Asymptotical tests in 22 comparative trials: (unconditional approach)
The unconditional Barnard's test for the comparison of two independent proportions is difficult to apply even with moderately large samples. The alternative is to use a ?2 type, arc sine or mid-p asymptotic test. In the paper, the authors evaluate some 60 of these tests, some new and others that are already familiar. For the ordinary significances, the optimal tests are the arc sine methods (with the improvement proposed by Anscombe), the ?2 ones given by Pearson (with a correction for continuity of 2 or of 1 depending on whether the sample sizes are equal or different) and the mid-p-value ones given by Fisher (using the criterion proposed by Armitage, when applied as a two-tailed test). For one-(two) tailed tests, the first method generally produces reliable results E>10.5 (E>9 and unbalanced samples), the second method does so for E>9(E>6) and the third does so for all cases, although for E?6(E?10.5) it usually gives too many conservative results. E refers to the minimum expected quantity.
barnard's test mid-p-value arc sine transformation binomial proportions continuity correction fisher's exact test 22 tables unconditional test validity conditions