Statistical Practice as Argumentation: A Sketch of a Theory of Applied Statistics

We have theories of statistics and we use statistical methods to solve subject matter problems. One might expect that the theories would affect how the methods are used, but they do so only superficially, because all statistical theories are quite incomplete as descriptions of and prescriptions for statistical practice. This paper sketches an extension of Bayesian theory that might address this incompleteness. The extension is based on five ideas: 1. The product of a statistical analysis is an argument — not an HPD region, posterior distribution, decision, or other data summary, but the entire argument, including premises and logical steps. 2. Arguments come in several logically distinct types, with an argument’s type being defined by the form of its conclusion. The paper catalogs the types of argument and identifies the main burden of each. 3. EDA and model-building activities establish a plausible, tractable baseline argument for a given problem and dataset. 4. Diagnostics and sensitivity analyses vary the premises of the baseline argument and display the resulting variation in the conclusion (as opposed to intermediate quantities). 5. An argument is strong to the extent that: its premises are conclusions of strong arguments, or the region of premises yielding the same conclusion is large. A simple example demonstrates the mechanics of the extended theory. The example is then generalized to draw implications for statistical foundations, methods, and computing. This paper amounts to a research agenda, so it poses more problems than it solves.