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# Mathematical Statistics and Metastatistical Analysis

Erkenntnis (1975-)
Vol. 34, No. 2 (Mar., 1991), pp. 211-236
Stable URL: http://www.jstor.org/stable/20012337
Page Count: 26
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## Abstract

This paper deals with meta-statistical questions concerning frequentist statistics. In Sections 2 to 4 I analyse the dispute between Fisher and Neyman on the so called logic of statistical inference, a polemic that has been concomitant of the development of mathematical statistics. My conclusion is that, whenever mathematical statistics makes it possible to draw inferences, it only uses deductive reasoning. Therefore I reject Fisher's inductive approach to the statistical estimation theory and adhere to Neyman's deductive one. On the other hand, I assert that Neyman-Pearson's testing theory, as well as Fisher's tests of significance, properly belong to decision theory, not to logic, neither deductive nor inductive. I then also disagree with Costantini's view of Fisher's testing model as a theory of hypothetico-deductive inferences. In Section 5 I disapprove $\text{Hacking}_{1}$'s evidentialists criticisms of the Neyman-Pearson's theory of statistics (NPT), as well as $\text{Hacking}_{2}$'s interpretation of NPT as a theory of probable inference. In both cases Hacking misses the point. I conclude, by claiming that Mayo's conception of the Neyman-Pearson's testing theory, as a model of learning from experience, does not purport any advantages over Neyman's behavioristic model.

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