In certain circumstances, one wishes to test one hypothesis only if certain other hypotheses have been rejected. This ordering of hypotheses simplifies the task of controlling the probability of rejecting any true hypothesis. In an example from an observational study, a treated group is shown to...

Some experiments involve more than one random assignment of treatments to units. An analogous situation arises in certain observational studies, although randomization is not used, so each assignment may be biased. If each assignment is suspect, it is natural to ask whether there are separate...

Outside the field of statistics, the literature on observational studies offers advice about research designs or strategies for judging whether or not an association is causal, such as multiple operationalism or a dose-response relationship. These useful suggestions are typically informal and...

There are two treatments, each of which may be applied or withheld, yielding a 2 x 2 factorial arrangement with three degrees of freedom between groups. The differential effect of the two treatments is the effect of applying one treatment in lieu of the other. In randomised experiments, the...