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Journal Article

The Robustness of Homogeneity Tests in 2 x N Tables

R. C. Lewontin and J. Felsenstein
Biometrics
Vol. 21, No. 1 (Mar., 1965), pp. 19-33
DOI: 10.2307/2528349
Stable URL: http://www.jstor.org/stable/2528349
Page Count: 15
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The Robustness of Homogeneity Tests in 2 x N Tables
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Abstract

A Monte Carlo investigation of 2 X n tables with fixed marginals has been performed. The results of the Monte Carlo distribution show that the probability of Type I error given by the conventional x 2 test is in general conservative of 5 or more degrees of freedom even when expectations of successes are very small in each cell. A very conservative rule of operation would be that if expectations are 1 or greater the test is certainly conservative at the 5%, 2% or 1% level of significance and that for most cases even fractional expectations do not affect the test. For those cases of fractional expectations in which the x 2 test is non-conservative, the deviations of the true α values from those given by the x 2 distribution are quite small.

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