Statistical Evidence: A Likelihood Paradigm (Chapman & HallCRC Monographs on Statistics & Applied Probability) by Richard Royall

Author:Richard Royall [Royall, Richard]
Language: eng
Format: epub
Publisher: CRC Press
Published: 2017-11-21T23:00:00+00:00

3.10 Summary

Today’s statistical practice is directed by an informal blending of Neyman–Pearson theory with concepts and interpretations that ‘are not a part of that theory. We call this approach Fisherian. Scientific applications of hypothesis testing, for example, are usually of a type so different from the procedures described by Neyman–Pearson theory that they are given a special name, tests of significance. There are actually two distinct types of significance test, namely p-value procedures and rejection trials. Both explicitly attempt to do what Neyman–Pearson theory does not – to quantify the strength of statistical evidence. Significance tests fail in this endeavor because they rest on the faulty foundation of the law of improbability. Fisherian methods in general, as tools for representing and interpreting statistical data as evidence, fail for the same reason – they rest on the law of improbability and violate the law of likelihood.

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