## Likelihood Ratio

A quantity used to test Nested Hypotheses. Let be a Nested Hypothesis with Degrees of Freedom within (which has Degrees of Freedom), then calculate the Maximum Likelihood of a given outcome, first given , then given . Then

Comparison of this ratio to the critical value of the Chi-Squared Distribution with Degrees of Freedom then gives the Significance of the increase in Likelihood.

The term likelihood ratio is also used (especially in medicine) to test nonnested complementary hypotheses as follows,