A Comparison of the Chi-Square Test for 1 df and the Fisher Exact Test

The chi-square test was compared with the Fisher exact test using Ns ranging from 3 to 69. Contrary to expectations, there was closer agreement between the two tests with the smaller Ns. The chi-square test gave very good approximations of the true probabilities--especially when the two groups being compared were nearly equal in sample size--but only if it was used as a one- tailed test. If the groups being compared had very unequal sample sizes ratios of 71 and greater, the chi-square test sometimes gave questionable results. A table of one-tailed probabilities is provided.