Inference of casual risk differences: testing statistical hypotheses

The use of unconditional tests for comparing hypotheses on the 2×2 binomial trial is still not widespread in the applications, despite these preserve the signi cance level and usually are more powerful than conditional exact tests for moderate to small samples. Previously, this was due to the bigger computational demand of this approach with respect to the conditional approach. Today, softwares can easily compute the p-values of both conditional and unconditional tests. In this thesis the Suissa and Shuster (1985)'s unconditional test is reviewed and a new R algorithm aimed to derive exact unconditional p-values is proposed. We use both the classical Lehmann (1959)'s procedure and the Berger and Boos (1994)'s procedure, which calculates the p-values by maximizing the null power function on a con dence interval for the nuisance parameter. Optimal values for the con dence level are derived for di erent degrees of imbalance of the sample sizes. Furthermore, we propose the use of the unconditional approach for testing statistical hypotheses within the framework of the Rubin Causal Model.