Interval estimates are commonly used to descriptively communicate the degree of uncertainty in numerical values. Conventionally, low alpha levels (e.g., .05) ensure a high probability of capturing the target value between interval endpoints. Here, we test whether alpha levels and individual differences in numeracy influence distributional inferences. In the reported experiment, participants received prediction intervals for fictitious towns’ annual rainfall totals (assuming approximately normal distributions). Then, participants estimated probabilities that future totals would be captured within varying margins about the mean, indicating the approximate shapes of their inferred probability distributions. Results showed that low alpha levels (vs. moderate levels; e.g., .25) more frequently led to inferences of over-dispersed approximately normal distributions or approximately uniform distributions, reducing estimate accuracy. Highly numerate participants made more accurate estimates overall, but were more prone to inferring approximately uniform distributions. These findings have important implications for presenting interval estimates to various audiences.

Overprecision is the most robust type of overconfidence. We present a new method that significantly reduces this bias and offers insight into its underlying cause. In three experiments, overprecision was significantly reduced by forcing participants to consider all possible outcomes of an event. Each participant was presented with the entire range of possible outcomes divided into intervals, and estimated each interval’s likelihood of including the true answer. The superiority of this Subjective Probability Interval Estimate (SPIES) method is robust to range widths and interval grain sizes. Its carryover effects are observed even in subsequent estimates made using the conventional, 90% confidence interval method: judges who first made SPIES judgments considered a broader range of values in subsequent conventional interval estimates as well.