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Multivariate Information Transmission

Published online by Cambridge University Press:  01 January 2025

William J. McGill
William J. McGill*
Affiliation:
Massachusetts Institute of Technology
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Abstract

A multivariate analysis based on transmitted information is presented. It is shown that sample transmitted information provides a simple method for measuring and testing association in multi-dimensional contingency tables. Relations with analysis of variance are pointed out, and statistical tests are described.

Type
Original Paper
Information
Psychometrika , Volume 19 , Issue 2 , June 1954 , pp. 97 - 116
Copyright
Copyright © 1954 Psychometric Society

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Footnotes

*

This work was supported in part by the Air Force Human Factors Operations Research Laboratories, and in part jointly by the Army, Navy, and Air Force under contract with the Massachusetts Institute of Technology.

†

Several of the indices and tests discussed in this paper have been developed independently by J. E. Keith Smith (11) at the University of Michigan, and by W. R. Garner at Johns Hopkins University.

References

Fano, R. M.. The transmission of information II, Cambridge: Massachusetts Institute of Technology, 1950Google Scholar
Garner, W. R., Hake, H. W.. Amount of information in absolute judgments. Psychol. Rev., 1951, 58, 446–459CrossRefGoogle Scholar
Dolansky, L.. Table of p log p, Cambridge: Massachusetts Institute of Technology, 1952Google Scholar
McGill, W. J.. Multivariate transmission of information and its relation to analysis of variance, Cambridge: Massachusetts Institute of Technology, 1953Google Scholar
Miller, G. A.. What is information measurement?. Amer. Psychologist, 1953, 8, 3–11CrossRefGoogle Scholar
Miller, G. A. and Madow, W. J. Information measurement for the multinomial distribution (in preparation).Google Scholar
Mood, A. M.. Introduction to the theory of statistics, New York: McGraw-Hill, 1950Google Scholar
Newman, E. B.. Computational methods useful in analyzing series of binary data. Amer. J. Psychol., 1951, 64, 252–262CrossRefGoogle ScholarPubMed
Pearson, K., Stouffer, S. A., David, F. N.. Further applications in statistics of the Bessel function. Biometrika, 1932, 24, 293–350Google Scholar
Shannon, C. E., Weaver, W.. The mathematical theory of communication, Urbana: University of Illinois Press, 1949Google Scholar
Smith, J. E. Keith Multivariate attribute analysis (in preparation).Google Scholar
Stumper, F. L.. A bibliography of information theory, Cambridge: Massachusetts Institute of Technology, 1953Google Scholar