A Primer on Visualizations for Comparing Populations, Including the Issue of Overlapping Confidence Intervals

A Joint Confidence Region for an Overall Ranking of Populations

“…Wright et al . ()). This is the approach that is currently taken by the Census Bureau's ACS and illustrated earlier with Table .…”

“…The underlying confidence intervals (23.5, 24.3) and (24.2, 26.4) for mean travel time (Table , under independence) respectively for Alabama and for Delaware overlap, as do their underlying confidence intervals for rank. In either case, we cannot safely determine whether the mean travel times or the ranks of Alabama and Delaware are necessarily significantly different, because it is known that the method of examining overlap of pairs of confidence intervals should not be used for formal hypothesis testing (Schenker and Gentleman, ; Wright et al ., ). If the primary goal is to make formal pairwise comparisons, then we suggest using a method that is specifically designed for this such as discussed by Wright et al .…”

“…If the primary goal is to make formal pairwise comparisons, then we suggest using a method that is specifically designed for this such as discussed by Wright et al . ().…”

“…Goldstein and Spiegelhalter () suggested the bootstrap as a means of obtaining interval estimates for ranks, as did Hall and Miller () and Wright et al . (, , ).…”

Graphing Within-Subjects Effects

“…Graphs can portray distributions and/or differences between distributions as well as relevant inferential statistics such as confidence intervals and significance tests. Although methods for including inferential statistics in graphs is an important topic and has been addressed in detail (Cousineau & O'Brien, 2014;Cumming & Finch, 2005;Wright, Klein, & Wieczorek, 2019), it is beyond the scope of this article to discuss the pros and cons of the various approaches or to recommend a specific one. Therefore, the example graphs shown here do not contain any inferential statistics.…”