On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals

TLDR

Data analysts often judge significance by checking overlap of confidence intervals, a simple but potentially flawed approach. The study compares the overlap technique to the standard significance test under common asymptotic assumptions. The authors compare the overlap method to the standard test assuming consistency, asymptotic normality, and independence. The overlap method is more conservative, rejecting the null less often and failing to reject it more frequently than the standard test, so rejection implies standard rejection but not vice versa.

Abstract

AbstractTo judge whether the difference between two point estimates is statistically significant, data analysts often examine the overlap between the two associated confidence intervals. We compare this technique to the standard method of testing significance under the common assumptions of consistency, asymptotic normality, and asymptotic independence of the estimates. Rejection of the null hypothesis by the method of examining overlap implies rejection by the standard method, whereas failure to reject by the method of examining overlap does not imply failure to reject by the standard method. As a consequence, the method of examining overlap is more conservative (i.e., rejects the null hypothesis less often) than the standard method when the null hypothesis is true, and it mistakenly fails to reject the null hypothesis more frequently than does the standard method when the null hypothesis is false. Although the method of examining overlap is simple and especially convenient when lists or graphs of confidence intervals have been presented, we conclude that it should not be used for formal significance testing unless the data analyst is aware of its deficiencies and unless the information needed to carry out a more appropriate procedure is unavailable.KEY WORDS: EfficiencyInferencePowerTest of significanceTwo-sample problemType I error