The Limited Role of Formal Statistical Inference in Scientific Inference

ABSTRACT Such is the grip of formal methods of statistical inference—that is, frequentist methods for generalizing from sample to population in enumerative studies—in the drawing of scientific inferences that the two are routinely deemed equivalent in the social, management, and biomedical sciences. This, despite the fact that legitimate employment of said methods is difficult to implement on practical grounds alone. But supposing the adoption of these procedures were simple does not get us far; crucially, methods of formal statistical inference are ill-suited to the analysis of much scientific data. Even findings from the claimed gold standard for examination by the latter, randomized controlled trials, can be problematic. Scientific inference is a far broader concept than statistical inference. Its authority derives from the accumulation, over an extensive period of time, of both theoretical and empirical knowledge that has won the (provisional) acceptance of the scholarly community. A major focus of scientific inference can be viewed as the pursuit of significant sameness, meaning replicable and empirically generalizable results among phenomena. Regrettably, the obsession with users of statistical inference to report significant differences in data sets actively thwarts cumulative knowledge development. The manifold problems surrounding the implementation and usefulness of formal methods of statistical inference in advancing science do not speak well of much teaching in methods/statistics classes. Serious reflection on statistics' role in producing viable knowledge is needed. Commendably, the American Statistical Association is committed to addressing this challenge, as further witnessed in this special online, open access issue of The American Statistician.