Probabilistic Parameter Estimates that Require Less Small Print

James A. Hanley

The American Statistician, 2026, vol. 80, issue 2, 258-264

Abstract: Although we have had nearly a century to refine it, our teaching of confidence intervals for parameters is still imperfect. Despite all of our warnings regarding these intervals, it is not uncommon for end-users to mis-interpret them. We discuss some possible reasons for this, and using a printed figure and a Shiny app, work through a simple and close-to-home example while trying to avoid many of these traps. We urge teachers to (a) begin with contexts that require less technical knowledge, or where the technical details can be kept out of the way (b) avoid the traditional (and symmetric) ’‘point estimate ± a z- or t-based margin of error” confidence intervals that lead to lazy and muddled thinking (c) start with a direct approach—rather than an indirect frequentist one that can end up being misinterpreted and (d) encourage the reverse logic that asks what parameter values might have produced the data we see, rather than what data values will be produced by a parameter value.

Date: 2026
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DOI: 10.1080/00031305.2025.2606079

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