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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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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

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