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Machine Short-Cuts in the Computation of Chisquare and the Contingency Coefficient

Published online by Cambridge University Press:  01 January 2025

John B. Carroll  and
C. C. Bennett
John B. Carroll
Affiliation:
Harvard University
C. C. Bennett
Affiliation:
Boston University
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Abstract

Rapid computational routines are presented for calculating x2 from frequency data in the following cases: (1) test of goodness of fit between an observed and a theoretical distribution; (2) test of independence of distributions displayed in an r ✗ c table; (3) test of independence of distributions displayed in an r ✗ 2 table. A rapid method of computing the contingency coefficient also follows from the procedure used in the second of these cases.

Type
Original Paper
Information
Psychometrika , Volume 15 , Issue 4 , December 1950 , pp. 441 - 447
Copyright
Copyright © 1950 The Psychometric Society

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References

* DuBois, P. H. Note on the calculation of the chi-square test for “goodness of fit.” Psychometrika, 1939, 4, 173–174.

* McNemar. Q. Psychological statistics. New York: Wiley, 1949.

† It can easily be shown that this formula, as well as formulas (2), (3), and (5), can be derived from the basic formula, .

* In this illustration we will use the first column, although the second column might be preferred by some computers. If the second column is used, Na and Nb are to be transposed.