If we're so different, why do we keep overlapping? When 1 plus 1 doesn't make 2.

tistical results in medical journals have emphasized confidence intervals (CIs) as an adjunct to, or even a replacement for, statistical tests and p values. Because of the intimate links between the 2 concepts, authors now use statements like “the 95% CI overlaps 0” where they would formerly have stated “the difference is not statistically significant at the 5% level.” Although this interchangeability is technically correct in 1-sample situations, it does not carry over fully to comparisons involving 2 samples. A frequently encountered misconception is that if 2 independent 95% CIs overlap each other, as they do in Fig. 1, then a statistical test of the difference will not be statistically significant at the 5% level. Why is this not necessarily so? Consider the means in 2 independent groups, meanA and meanB, with for simplicity meanA being the smaller of the 2. The 95% CI for the mean in group A is approximately given by meanA plus or minus twice the standard error of the mean for that group, SEA, and correspondingly for group B. A mathematical check for whether these CIs overlap is given by adding the distance 2SEA (from meanA to the upper bound of the CI) to 2SEB and comparing this sum with the distance between the 2 means, that is, meanB minus meanA (Fig. 2). The CIs overlap when