On the Validity Condition of the Chi-Squared Test in 2 2 Tables

摘要: 2x 2 contingency table is usually analyzed by using the chi-squared asymptotic test, with Yates' continuity correction (c=n/2, where n total size of sample). This correct one when test an approximation to Fisher's exact (conditional) test. When used as Barnard's (unconditional) for comparing two independent proportions (two samples n1 and n2, or contrasting independence (one sample a n), c different (c=1 if ? n2 c=2 = in first case; c=0.5 second). Whatever case, it traditional affirm that valid E>5, E minimum expected quantity. Today recognized this condition too general may not be appropriate. In case correction, Martin Andres Herranz Tejedor (2000) proved validity must type E>E* --where E* known function depending on marginals table-- checking equivalent asymmetry base statistic (a hypergeometric random variable). present article authors prove argument other corrections, moreover, value obtained all three cases. Given reaches absolute maximum, can affirmed tests referred are E>19.2, 14.9 6.2 (or E>8.1, 7.7 3.9 500) respectively previous models (although model two-tailed E>0 sufficient).