The 95% confidence intervals (95% CI) around a value are the range within which there is a 95% chance that the true value lies. Similarly, the 95% CIs around a difference are the range in which there is a 95% chance that the true difference lies.
If the means of two groups have overlapping 95% CIs, then the two groups are not statistically significantly different. If the 95% CI of the difference between two groups overlaps zero, then the difference between the two groups in not statistically significant.
Statistical and clinical significance should not be confused. A very large study can generate very narrow 95% CIs (or very small p values) for very small differences, which may be of no clinical significance at all. By contrast, a small study may fail to show a statistically significant effect even if the effect is both large and clinically important.
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