A Finite Sample Augmented LR Test for Mediation

Testing for mediation suffers from low power near the origin. This can be addressed by augmenting the LR critical region as discussed in previous work within an asymptotic framework. In this paper we consider exact distributions of test statistics and use this to derive optimal augmentation regions for arbitrary sample sizes. The resulting test is very simple and reliable, making it relevant for empirical research, even with a very small number of observations. This new test is α-coherent, as required for the p-values, which are easily calculated for the new test. Simulations confirm robust power improvement and size control, even with non-normal errors.