Optimal Unconditional Asymptotic Test in 2 × 2 Multinomial Trials

摘要: Abstract The generally most powerful unconditional exact test for testing independence in a 2 × 2 multinomial trial is Barnard's test, but at present it impossible to apply samples of even moderate size. Alternatively, can be used as an asymptotic method. This paper evaluates 10 different approximations (as well 48 others not included here) under the criterion that optimal approximation one which produces p-value differs from by less than given quantity. best method based on Pirie and Hamdan's chi-squared statistics –  = {|N 11 N 22 − N 12 21| − 0.5}2(N − 1)/{N 1• 2• •1 •2} valid, ordinary significances one(two)tailed-tests, if minimum expected quantity E larger or equal 2.5 (1.5). However, when valid may fail between 1% 5% times (the failures are sometimes liberal conservative). If wants avoid failure, will have rather more 9. (Present computatio...