Coherence in observational studies

It is often said that the coherence of an association between a treatment and outcomes is important in judging whether the association is causal. An attempt is made to quantify the evidence provided by a coherent association. This is done in two steps. First, a test is developed to detect a coherent association. The test is a generalization of the tests of Mann and Whitney, Wilcoxon, and Gehan. Second, the sensitivity of the test to hidden bias is examined. The question is whether a coherent pattern of associations implies less sensitivity to hidden biases. An example is considered in detail.