A statistic used in an alternative to the chi-squared test of goodness-of-fit. The two test statistics usually have similar values and both have approximate chi-squared distributions when the model under test is a correct description of the data. The G² test is usually preferred when comparing hierarchical models. If the observed cell frequencies are denoted by O₁, O₂,…, O_k and the corresponding expected cell frequencies (see expected frequency) by E₁, E₂,…, E_k, respectively, G² is given bywhere ln is the natural logarithm. The test results from the work of Neyman and Egon Pearson, who first used the term ‘likelihood ratio’ in a 1931 paper.