Fisher ( 1945a , 1945b , 1955 , 1956 , 1960 ) criticised the Neyman-Pearson approach to hypothesis testing by arguing that it relies on the assumption of “repeated sampling from the same population.” The present article considers the responses to this criticism provided by Pearson ( 1947 ) and Neyman ( 1977 ). Pearson interpreted alpha levels in relation to imaginary replications of the original test. This interpretation is appropriate when test users are sure that their replications will be equivalent to one another. However, by definition, scientific researchers do not possess sufficient knowledge about the relevant and irrelevant aspects of their tests and populations to be sure that their replications will be equivalent to one another. Pearson also interpreted the alpha level as a personal rule that guides researchers’ behavior during hypothesis testing. However, this interpretation fails to acknowledge that the same researcher may use different alpha levels in different testing situations. Addressing this problem, Neyman proposed that the average alpha level adopted by a particular researcher can be viewed as an indicator of that researcher’s typical Type I error rate. Researchers’ average alpha levels may be informative from a metascientific perspective. However, they are not useful from a scientific perspective. Scientists are more concerned with the error rates of specific tests of specific hypotheses, rather than the error rates of their colleagues. It is concluded that neither Neyman nor Pearson adequately rebutted Fisher’s “repeated sampling” criticism. Fisher’s significance testing approach is briefly considered as an alternative to the Neyman-Pearson approach.

中文翻译：

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“从同一人群重复采样？” 对内曼和皮尔逊对费舍尔的回应的批评

Fisher（1945a，1945b，1955、1956、1960）批评了Neyman-Pearson的假设检验方法，认为该方法依赖于“从同一人口重复抽样”的假设。本文考虑了皮尔森（Pearson，1947年）和内曼（Neyman，1977年）对这种批评的回应。皮尔逊（Pearson）解释了与原始测试的假想复制有关的阿尔法水平。当测试用户确定他们的复制将彼此等效时，这种解释是适当的。但是，根据定义，科学研究人员对测试和总体的相关和不相关方面没有足够的知识，无法确保他们的重复彼此相同。皮尔森也将阿尔法水平解释为指导假设检验中研究人员行为的个人规则。但是，这种解释未能承认同一研究人员可能在不同的测试情况下使用不同的alpha级别。为了解决这个问题，内曼建议将特定研究人员采用的平均alpha水平视为该研究人员典型I型错误率的指标。从超科学的角度来看，研究人员的平均阿尔法水平可能是有益的。但是，从科学角度看，它们没有用。科学家更关注特定假设的特定检验的错误率，而不是同事的错误率。结论是，内曼和皮尔逊都没有充分驳斥费舍尔的“重复抽样”批评。