A Modified Sequential Probability Ratio Test

We describe a modified sequential probability ratio test that can be used to reduce the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. Examples are provided for $z$ tests, $t$ tests, and tests of binomial success probabilities. A description of a software package to implement the test designs is provided. We compare the sample sizes required in fixed design tests conducted at 5$\mathrm{\%}$ significance levels to the average sample sizes required in sequential tests conducted at 0.5$\mathrm{\%}$ significance levels, and we find that the two sample sizes are approximately equal.