Presenting the Probabilities of Different Effect Sizes: Towards a Better Understanding and Communication of Statistical Uncertainty

How should social scientists understand and communicate the uncertainty of statistically estimated causal effects? It is well-known that the conventional significance-vs.-insignificance approach is associated with misunderstandings and misuses. Behavioral research suggests people understand uncertainty more appropriately in a numerical, continuous scale than in a verbal, discrete scale. Motivated by these backgrounds, I propose presenting the probabilities of different effect sizes. Probability is an intuitive continuous measure of uncertainty. It allows researchers to better understand and communicate the uncertainty of statistically estimated effects. In addition, my approach needs no decision threshold for an uncertainty measure or an effect size, unlike the conventional approaches, allowing researchers to be agnostic about a decision threshold such as p<5\% and a justification for that. I apply my approach to a previous social scientific study, showing it enables richer inference than the significance-vs.-insignificance approach taken by the original study. The accompanying R package makes my approach easy to implement.