G-test
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A G-test is a likelihood ratio test or a maximum likelihood statistical significance test.
References
2016
- (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/G-test 2016-08-13
- In statistics, G-tests are likelihood-ratio or maximum likelihood statistical significance tests that are increasingly being used in situations where chi-squared tests were previously recommended.
- [math]\displaystyle{ G = 2\sum_{i} {O_{i} \cdot \ln\left(\frac{O_i}{E_i}\right)}, }[/math]
- where Oi is the observed count in a cell, Ei is the expected count under the null hypothesis, ln denotes the natural logarithm, and the sum is taken over all non-empty cells.
- G-tests have been recommended at least since the 1981 edition of the popular statistics textbook by Robert R. Sokal and F. James Rohlf.
- Distribution and usage
- Given the null hypothesis that the observed frequencies result from random sampling from a distribution with the given expected frequencies, the distribution of G is approximately a chi-squared distribution, with the same number of degrees of freedom as in the corresponding chi-squared test.
- For very small samples the multinomial test for goodness of fit, and Fisher's exact test for contingency tables, or even Bayesian hypothesis selection are preferable to the G-test.