Barnard's test

In statistics, Barnard's test is an exact test of the null hypothesis of independence of rows and columns in a contingency table. It is an alternative to Fisher's exact test but is more time-consuming to compute. The test was first published by George Alfred Barnard (1945, 1947) who claimed this test for 2×2 contingency tables is more powerful than Fisher's exact test.

Mehta and Senchaudhuri (2003) explain why Barnard's test can be more powerful than Fisher's under certain conditions.

When comparing Fisher’s and Barnard’s exact tests, the loss of power due to the greater discreteness of the Fisher statistic is somewhat offset by the requirement that Barnard’s exact test must maximize over all possible p-values, by choice of the nuisance parameter π. For 2 × 2 tables the loss of power due to the discreteness dominates over the loss of power due to the maximization, resulting in greater power for Barnard’s exact test. But as the number of rows and columns of the observed table increase, the maximizing factor will tend to dominate, and Fisher’s exact test will achieve greater power than Barnard’s.

Mato and Andres (1997) show how to compute the result of the test more quickly.

See also

• Fisher's exact test

References

• Barnard, G.A (1945). "A New Test for 2×2 Tables". Nature 156 (3954): 177. doi:10.1038/156177a0. 

• Barnard, G.A (1947). "Significance Tests for 2×2 Tables". Biometrika 34 (1/2): 123–138. JSTOR 2332517. 

• Mehta, Cyrus R.; Senchaudhuri, Pralay (2003) "Conditional versus Unconditional Exact Tests for Comparing Two Binomials" Retrieved 20 November 2009

• Mato, A. Silva; Andres, A. Martin (1997). "Simplifying the calculation of the P-value for Barnard's test and its derivatives". Statistics and Computing 7: 134–143. doi:10.1023/A:1018573716156. 

External links

• An implementation of Barnard’s exact test using R