Rubin, Mark (2020) “Repeated sampling from the same population?” A critique of Neyman and Pearson’s responses to Fisher. [Preprint]

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Abstract

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.

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Item Type:	Preprint
Creators:	Creators Email ORCID Rubin, Mark Mark.Rubin@newcastle.edu.au 0000-0002-6483-8561
Keywords:	Fisher; Neyman; Neyman-Pearson; replication crisis; Type I error; Type II error; Type III error
Subjects:	General Issues > Evidence General Issues > Explanation General Issues > Models and Idealization Specific Sciences > Probability/Statistics General Issues > Social Epistemology of Science
Depositing User:	Dr Mark Rubin
Date Deposited:	29 Sep 2020 13:27
Last Modified:	29 Sep 2020 13:27
Item ID:	18168
DOI or Unique Handle:	10.1007/s13194-020-00309-6
Subjects:	General Issues > Evidence General Issues > Explanation General Issues > Models and Idealization Specific Sciences > Probability/Statistics General Issues > Social Epistemology of Science
Date:	2020
URI:	https://philsci-archive.pitt.edu/id/eprint/18168

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