Do overlapping confidence intervals mean no difference?

Question

Group A has a 95% confidence interval for its mean of $[10,\ 14]$ , and group B has $[13,\ 17]$ . The intervals overlap (both include 13 to 14). A colleague concludes the two group means are not significantly different.

Is the colleague's conclusion valid?

Accepted Answer

Answer: no, not necessarily. Why overlap is not the right test. To compare two means you need a confidence interval for the difference, whose standard error is \sqrt{	ext{SE}A^{2} + 	ext{SE}B^{2}}. Judging by whether the two separate intervals overlap uses the wrong yardstick and is too conservative: intervals can overlap even when the difference interval excludes zero, so the difference can be significant despite visible overlap. The correct approach. Build the interval for \bar{x}B - \bar{x}A directly and check whether it contains zero. Only that interval answers the comparison question. …

Do overlapping confidence intervals mean no difference?

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