Interpreting confidence interval overlap - you might be doing it wrong!

People will often compare two confidence intervals and if they do not overlap, take that as evidence of a 'significant' difference. However, in doing so people are performing a 'test' with a much smaller significance level than they think. You can have a 'significant' difference even when the confidence intervals overlap. In this video Darryl explains how that can happen and suggest an alternative approach for comparing two estimated quantities.