Statistics

An instrument or instrumental variable manipulates a treatment and affects the outcome only indirectly through its manipulation of the treatment. For instance, encouragement to exercise might increase cardiovascular fitness, but only indirectly to the extent that it increases exercise. If...

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...

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...