Robust hybrid tests for the two-sample location problem

The t-test is uniformly most powerful for comparing the location parameters of two normal distributed populations. For non-normal data, robust tests can be more powerful than the t-test. We introduce a new parametric test statistic combining the p-values of the t-test and robust tests. In the normal distribution situation, this new test has a very small power loss compared to the t-test, but in the non-normal situation higher power than the t-test. The Pitman efficiency of 3pi(-1) = 0.955 gives an upper bound on the efficiency of nonparametric tests in the normal situation. Our new test (which is parametric) exceeds the Pitman bound when the sample sizes are small.