Abstract
The Fisher and Neyman-Pearson approaches to testing statistical hypotheses are compared with respect to their attitudes to the interpretation of the outcome, to power, to conditioning, and to the use of fixed significance levels. It is argued that despite basic philosophical differences, in their main practical aspects the two theories are complementary rather than contradictory and that a unified approach is possible that combines the best features of both. As applications, the controversies about the Behrens-Fisher problem and the comparison of two binomials (2×2 tables) are considered from the present point of view.
This research was supponed by National Science Foundation Grant DMS-8908670. The author thanks the referees for helpful suggestions, Sandy Zabell for suggesting improvement to an early version of the article, and his wife Juliet Shaffer for diSCUSSIOns and critical comments at all stages.
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Lehmann, E.L. (2012). The Fisher, Neyman-Peerson Theories of Testing Hypotheses: One Theory or Two?. In: Rojo, J. (eds) Selected Works of E. L. Lehmann. Selected Works in Probability and Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1412-4_19
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