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When I look at scientific papers, bar charts I usually come to see are shown with mean +/- sem (standard error of the mean).

As stated here,

When standard error (SE) bars do not overlap, you cannot be sure that the difference between two means is statistically significant

and

If 95% CI error bars do not overlap, you can be sure the difference is statistically significant (P < 0.05).

Even if the reverse is not true, why don't we always use the confidence interval instead of the sem in bar charts, since it seems more informative ?

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    $\begingroup$ Check for one example here: stats.stackexchange.com/questions/190223/… $\endgroup$
    – Tim
    Commented Mar 17, 2016 at 16:02
  • $\begingroup$ They are called dynamite plots biostat.mc.vanderbilt.edu/wiki/pub/Main/TatsukiRcode/… $\endgroup$
    – mdewey
    Commented Mar 17, 2016 at 18:14
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    $\begingroup$ Which confidence interval would you show? 95%? 99%? 99.9%? You would need to make choices; but SEM is SEM, there is no ambiguity. This might be one reason. Another reason might be that SEMs are smaller. $\endgroup$
    – amoeba
    Commented Mar 18, 2016 at 0:35

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SE and CI give us different - albeit related - information about the data. SE tells us about the variability of the mean values, e.g. if we were to repeat the study. CI tells us about the accuracy of our estimates. They are related because SE is used to calculate the CIs.

The why for using one or the other thus comes down to what the author wants to convey. If you are reporting the results of a statistical test elsewhere in your report/publication, using CIs might be considered extraneous as you already have a measure of statistical significance in the P value from the test.

While SE may have become de rigueur, this excellent paper shows clearly some of the many pitfalls related to just sticking with SE by default. Bottom line: think about what story your data are telling, and use appropriate figures to represent this story accurately.

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