The approximate randomization test as an alternative to the F test in analysis of variance

In experimental psychology it is usually difficult to show that populations sampled meet the requirements for the use of t or F tests, or even that they are similar to populations sampled in Monte Carlo experiments designed to demonstrate the robustness of these parametric tests. Consequently, a test which makes weaker requirements without sacrificing power or versatility should be preferred. It is shown that this is true of modified approximate randomization tests, which, like the randomization tests on which they are based, use observed scores to set up a sampling distribution. The tests are versatile, since they can be used on factorial designs of any complexity and the results of Monte Carlo experiments indicate that their power approximates that of the F test when the assumptions underlying the latter are met and is significantly greater when the populations sampled are made up of two normal distributions with different means. It is concluded that, where adequate computing facilities are available, the approximate randomization test is preferable to an F test for analysis of variance designs.