The Neyman-Pearson theory as decision theory, and as inference theory; with a criticism of the Lindley-savage argument for Bayesian theory

The concept of a decision, which is basic in the theories of Neyman Pearson, Wald, and Savage, has been judged obscure or inappropriate when applied to interpretations of data in scientific research, by Fisher, Cox, Tukey, and other writers. This point is basic for most statistical practice, which is based on applications of methods derived in the Neyman-Pearson theory or analogous applications of such methods as least squares and maximum likelihood. Two contrasting interpretations of the decision concept are formulated: behavioral, applicable to 'deci sions' in a concrete literal sense as in acceptance sampling; and evidential, applicable to 'decisions' such as 'reject H{ in a research context, where the pattern and strength of statistical evidence concerning statistical hypotheses is of central interest. Typical standard practice is charac terized as based on the confidence concept of statistical evidence, which is defined in terms of evidential interpretations of the 'decisions' of decision theory. These concepts are illustrated by simple formal examples with interpretations in genetic research, and are traced in the writings of Neyman, Pearson, and other writers. The Lindley-Savage argument for Bayesian theory is shown to have no direct cogency as a criticism of typical standard practice, since it is based on a behavioral, not an evidential, interpretation of decisions.

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