Effective communication of standard errors and confidence intervals

Abstract

When reporting estimates and associated standard errors (ses) or confidence intervals (CIs), the standard formats, “estimate (se)” and “estimate (95% CI: [lower, upper]),” can be confusing in text; in tables they hinder comparisons. Furthermore, some readers can misinterpret the CI format as indicating equal support for all reported values. To remedy these deficits, we recommend formats that (1) improve clarity in text and tables and (2) emphasize that an estimate and its associated uncertainty should be “connected at the hip” as a single unit. We recommend displaying an estimate with its se using est(se) and displaying an estimate with its CI using the triple of percentiles, 2.55097.5. The first author encouraged these formats in articles published in the Journal of the American Statistical Association, Applications and Case Studies articles. In their discussion of estimated deaths in Irag, Zeger and Johnson (2007) extended the CI format to the 5-number summary, 2.525507597.5. This display is reminiscent of the 5-number summary introduced by Tukey (1977). In both CI formats, the decreasing point size communicates decreasing likelihood. Indeed, the 5-number summary graphic is reminiscent of a likelihood function or posterior distribution.