Type I error rate of the chi-square test in independence in R × C tables that have small expected frequencies.

Abstract

Sampling experiments are reported that show that the uncorrected chi-square test of independence is exceptionally robust with respect to small expected frequencies in ^h R × C ^H 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)

Statistical simulation on microcomputers

“…For example, all of the sampling experiments reported by Norton (1952) can be replicated in one night. This performance is better than that achieved in previous years (e.g., Bradley, Bradley, McGrath, & Cutcomb, 1979) when simulations were run at night (in batch) on a mainframe timesharing system.The purpose of the present paper is twofold. First, we hope to illustrate the feasibility of conducting large-scale statistical simulations on microcomputers-an activity normally associated with larger machines.…”

“…For example, all of the sampling experiments reported by Norton (1952) can be replicated in one night. This performance is better than that achieved in previous years (e.g., Bradley, Bradley, McGrath, & Cutcomb, 1979) when simulations were run at night (in batch) on a mainframe timesharing system.…”

“…The software, called DATASIM (Bradley, 1988), is designed to generate large numbers of randomized datasets from populations specified by the user, and to "capture" and analyze the sampling distributions of statistics computed on the individual datasets. 'This provides a convenient way to conduct sampling experiments investigating the effects of violating assumptions on the Type I or Type II error rates of statistical tests (Bradley, 1989a(Bradley, , 1989b.Correspondence may be addressed 10 Drake R. Bradley. Department of Psychology, Bales College.…”

“…This provides a convenient way to conduct sampling experiments investigating the effects of violating assumptions on the Type I or Type II error rates of statistical tests (Bradley, 1989a(Bradley, , 1989b.…”

Going outside the box: skills development, cultural change and the use of on-line resources

“…In fact, however, the chi-squared test remains robust even under these circumstances. This has been well established in the case of 2 x 2 contingency tables (Richardson, 1994), but it is also true in the case of larger contingency tables (Bradley et al, 1979). The test does become markedly conservative with small sample sizes when the different levels of the row or column variables are not equiprobable, and so researchers need to be cautious when interpreting nonsignificant results.…”