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g-test

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.The general formula for G is G = 2 ∑ i O i ⋅ ln ⁡ ( O i E i ) , {\displaystyle G=2\sum _{i}{O_{i}\cdot \ln \left({\frac {O_{i}}{E_{i}}}\right)},} where O i ≥ 0 {\textstyle O_{i}\geq 0} is the observed count in a cell, E i > 0 {\textstyle E_{i}>0} is the expected count under the null hypothesis, ln {\textstyle \ln } denotes the natural logarithm, and the sum is taken over all non-empty cells. Furthermore, the total observed count should be equal to the total expected count:where N {\textstyle N} is the total number of observations. G-tests have been recommended at least since the 1981 edition of Biometry, a statistics textbook by Robert R. Sokal and F. James Rohlf.

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