Effects attributable to treatment: Inference in experiments and observational studies with a discrete pivot

In randomisation and permutation inference, pivotal arguments remove the hy pothesised treatment effect, thereby basing inferences on the null distribu tion in which the treatment has no effect. This is common, for instance, wi th additive treatment effects. The current paper uses 'attributable effects ' to expand substantially the scope of pivotal arguments. Attributable effe cts are defined for three cases, namely the 2 x 2 contingency table, displa cement effects and the Mann-Whitney-Wilcoxon statistic, and in each case re moving an appropriate attributable effect restores the familiar null random isation distribution of the associated statistic, yielding exact inferences . The procedure extends immediately for use in sensitivity analysis in nonr andomised observational studies.