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Likelihood Ratio


A quantity used to test nested hypotheses. Let H^' be a nested hypothesis with n^' degrees of freedom within H (which has n degrees of freedom), then calculate the maximum likelihood of a given outcome, first given H^', then given H. Then

 LR=([likelihood H'])/([likelihood H]).

Comparison of -2ln(LR) to the critical value of the chi-squared distribution with n-n^' 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]).

See also

Negative Likelihood Ratio, Sensitivity, Specificity

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References

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 2, 3rd ed. New York: Wiley, pp. 211-212, 1971.Hoel, P. G. "Likelihood Ratio Tests." §9.1.4 in Introduction to Mathematical Statistics, 3rd ed. New York: Wiley, pp. 220-228, 1962.

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Likelihood Ratio

Cite this as:

Weisstein, Eric W. "Likelihood Ratio." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LikelihoodRatio.html

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