Statistical Proof

Statistical proof is the rational demonstration of degree of certainty for a proposition, hypothesis or theory that is used to convince others subsequent to a statistical test of the supporting evidence and the types of inferences that can be drawn from the test scores. Statistical methods are used to increase our understanding of the facts and the proof demonstrates the validity and logic of inference with explicit reference to a hypotheses, the experimental data, the facts, the test, and the odds. Proof has two essential aims, the first is to convince and the second is to explain the proposition through peer and public review.

The burden of proof rests on the demonstrable application of the statistical method, disclosure of the assumptions, and the relevance that the test has with respect to a genuine understanding of the data relative to the external world. There are adherents to several different statistical philosophies of inference, such as Bayes theorem versus the likelihood function, or positivism versus critical rationalism. These methods of reason have direct bearing on statistical proof and its interpretations in the broader philosophy of science.

A common demarcation between science and non-science is the hypothetico-deductive proof of falsification developed by Karl Popper, which is well a established practice in the tradition of statistics. Other modes of inference, however, may include the inductive and abductive modes of proof. Scientists do not use statistical proof as a means to attain certainty, but to falsify claims and explain theory. Science cannot achieve absolute certainty nor is it a continuous march toward an objective truth as the vernacular as opposed to the scientific meaning of the term "proof" might imply. Statistical proof offers a kind of proof of a theories falsity and the means to learn heuristically through repeated statistical trials and experimental error. Statistical proof also has applications in legal matters with implications for the legal burden of proof.