, Volume 34, Issue 2, pp 211–236

Mathematical statistics and metastatistical analysis

  • Andrés Rivadulla

DOI: 10.1007/BF00385721

Cite this article as:
Rivadulla, A. Erkenntnis (1991) 34: 211. doi:10.1007/BF00385721


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 Hacking1's evidentialists criticisms of the Neyman-Pearson's theory of statistics (NPT), as well as Hacking2'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.

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Andrés Rivadulla
    • 1
  1. 1.Departamento de Lógica y Filosofía de la CienciaUniversidad ComplutenseMadridSpain