Seems like an important paper, and a very cool website.
In this paper, we argue that advocacy of CIs is based on a folk understanding rather than a principled understanding of CI theory. We outline three fallacies underlying the folk theory of CIs, and place these in the philosophical and historical context of CI theory proper. Through an accessible example adapted from the statistical literature, we show how CI theory differs from the folk theory of CIs. Finally, we show the fallacies of confidence in the context of a CI advocated and commonly used for ANOVA and regression analysis, and discuss the implications of the mismatch between CI theory and the folk theory of CIs.