On Formulating Pearson’s Chi-Squared Statistic in Two-Way Frequency Tables

Authors

  • Lynn Roy LaMotte LSU School of Public Health, New Orleans, U.S.A.

DOI:

https://doi.org/10.17713/ajs.v35i2&3.376

Abstract

The standard form of Pearson’s chi-squared statistic ignores variation due to estimating the mean vector in settings where the mean vector is not completely specified by the null hypothesis, as is the case when testing for homogeneity or independence in two-way tables. The root form of the statistic is formulated here with and without that additional variance included, resulting in somewhat different expressions.

References

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Cramér, H. (1946). Mathematical Methods of Statistics. Princeton, N.J.: Princeton University Press.

Haldane, J. B. S. (1940). The mean and variance of Chi2, when used as a test of homogeneity, when expectations are small. Biometrika, 31, 346-355.

Pearson, K. (1900). On the criterion that a given set of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philos. Mag., Series 5, 50, 157-172.

Steyn, H. S., and Stumpf, R. H. (1984). Exact distributions associated with an h × k contingency table. South African Statistical Journal, 18, 135-159.

Upton, G. J. G. (1982). A comparison of alternative tests for the 2 × 2 comparative trial. Journal of the Royal Statistical Society A, 145, 86-105.

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Published

2016-04-03

How to Cite

LaMotte, L. R. (2016). On Formulating Pearson’s Chi-Squared Statistic in Two-Way Frequency Tables. Austrian Journal of Statistics, 35(2&3), 299–306. https://doi.org/10.17713/ajs.v35i2&3.376

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Articles