A note on combining dependent tests of significance

In combining several tests of significance the individual test statistics are allowed to be dependent. By choosing the weighted inverse normal method for the combination, the dependency of the original test statistics is then characterized by a correlation of the transformed statistics. For this correlation a confidence region, an unbiased estimator and an unbiased estimate of its variance are derived. The combined test statistic is extended to include the case of possibly dependent original test statistics. A simulation study shows the performance of the actual significance level.