Likelihood-ratio Test
In statistics, a likelihood ratio test is a statistical test used to compare the fit 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 ratio, which expresses how many times more likely the data are under one model than the other. This likelihood ratio, or equivalently its logarithm, can then be used to compute a p-value, or compared to a critical value to decide whether to reject the null model in favour of the alternative model. When the logarithm of the likelihood ratio is used, the statistic is known as a log-likelihood ratio statistic, and the probability distribution of this test statistic, assuming that the null model is true, can be approximated using Wilks' theorem.
In the case of distinguishing between two models, each of which has no unknown parameters, use of the likelihood ratio test can be justified by the Neyman–Pearson lemma, which demonstrates that such a test has the highest power among all competitors.
Read more about Likelihood-ratio Test: Use, Background, Simple-versus-simple Hypotheses, Definition (likelihood Ratio Test For Composite Hypotheses)
Famous quotes containing the word test:
“First follow Nature, and your judgment frame
By her just standard, which is still the same;
Unerring Nature, still divinely bright,
One clear, unchanged, and universal light,
Life, force, and beauty must to all impart,
At once the source, and end, and test of art.”
—Alexander Pope (1688–1744)