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Choice of test for association in small sample unordered r × c tables
Author(s) -
Lydersen S.,
Pradhan V.,
Senchaudhuri P.,
Laake P.
Publication year - 2007
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.2839
Subject(s) - statistics , exact test , mathematics , pearson's chi squared test , chi square test , p value , sample size determination , test statistic , statistic , likelihood ratio test , statistical hypothesis testing , type i and type ii errors , contingency table , test (biology) , paleontology , biology
Pearson's chi‐squared, the likelihood‐ratio, and Fisher–Freeman–Halton's test statistics are often used to test the association of unordered r × c tables. Asymptotical, exact conditional, or exact conditional with mid‐p adjustment methods are commonly used to compute the p‐value . We have compared test power and significance level for these test statistics and p‐value calculations in small sample r × c tables, mostly 3 × 2 and some with both r and c are greater than 2. After extensive simulations, in general we recommend using an exact conditional mid‐p test with Pearson's chi‐squared or Fisher–Freeman–Halton's statistic, which usually is the most powerful test yet preserve the approximate significance level. Moreover, we recommend that the asymptotic Pearson's chi‐squared or other asymptotic tests not be used for small sample r × c tables. Copyright © 2007 John Wiley & Sons, Ltd.