Likelihood-ratio test - Wikipedia, the free encyclopedia

In stat ist ics, a likelihood rat io test is a stat ist ical test used to compare the f it of two models, one of which (the null model) is a special case of the other (the alternative model). The test is based on the likelihood rat io, which expresses how many t imes more likely the data are under one model than the other. This likelihood rat io, or equivalent ly its logarithm, can then be used to compute a pvalue, or compared to a crit ical value to decide whether to reject the null model in favour of the alternat ive model. When the logarithm of the likelihood rat io is used, the stat ist ic is known as a log-likelihood rat io stat ist ic, and the probability distribut ion of this test stat ist ic, assuming that the null model is t rue, can be approximated using Wilks' theorem.