A Comparison of Some Approximate F-tests.

When an experiment is run with a factorial layout and some of the factors are random effects, there may not be an exact test for some effect of interest. This paper considers three statistics that could be used to test that hypothesis using a ratio of linear combinations of independent Chi-square statistics. The common case, utilizing four Chi-square statistics, is examined for a number of configurations of nuisance parameters. Both the power and the probability of a type I error are used in the comparison. Two statistics appear to be equally good over a large region and, in certain situations, the statistics involving the subtraction of Chi-square statistics is shown to be more stable. [ABSTRACT FROM AUTHOR]