Inference by eye: Reading the overlap of independent confidence intervals

When 95 per cent confidence intervals (CIs) on independent means do not overlap, the two-tailed p-value is less than 0.05 and there is a statistically significant difference between the means. However, p for non-overlapping 95 per cent CIs is actually considerably smaller than 0.05: If the two CIs just touch, p is about 0.01, and the intervals can overlap by as much as about half the length of one CI arm before p becomes as large as 0.05. Keeping in mind this rule-that overlap of half the length of one arm corresponds approximately to statistical significance at p = 0.05-can be helpful for a quick appreciation of figures that display CIs, especially if precise p-values are not reported. The author investigated…