When metrics matter: How reasoning in different metrics impacts judgments of uncertainty

The uncertainty of a point estimate, often conceptualized and quantified via a prediction interval, can vary in both magnitude (e.g., width) and symmetry. Further, when people make many types of estimates, they can use different but equitable metrics (e.g., feet vs. meters). In a series of experiments, we investigate whether using different metrics impacts people's estimates of uncertainty. Three empirical regularities guide our focus: First, people believe risk scales with magnitude, reporting greater uncertainty for bigger point estimates, leading to inconsistent prediction intervals across metrics differing by a fixed additive constant. Second, people are insufficiently sensitive to unit changes, leading to inconsistent prediction interval widths across metrics differing by a multiplicative constant. Third, people tend to assume that distributions are symmetric, leading to inconsistent symmetry across metrics differing by an inverse transformation. Together, these three regularities exemplify how uncertainty estimations are sensitive to metric in substantive ways.