Bartlett's test is a modification of the corresponding likelihood ratio test designed to make the approximation to the \ chi ^ 2 _ { k-1 } distribution better ( Bartlett, 1937 ).
12.
This distribution often arises in the power analysis of statistical tests in which the null distribution is ( perhaps asymptotically ) a chi-squared distribution; important examples of such tests are the likelihood ratio tests.
13.
The most important paper in this series is where Hsu obtains the first optimum property for the likelihood ratio test of the univariate linear hypothesis, in fact essentially the first nonlocal optimum property for any hypothesis specifying the value of more than one parameter.
14.
For fixed effects testing, they say, a likelihood ratio test for REML fits is not feasible, because changing the fixed effects specification changes the meaning of the mixed effects, and the restricted model is therefore not nested within the larger model.
15.
A "'likelihood ratio test "'is any test with critical region ( or rejection region ) of the form \ { x \ mid \ Lambda \ le c \ } where c is any number satisfying 0 \ le c \ le 1.
