Two-population sequential tests with three hypotheses

A sequential procedure is proposed for choosing one of three hypotheses concerning the difference between the means of two normal populations. It is shown that error probabilities are approximately independent of the sampling rule for a wide class of sampling rules, and approximate expressions are derived for these probabilities. A data-dependent sampling rule is given for minimizing any weighted average of the average sample numbers on the two populations, with the weights being allowed to depend on the difference between the means. It is shown that the rule is asymptotically optimal for the procedure, and simulation results indicate that it is nearly optimal for small sample sizes.