Barnard's test
Encyclopedia
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.
Mato and Andres (1997) show how to compute the result of the test more quickly.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, Barnard's test is an exact test
Exact test
In statistics, an exact test is a test where all assumptions upon which the derivation of the distribution of the test statistic is based are met, as opposed to an approximate test, in which the approximation may be made as close as desired by making the sample size big enough...
of the null hypothesis
Null hypothesis
The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. The null hypothesis typically corresponds to a general or default position...
of independence of rows and columns in a contingency table
Contingency table
In statistics, a contingency table is a type of table in a matrix format that displays the frequency distribution of the variables...
. It is an alternative to Fisher's exact test
Fisher's exact test
Fisher's exact test is a statistical significance test used in the analysis of contingency tables where sample sizes are small. It is named after its inventor, R. A...
but is more time-consuming to compute. The test was first published by George Alfred Barnard
George Alfred Barnard
George Alfred Barnard was a British statistician known particularly for his work on the foundations of statistics and on quality control.-Biography:...
(1945, 1947) who claimed this test for 2×2 contingency tables is more powerful
Statistical power
The power of a statistical test is the probability that the test will reject the null hypothesis when the null hypothesis is actually false . The power is in general a function of the possible distributions, often determined by a parameter, under the alternative hypothesis...
than Fisher's exact test
Fisher's exact test
Fisher's exact test is a statistical significance test used in the analysis of contingency tables where sample sizes are small. It is named after its inventor, R. A...
.
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.