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Measurement and Statistics: Towards a Clarification of the Theory of “Permissible Statistics”

Published online by Cambridge University Press:  14 March 2022

Richard E. Robinson
Richard E. Robinson*
Affiliation:
University of British Columbia
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Abstract

Much of the criticism of Stevens's criterion for permissible statistics as applied to measurement data results from a lack of clarity in Stevens's position. In this paper set-theoretical notions have been used to clarify that position. We define a sig-function as a function defined on numerical assignments. If u and ℜ are empirical and numerical relational systems, respectively, then a sig-function F is constant on u with respect to ℜ if, and only if, the value of F is the same for all numerical assignments for u with respect to ℜ. Using these notions we prove rigorously certain generalizations of Stevens's results.

Type
Research Article
Information
Philosophy of Science , Volume 32 , Issue 3 , July 1965 , pp. 229 - 243
Copyright
Copyright © Philosophy of Science Association 1965

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