Mathematical statistics and metastatistical analysis
 Andrés Rivadulla
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This paper deals with metastatistical 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 NeymanPearson'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 hypotheticodeductive inferences.
In Section 5 I disapprove Hacking_{1}'s evidentialists criticisms of the NeymanPearson's theory of statistics (NPT), as well as 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 NeymanPearson's testing theory, as a model of learning from experience, does not purport any advantages over Neyman's behavioristic model.
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 Title
 Mathematical statistics and metastatistical analysis
 Journal

Erkenntnis
Volume 34, Issue 2 , pp 211236
 Cover Date
 19910301
 DOI
 10.1007/BF00385721
 Print ISSN
 01650106
 Online ISSN
 15728420
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Authors

 Andrés Rivadulla ^{(1)}
 Author Affiliations

 1. Departamento de Lógica y Filosofía de la Ciencia, Universidad Complutense, E28040, Madrid, Spain