Predict, Control, and Replicate to Understand: How Statistics Can Foster the Fundamental Goals of Science.

Abstract

Scientists abstract hypotheses from observations of the world, which they then deploy to test their reliability. The best way to test reliability is to predict an effect before it occurs. If we can manipulate the independent variables (the efficient causes) that make it occur, then ability to predict makes it possible to control. Such control helps to isolate the relevant variables. Control also refers to a comparison condition, conducted to see what would have happened if we had not deployed the key ingredient of the hypothesis: scientific knowledge only accrues when we compare what happens in one condition against what happens in another. When the results of such comparisons are not definitive, metrics of the degree of efficacy of the manipulation are required. Many of those derive from statistical inference, and many of those poorly serve the purpose of the cumulation of knowledge. Without ability to replicate an effect, the utility of the principle used to predict or control is dubious. Traditional models of statistical inference are weak guides to replicability and utility of results. Several alternatives to null hypothesis testing are sketched: Bayesian, model comparison, and predictive inference (p rep). Predictive inference shows, for example, that the failure to replicate most results in the Open Science Project was predictable. Replicability is but one aspect of scientific understanding: it establishes the reliability of our data and the predictive ability of our formal models. It is a necessary aspect of scientific progress, even if not by itself sufficient for understanding.