Advice: Don't pay much attention to whether error bars overlap

When two SEM error bars overlap

When you view data in a publication or presentation, you may be tempted to draw conclusions about the statistical significance of differences between group means by looking at whether the error bars overlap. It turns out that examining whether or not error bars overlap tells you less than you might guess. However, there is one rule worth remembering:

When SEM bars for the two groups overlap, you can be sure the difference between the two means is not statistically significant (P>0.05).

When two SEM error bars do not overlap

The opposite is not true. Observing that the top of one standard error (SE) bar is under the bottom of the other SE error bar does not let you conclude that the difference is statistically significant. The fact that two SE error bars do not overlap does not let you make any conclusion about statistical significance. The difference between the two means might be statistically significant or the difference might not be statistically significant. The fact that the error bars do not overlap doesn't help you distinguish the two possibilities.

Other kinds of error bars

If the error bars represent standard deviation rather than standard error, then no conclusion is possible. The difference between two means might be statistically significant or the difference might not be statistically significant. The fact that the SD error bars do or do not overlap doesn't help you distinguish between the two possibilities.