Always Usable Limited-Length Sequential Permutation Tests for Two-Way ANOVA.

The data are independent observations from two or more sources. Under the null hypothesis, observations from the same source have a common unknown distribution can be arbitrary. Observations are obtained in successive groups each containing a set of specified size from each source, with a stated maximum number of groups available. An overall test consists of a succession of subtests and is significant when at least one subtest is significant. Exact null probabilities are obtainable, through use of appropriate permutation models and special kinds of subtest statistics. The subtests are such that the significance level of each new subtest is independent of preceding subtest results. The overall test terminates when a significant subtest occurs with saving in time and expense. Subtests are always included wherein the second and each following group is compared with the totality of previous groups to investigate whether observations from the same source continue to be from the same population. Ordinarily, a single comprehensive subtest occurs for each comparison. However, a separate subtest could occur for each source. Also, an additional subtest or separate subtests for sources could be made to investigate whether the first group satisfies the null hypothesis. Unconditional tests can be obtained when ranks are used and in some other cases. Some possible uses in quality control are outlined. Author