Comparative performance of three statistical tests of homogeneity for sparse I × j contingency tables

Parshall, Cynthia D.; Kromrey, Jeffrey D.; Dailey, Ronald J.

doi:10.1080/00927879908826840

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2007

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“…Moreover, they found that Pearson's asymptotic test outperforms the asymptotic LR test. Parshall et al [17] studied various test statistics for asymptotic tests in small sample r × c tables. They found that the Pearson statistic and the Read and Cressie statistic give conservative tests, while the LR statistic is quite liberal.…”

Section: Resultsmentioning

confidence: 99%

Choice of test for association in small sample unordered r × c tables

Lydersen

Pradhan

Senchaudhuri

et al. 2007

Statistics in Medicine

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Pearson's chi-squared, the likelihood-ratio, and Fisher-Freeman-Halton's test statistics are often used to test the association of unordered r x 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 x c tables, mostly 3 x 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 x c tables.

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Section: Resultsmentioning

confidence: 99%