[R] On Corrections for Chi-Sq Goodness of Fit Test

Michael Fuller mmfuller at unm.edu
Mon Dec 19 22:24:32 CET 2011

My question regards the philosophy behind how R implements corrections to chi-square statistical tests. At least in recent versions (I'm using 2.13.1 (2011-07-08) on OSX 10.6.8.), the chisq.test function applies the Yates continuity correction for 2 by 2 contingency tables. But when used as a goodness of fit test (GoF, aka likelihood ratio test), chisq.test does not appear to implement any corrections for widely recognized problems, such as small sample size, non-uniform expected frequencies, and one D.F. 

From the help page:
"In the goodness-of-fit case simulation is done by random sampling from the discrete distribution specified by p, each sample being of size n = sum(x)."

Is the thinking that random sampling completely obviates the need for corrections? Wouldn't the same statistical issues still apply (e.g. poor continuity approximation with one D.F., problems with non-uniform expected frequencies, etc) with random sampling?

Michael M. Fuller, Ph.D.
Department of Biology
University of New Mexico
Albuquerque, NM

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