The boundary effect: Perceived post hoc accuracy of prediction intervals

Abstract

Predictions of magnitudes (costs, durations, environmental events) are often given as uncertainty intervals (ranges). When are such forecasts judged to be correct? We report results of four experiments showing that forecasted ranges of expected natural events (floods and volcanic eruptions) are perceived as accurate when an observed magnitude falls inside or at the boundary of the range, with little regard to its position relative to the “most likely” (central) estimate. All outcomes that fell inside a wide interval were perceived as equally well captured by the forecast, whereas identical outcomes falling outside a narrow range were deemed to be incorrectly predicted, in proportion to the magnitude of deviation. In these studies, ranges function as categories, with boundaries distinguishing between right or wrong predictions, even for outcome distributions that are acknowledged as continuous, and for boundaries that are arbitrarily defined (for instance, when the narrow prediction interval is defined as capturing 50 percent and the wide 90 percent of all potential outcomes). However, the boundary effect is affected by label. When the upper limit of a range is described as a value that “can” occur (Experiment 5), outcomes both below and beyond this value were regarded as consistent with the forecast.

Keywords

• prediction
• forecasting
• prediction intervals