Understanding the misunderstanding: Why confidence intervals are poorly understood and evaluating proposed solutions across sensory modalities

Abstract

The error bar representation of a confidence interval is the most ubiquitous display of uncertainty in statistical analysis. However, despite this, error bars are poorly understood even by seasoned scientists and researchers across disciplines. The root of this misunderstanding is not certain, but researchers have posited several hypotheses ranging from the structure of the display itself, to how it is presented in the classroom. Studies have thus far been either incomplete or inconclusive, leading some to call for the elimination of the use of error bars entirely. However, research into statistics education (suggesting the error bar representation may not even be taught in contemporary classrooms) demonstrates that a lack of exposure in an educational likely contributes to the displays’ poor level of discernment. Furthermore, promising research into auditory uncertainty displays suggests that sound may be a better medium to present this information than vision. The studies conducted in this dissertation demonstrate that not only are auditory displays viable alternatives to visual representations of confidence intervals (i.e., error bars), but when used together can improve overall performance. Furthermore, the presence of visual displays was shown to enhance performance on questions involving confidence intervals, but not on other topics, suggesting that confidence intervals may hold a unique status when it comes how they are affected by alternative display types. Limited training was also shown to improve performance, suggesting that if confidence interval displays were taught in classrooms, overall performance could improve and lead students to understand this topic just as well as other statistical concepts. The success of the auditory representation could also lead to the creation of cheaper, more universally designed, materials to help convey uncertainty to all students, regardless of sensory ability.