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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.
The likelihood ratio of a test provides a way to estimate the pre- and post-test probabilities of having a condition. With pre-test probability and likelihood ratio given, then, the post-test probabilities can be calculated by the following three steps: [17]
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.
The likelihood ratio is central to likelihoodist statistics: the law of likelihood states that 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.
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]
Note: Fisher's G-test in the GeneCycle Package of the R programming language (fisher.g.test) does not implement the G-test as described in this article, but rather Fisher's exact test of Gaussian white-noise in a time series. [10] Another R implementation to compute the G statistic and corresponding p-values is provided by the R package entropy.
In practice, the likelihood ratio is often used directly to construct tests — see likelihood-ratio test.However it can also be used to suggest particular test-statistics that might be of interest or to suggest simplified tests — for this, one considers algebraic manipulation of the ratio to see if there are key statistics in it related to the size of the ratio (i.e. whether a large ...
Pearson's chi-squared test or Pearson's test is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., Yates , likelihood ratio , portmanteau test in time series , etc.) – statistical ...