Decoupling Visualization and Testing when Presenting Confidence Intervals

Confidence intervals are ubiquitous in the presentation of social science models, data, and effects. When several intervals are plotted together, one natural inclination is to ask whether the estimates represented by those intervals are significantly different from each other. Unfortunately, there is no general rule or procedure that would allow us to answer this question from the confidence intervals alone. It is well known that using the overlaps in 95% confidence intervals to perform significance tests at the 0.05 level does not work. Recent scholarship has developed and refined a set of tools for inferential confidence intervals that permit inference on confidence intervals with the appropriate type I error rate in many different bivariate contexts. These are all based on the same underlying idea of identifying the multiple of the standard error (i.e., a new confidence level) such that the overlap in confidence intervals matches the desired type I error rate. These procedures remain stymied by multiple simultaneous comparisons. We propose an entirely new procedure for developing inferential confidence intervals that decouples the testing and visualization that can overcome many of these problems in any visual testing scenario. We provide software in R and Stata to accomplish this goal.