Beyond Statistics: Accepting the Null Hypothesis in Mature Sciences

Abstract

Scientific theories explain phenomena using simplifying assumptions—for instance, that the speed of light does not depend on the direction in which the light is moving, or that the shape of a pea plant’s seeds depends on a small number of alleles randomly obtained from its parents. These simplifying assumptions often take the form of statistical null hypotheses; hence, supporting these simplifying assumptions with statistical evidence is crucial to scientific progress, though it might involve “accepting” a null hypothesis. We review two historical examples in which statistical evidence was used to accept a simplifying assumption (that there is no luminiferous ether and that genetic traits are passed on in discrete forms) and one in which the null hypothesis was not accepted despite repeated failures (gravitational waves), drawing lessons from each. We emphasize the role of the scientific context in acceptance of the null: Accepting a null hypothesis is never a purely statistical affair.