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
![LR=([likelihood H'])/([likelihood H]).](/images/equations/LikelihoodRatio/NumberedEquation1.svg) |
Comparison of 
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,
![LR=([true positive rate])/([false positive rate])=([sensitivity])/(1-[specificity]).](/images/equations/LikelihoodRatio/NumberedEquation2.svg) |
