Recommended tests for association in 2×2 tables

Unit for Applied Clinical Research, Department of Cancer Research and Molecular Medicine, Norwegian University of Science and Technology, Trondheim, Norway.
Statistics in Medicine (Impact Factor: 1.83). 03/2009; 28(7):1159-75. DOI: 10.1002/sim.3531
Source: PubMed


The asymptotic Pearson's chi-squared test and Fisher's exact test have long been the most used for testing association in 2x2 tables. Unconditional tests preserve the significance level and generally are more powerful than Fisher's exact test for moderate to small samples, but previously were disadvantaged by being computationally demanding. This disadvantage is now moot, as software to facilitate unconditional tests has been available for years. Moreover, Fisher's exact test with mid-p adjustment gives about the same results as an unconditional test. Consequently, several better tests are available, and the choice of a test should depend only on its merits for the application involved. Unconditional tests and the mid-p approach ought to be used more than they now are. The traditional Fisher's exact test should practically never be used.

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    • "The other two widely applied methods in 2 × 2 contingency tables, i.e., Pearson's chisquared test (Pearson, 1900) and Fisher's exact test (Fisher, 1925), were not considered a good fit for this study. This is because the chisquared test is not suitable for smaller samples and Fisher's exact test, though valid for small sample sizes, is conservative and not as powerful as Barnard's exact test (Mehta and Hilton, 1993; Mehta and Senchaudhuri, 2003; Lydersen et al., 2009). As an alternative to Fisher's exact test, the non-parametric Barnard's exact test is more powerful because of its requirement to maximize over all possible p-values by considering the nuisance parameter(s), which compensates the loss of statistical power caused by the greater discreteness of the Fisher statistic (Galili, 2010; Mehta and Senchaudhuri, 2003). "

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    • "Baseline-adjusted between-group differences for all continuous endpoints were assessed with the use of analysis-of-covariance using outcome measurements at predefined time points as response variables, and treatment and baseline measurements as covariates. Dichotomous endpoints were compared with the Pearson chi-square test or Suissa-Shuster exact unconditional test, depending on expectedvalue distribution[24]. No adjustments for multiple analyses were made, owing to highly correlated endpoints. "
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