Error Bar Overlap Significant
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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. Let's look at two contrasting examples. https://egret.psychol.cam.ac.uk/statistics/local_copies_of_sources_Cardinal_and_Aitken_ANOVA/errorbars.htm What can you conclude when standard error bars do not overlap? When standard error (SE) bars do not overlap, you cannot be sure that the difference between two means is statistically significant. Even though the error bars do not overlap in experiment 1, the difference is not statistically significant (P=0.09 by unpaired t test). This is also true when you compare proportions with a chi-square test. What error bar can you conclude when standard error bars do overlap? No surprises here. When SE bars overlap, (as in experiment 2) you can be sure the difference between the two means is not statistically significant (P>0.05). What if you are comparing more than two groups? Post tests following one-way ANOVA account for multiple comparisons, so they yield higher P values than t tests comparing just two groups. So error bars overlap the same rules apply. If two SE error bars overlap, you can be sure that a post test comparing those two groups will find no statistical significance. However if two SE error bars do not overlap, you can't tell whether a post test will, or will not, find a statistically significant difference. What if the error bars do not represent the SEM? Error bars that represent the 95% confidence interval (CI) of a mean are wider than SE error bars -- about twice as wide with large sample sizes and even wider with small sample sizes. If 95% CI error bars do not overlap, you can be sure the difference is statistically significant (P < 0.05). However, the converse is not true--you may or may not have statistical significance when the 95% confidence intervals overlap. Some graphs and tables show the mean with the standard deviation (SD) rather than the SEM. The SD quantifies variability, but does not account for sample size. To assess statistical significance, you must take into account sample size as well as variability. Therefore, observing whether SD error bars overlap or not tells you nothing about whether the difference is, or is not, statistically significant. What