Estimation and inference in the same-different test

On the basis of simulations, we show that the coverage probability of the Wald-based 95% CI for δ is often far from 95%, whereas the coverage probability of the profile likelihood-based CI is close to the desired 95%. We also show how the likelihood framework can be used to combine information from independent experiments possibly using different discrimination protocols to obtain inference for a common δ. Finally, we provide a free R package with an implementation of the likelihood methodology presented in this paper.