For real-valued parameters, significance tests can be motivated as three-decision methods, in which we either assert the sign of the parameter above or below a specified null value, or say nothing either way. Tukey viewed this as a “sensible formulation” of tests, unlike the widely taught null hypothesis significance testing (NHST) system that is today's default. We review the three-decision framework, collecting the substantial literature on how other statistical tools can be usefully motivated in this way. These tools include close Bayesian analogs of frequentist power calculations, p-values, confidence intervals, and multiple testing corrections. We also show how three-decision arguments can straightforwardly resolve some well-known difficulties in the interpretation and criticism of testing results. Explicit results are shown for simple conjugate analyses, but the methods discussed apply generally to real-valued parameters.

中文翻译：

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三决策方法：显著性检验的合理公式 — 以及许多其他内容


对于实值参数，显著性检验可以采用三决策方法，其中我们要么断言参数的符号高于或低于指定的 null 值，要么不以任何一种方式说。Tukey 认为这是一种“合理的公式”检验，与当今广泛教授的零假设显著性检验 （NHST） 系统不同。我们回顾了三决策框架，收集了大量关于如何以这种方式有效激励其他统计工具的文献。这些工具包括频率幂计算的接近贝叶斯类似物、p 值、置信区间和多次检验校正。我们还展示了三项决定论证如何直接解决测试结果解释和批评中的一些众所周知的困难。显示了简单共轭分析的显式结果，但讨论的方法通常适用于实值参数。