense, close analogues of familiar one‐ and two‐sided tests are always the optimal decision. We argue that this simplicity could aid non‐experts’ understanding and use of tests—and help them to think critically about whether or not tests are appropriate tools for answering their questions of interest. Several extensions are also considered, showing that the simple idea of determining the signs of parameters yields a rich framework for inference.

中文翻译:

知道征兆:双向测试的直接且普遍的动机

双面p值的许多众所周知的问题是由于它们在假设检验中的使用,以及关于点零假设的“拒绝接受”结论。我们提出了基于p值的测试的另一种动机,将其视为对基本参数符号的评估,在此我们可以得出结论,该参数是正值还是负值,或者只是不作任何说明。我们的方法是决策理论,但是(通常)我们会考虑所有可能的效用函数集。这样做,我们说明了在特定意义上,总是总是熟悉的单面和双面测试的紧密相似之处最佳决策。我们认为这种简单性可以帮助非专家理解和使用测试,并帮助他们批判性地思考测试是否是回答他们感兴趣的问题的合适工具。还考虑了几个扩展,表明确定参数符号的简单思想产生了丰富的推理框架。
更新日期:2019-12-26
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