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The use of significance tests to express statistical evidence has a long history.

As discussed in Chapter 8, Birnbaum introduces (), the evidential meaning of obtaining data as an instance of experiment E. Following Birnbaum, various authors have wrestled with the problem of developing a single set of postulates under which statistical inference can be made coherent. But as we claim in Section 8.3, ()does not exist. Evidence is grounds for belief—an imprecise concept. There must be many valid reasons for believing and hence many ways of making the evidence concept precise. Most of our beliefs are held because mother—or someone else we trust—told us so. The law trusts sworn testimony. Scientific and statistical evidence are other different grounds for belief—supposedly particularly reliable kinds. Instead of () we are concerned with (), the evidential meaning of observing v as an instance of E, in the context of theory T.

On the inside of the front cover of each issue of its , the American Statistical Association declares that it is a scientific organization. In what sense is statistics scientific? There are several common usages of the word “science.” First, science is sometimes used as a synonym for systematized knowledge. Or, in more detail, a science is the systematized knowledge produced by the study of the structure of a class of concepts. A second usage is that science is explanation. Third and more narrowly, science is sometimes taken to mean the systemized knowledge of “nature,” of the “real world.” A fourth usage, due to Karl Pearson, is that any field of study which employs the scientific method of hypothesis, deduction and experiment is a science. A fifth usage is common in physics; Ruhla (1993) writes “prediction = science.”

We start from the view that the purpose of statistical theory is to and what we choose to present as statistical evidence, i.e., what data and reasoning should cause us to adopt certain conclusions. We arrive at the position that there are kinds of statistical evidence, each of which lends a different explanatory insight and none of which is perfect. The explanatory models which we consider—along with their criteria—appear in Table 14.1.