The Annals of Mathematical Statistics

The $\chi^2$ Test of Goodness of Fit

William G. Cochran

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This paper contains an expository discussion of the chi square test of goodness of fit, intended for the student and user of statistical theory rather than for the expert. Part I describes the historical development of the distribution theory on which the test rests. Research bearing on the practical application of the test--in particular on the minimum expected number per class and the construction of classes--is discussed in Part II. Some varied opinions about the extent to which the test actually is useful to the scientist are presented in Part III. Part IV outlines a number of tests that have been proposed as substitutes for the chi square test (the $\omega^2$ test, the smooth test, the likelihood ratio test) and Part V a number of supplementary tests (the run test, tests based on low moments, subdivision of chi square into components).

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Ann. Math. Statist. Volume 23, Number 3 (1952), 315-345.

First available in Project Euclid: 28 April 2007

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Cochran, William G. The $\chi^2$ Test of Goodness of Fit. Ann. Math. Statist. 23 (1952), no. 3, 315--345. doi:10.1214/aoms/1177729380.

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