Summary: Abraham Wald developed the Sequential Probability Ratio Test in the 1940’s to perform simple vs. simple hypothesis tests that would control both Type I and Type II error rates. Some applications require a test of three hypotheses. In addition, to perform a simple vs. composite two- sided test, a three-hypotheses test with all hypotheses simple has been suggested. Methods have been proposed that will test three hypotheses sequentially. They range widely in simplicity and accuracy.
In this paper, approximate probabilities of error for Armitage’s test are derived. A method of adjusting the error rates used to establish the decision boundaries in order to attain the nominal error rates is developed. The procedure is compared to existing ones by Monte-Carlo simulation.