Effects and Associations
This chapter is somewhat different from most of the other chapters in the book. The main concern here is not statistical inference, that is, generalization from the sample to the underlying population, rather inference about expected effects of a potential treatment. Effects can be causal, evidential, and attributable, so even the formulation of the question requires some thought. As will be illustrated, such an inference would not be straightforward, even if the analyst had access to full population data. The conventional wisdom is that from data one can infer associations, but association is not necessarily causation. First, a closer look is taken at this statement, in particular, the meanings of causation and how they relate to the statistical analysis. Then, various concepts of association are discussed, out of which the one measured by the odds ratio is only one possibility. The position taken is that the different published ideas as to how to measure association are, in fact, measures of different concepts of associations. Measuring effects is a related but distinct task. The traditional theory of testing the existence and measuring the size of an effect is based on a particular way of collecting data about the responses to different treatments. This data collection procedure, the so-called designed experiment, is described, and it is explained why it is considered appropriate to establish the existence of effects. The other traditional data collection design, called observational study, is also described, and the fundamental difference with respect to measuring effects is highlighted. Next, we give a very short overview of some of the contemporary approaches to establishing effects, even causal effects, based on observational data. Such a thing was considered traditionally impossible, and the ideas summarized here, although perhaps not yet universally accepted, already have had a great impact on statistical thinking.
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