Given a piece of evidence and two hypotheses $H_{i}$ and $H_{j},$ the likelihood ratio between them is the ratio of the likelihood each hypothesis assigns to $e_{0} .$

For example, imagine the evidence is $e$ = "Mr. Boddy was knifed", and the hypotheses are $H_{P}$ = "Professor Plum did it" and $H_{W}$ = "Mrs. White did it." Let's say that, if Professor Plum were the killer, we're 25% sure he would have used a knife. Let's also say that, if Mrs. White were the killer, there's only a 5% chance she would have used a knife. Then the likelihood ratio of $e_{0}$ between $H_{P}$ and $H_{W}$ is 25/5 = 5, which says that $H_{P}$ assigns five times as much likelihood to $e$ as does $H_{W},$ which means that the evidence supports the "Plum did it" hypothesis five times as much as it supports the "Mrs. White did it" hypothesis.

A likelihood ratio of 5 denotes relative likelihoods of $(5 : 1) .$ Relative likelihoods can be multiplied by odds in order to update those odds, as per Bayes' rule.

Likelihood ratio