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Likelihood Ratio: An example "test" is that the physical exam finding of bulging flanks has a positive likelihood ratio of 2.0 for ascites. Estimated change in probability: Based on table above, a likelihood ratio of 2.0 corresponds to an approximately +15% increase in probability.
Diagram relating pre- and post-test probabilities, with the green curve (upper left half) representing a positive test, and the red curve (lower right half) representing a negative test, for the case of 90% sensitivity and 90% specificity, corresponding to a likelihood ratio positive of 9, and a likelihood ratio negative of 0.111.
The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.
False positive COVID-19 tests—when your result is positive, but you aren’t actually infected with the SARS-CoV-2 virus—are a real, if unlikely, possibility, especially if you don’t perform ...
The positive predictive value (PPV), or precision, is defined as = + = where a "true positive" is the event that the test makes a positive prediction, and the subject has a positive result under the gold standard, and a "false positive" is the event that the test makes a positive prediction, and the subject has a negative result under the gold standard.
The rest of the candidate conditions (for which there is no established likelihood ratio for the test at hand) can, for simplicity, be adjusted by subsequently multiplying all candidate conditions with a common factor to again yield a sum of 100%.
To be clear: These limitations on Wilks’ theorem do not negate any power properties of a particular likelihood ratio test. [3] The only issue is that a χ 2 {\displaystyle \chi ^{2}} distribution is sometimes a poor choice for estimating the statistical significance of the result.
Two other standard generalizations of the likelihood ratio are (a) the generalized likelihood ratio as used in the standard, classical likelihood ratio test and (b) the Bayes factor. Importantly, neither (a) nor (b) are e-variables in general: generalized likelihood ratios in sense (a) are not e-variables unless the alternative is simple (see ...