We have suggested that confidence intervals do not support the inferences that their advocates believe they do. It is an interesting question how the theory of confidence intervals began with Neyman as a method of avoiding the problem of reasoning from data by making dichotomous statements (Neyman, 1937, 1941), eventually becoming a method that many believe is the best way to reason from data (e.g., G. Cumming & Fidler, 2009; G. Cumming & Finch, 2005) and a way to avoid dichotomous statements (e.g., G. Cumming, 2014; Hoekstra, Finch, Kiers, & Johnson, 2006; Wilkinson & Task Force on Statistical Inference, 1999). Regardless of how this confusion started, we believe it should be recognized that confidence interval theory offers only the shallowest of interpretations, and is not well-suited to the needs of scientists.
We do not believe that the theory of confidence intervals provides a viable foundation for the future of psychological methods. Confidence procedures that do not have Bayesian properties have other undesirable properties; confidence procedures that do have Bayesian properties can be justified using Bayesian theory. If we were to give up the use of confidence procedures, what would we lose? Abandoning the use of confidence procedures means abandoning a method that merely allows us to create intervals that include the true value with a fixed long-run probability. We suspect that if researchers understand that this is the only thing they will be losing, they will not consider it a great loss. By adopting Bayesian inference, they will gain a way of making principled statements about precision and plausibility. Ultimately, this is exactly what the advocates of CIs have wanted all along.