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Power comparison of two‐sided exact tests for association in 2 × 2 contingency tables using standard, mid p and randomized test versions
Author(s) -
Lydersen Stian,
Laake Petter
Publication year - 2003
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1671
Subject(s) - statistics , contingency table , mathematics , exact test , pearson's chi squared test , chi square test , type i and type ii errors , multinomial distribution , test statistic , likelihood ratio test , statistical hypothesis testing
Exact Pearson's chi square, likelihood ratio (LR), and Fisher's tests are obtained from the conditional distribution of its test statistic, given therow and column sums of the contingency table. The power and obtained significance level of the standard, mid p , and randomized versions of these tests are compared for two‐sided tests in 2 × 2 tables, using binomial and multinomial sampling. The mid p type I error probabilities seldom exceed thenominal significance level. The mid p and randomized test versions have approximately the same power, and higher power than the standard test version. The power of the Pearson's chi square, LR and Fisher's test differ, and they differ in approximately the same way for standard, mid p and randomized test versions for any given set of parameters. There is no general ranking between the three tests. In many cases, Pearson's chi square and Fisher's tests have almost equal power, and higher power than LR. In a few cases, perhaps characterized by poorly balanced designs, LR performs best. Fisher's test seems to be slightly more robust even if the design is poor. Copyright © 2003 John Wiley & Sons, Ltd.