Broccoli Reduces The Risk of Splenetic Fever! The use of induction and falsifiability in statistics and model selection

Abstract

The title, a headline, and a typical one, from a newspaper's "Health & Wellness" section, usually written by a reporter who has just read a medical journal, can only be the result of an inductive argument, which is an argument from known contingent premisses to the unknown. What are the premisses and what is unknown for this headline and what does it mean to statistics? The importance--and rationality--of inductive arguments and their relation to the frequently invoked, but widely and poorly misunderstood, notion of `falsifiability' are explained in the context of statistical model selection. No probability model can be falsified, and no hope for model buidling should be sought in that concept.