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The likelihood ratio is central to likelihoodist statistics: the law of likelihood states that the degree to which data (considered as evidence) supports one parameter value versus another is measured by the likelihood ratio. In frequentist inference, the likelihood ratio is the basis for a test statistic, the so-called likelihood-ratio test.
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.
Thus the likelihood-ratio test tests whether this ratio is significantly different from one, or equivalently whether its natural logarithm is significantly different from zero. 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 ...
It is possible to do a calculation of likelihood ratios for tests with continuous values or more than two outcomes which is similar to the calculation for dichotomous outcomes. For this purpose, a separate likelihood ratio is calculated for every level of test result and is called interval or stratum specific likelihood ratios. [4]
To compare effect sizes of the interactions between the variables, odds ratios are used. Odds ratios are preferred over chi-square statistics for two main reasons: [1] 1. Odds ratios are independent of the sample size; 2. Odds ratios are not affected by unequal marginal distributions.
The commonly used chi-squared tests for goodness of fit to a distribution and for independence in contingency tables are in fact approximations of the log-likelihood ratio on which the G-tests are based. [4] The general formula for Pearson's chi-squared test statistic is
Once the calculation of the likelihood ratio is made, the number calculated is turned into a statement to provide meaning to the statistic. For the previous example, if the LR calculated is x, then the LR means that the probability of the evidence is x times more likely if the sample contains the victim and the suspect than if it contains the ...
Given a model, likelihood intervals can be compared to confidence intervals. If θ is a single real parameter, then under certain conditions, a 14.65% likelihood interval (about 1:7 likelihood) for θ will be the same as a 95% confidence interval (19/20 coverage probability).