TYPE-I ERROR RATE OF THE CHI-SQUARE TEST OF INDEPENDENCE IN RXC TABLES THAT HAVE SMALL EXPECTED FREQUENCIES

Sampling experiments are reported that show that the uncorrected chi-square test of independence is exceptionally robust with respect to small expected frequencies in R × C contingency tables. In general, error rates that exceed .06 occurred only when both marginal probability distributions were extremely skewed and sample size was small. Nevertheless, the quality of the approximation of chi-square probabilities for exact multinomial probabilities was sometimes poor, although excessive errors in approximation by W. G. Cochran's (1952) criteria usually resulted from actual error rates being smaller, not larger, than the nominal level. A distinction is made between accuracy of approximation and control of the Type I error rate as considerations dictating the advisability of using an approximate test. (38 ref) (PsycINFO Database Record (c) 2006 APA, all rights reserved). © 1979 American Psychological Association.