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Analytic statistical methods are in very strong contrast with what is normally taught in most statistics textbooks, which describe the problem as one of “accepting” or “rejecting” hypotheses. In the real world of quality improvement, we must look for repeatability over many different populations. Walter Shewhart added the new concept of statistical control, which defines repeatability over time sampling from a process, rather than a population.

For example, the effectiveness of a drug may depend on the age of the patient, or previous treatment, or the stage of the disease. Ideally we want one treatment that works well in all foreseeable circumstances, but we may not be able to get it. Once we recognize that the aim of the study is to predict, we can see what range of possibilities are most important. We not only design studies to cover a wide range of circumstances, but to make the “inference gap” as small as possible.

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