The Interpretation of Scholars' Interpretations of Confidence Intervals: Criticism, Replication, and Extension of Hoekstra et al. (2014)

Hoekstra et al. (Psychonomic Bulletin & Review, 2014, 21:1157–1164) surveyed the interpretation of confidence intervals (CIs) by first-year students, master students, and researchers with six items expressing misinterpretations of CIs. They asked respondents to answer all items, computed the number of items endorsed, and concluded that misinterpretation of CIs is robust across groups. Their design may have produced this outcome artifactually for reasons that we describe. This paper discusses first the two interpretations of CIs and, hence, why misinterpretation cannot be inferred from endorsement of some of the items. Next, a re-analysis of Hoekstra et al.'s data reveals some puzzling differences between first-year and master students that demand further investigation. For that purpose, we designed a replication study with an extended questionnaire including two additional items that express correct interpretations of CIs (to compare endorsement of correct vs. nominally incorrect interpretations) and we asked master students to indicate which items they would have omitted had they had the option (to distinguish deliberate from uninformed endorsement caused by the forced-response format). Results showed that incognizant first-year students endorsed correct and nominally incorrect items identically, revealing that the two item types are not differentially attractive superficially; in contrast, master students were distinctively more prone to endorsing correct items when their uninformed responses were removed, although they admitted to nescience more often that might have been expected. Implications for teaching practices are discussed.