Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-23T22:45:50.045Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Anderson, N. H., Psych. Bull, 58 (1961), 305.CrossRefGoogle Scholar
[2] Austin, J. L., How to Do Things with Words, Cambridge, Mass., 1962.Google Scholar
[3] Burke, C. J., Psych. Rev., 60 (1953), 73.CrossRefGoogle Scholar
[4] Campbell, N. R., Physics the Elements, 1920; reprinted as Foundations of Science, New York, 1957.Google Scholar
[5] Campbell, N. R., An Account of the Principles of Measurement and Calculation, London, 1928.Google Scholar
[6] Campbell, N. R., Arist. Soc. Sup. Vol. 17 (1938), 121.Google Scholar
[7] Cohen, M. R. and Nagel, E., An Introduction to Logic and Scientific Method, New York, 1934.Google Scholar
[8] Ferguson, A. et al, The Advancement of Science, 2 (1940), 331.Google Scholar
[9] Helmholtz, H. von, Counting and Measuring, Leipzig, 1887, translated by C. L. Bryan, New York. 1930.Google Scholar
[10] Lord, F. M., Amer. Psych., 8 (1953), 750.CrossRefGoogle Scholar
[11] Robinson, R. E., Technical Report No. 55, Psych. Ser., Inst. for Math. Stud. in the Soc. Sci., Stanford, 1963.Google Scholar
[12] Scott, D. and Suppes, P., Jour. of Sym. Log., 23 (1958), 113.Google Scholar
[13] Stevens, S. S., Science, 103 (1946), 677.CrossRefGoogle Scholar
[14] Stevens, S. S., Measurement: Definitions and Theories, edited by C. W. Churchman and P. Ratoosh, New York, 1959, pp. 18–63.Google Scholar
[15] Suppes, P., Portug. Math., 10 (1951), 163.Google Scholar
[16] Suppes, P., Measurement: Definitions and Theories, edited by C. W. Churchman and P. Ratoosh, New York, 1959, pp. 129–143.Google Scholar
[17] Suppes, P. and Zinnes, J. L., Handbook of Mathematical Psychology, edited by R. D. Luce, R. R. Bush, and E. Galanter, New York, 1963, Vol. 1, pp. 1–76.Google Scholar
[18] Tarski, A., Indag. Math., 16 (1954), 572, 582; 17 (1955), 56.Google Scholar

A correction has been issued for this article:

Erratum