I would like to display information both about the distribution of the population and the certainty in the measurements in the same plot. Would there be any use of having dual error bars in a barchart to achieve this? That is, two vertical error bars per bar to show both standard deviation and standard error or confidence interval.

Or would you rather recommend something like a box/violin/bean plot with added means and sem/ci? Or bar plot with SD + stars for significant differences? I like plots that include the distribution shape since they display the information more completely but are also a little bit busy when I have many samples. Barcharts are practical when I want to group bars in pairs (or more) and they are easily interpreted (maybe oversimplifying sometimes I guess...).

However, I have never seen a bar chart with dual error bars, so I suspect there are some strong arguments against this and some good alternatives as well, just that I might not know of them or not appreciate them enough.

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    $\begingroup$ I've seen Andrew Gelman use thicker bars for different levels of confidence/credible intervals (see Figure 3), but I haven't seen anyone intentionally superimpose bars using different estimates of the standard error. I imagine they would be a bit difficult to interpret. See this thread on error bars for paired experiments that has related discussion and references of interest. $\endgroup$ – Andy W Oct 31 '14 at 19:29
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    $\begingroup$ Yeah, I have seen some violin plots using that concept or similar styles. I was thinking along the lines of error bar next to each other and with narrower caps rather than superimposing. Then one could be black and one grey to easily compare between bars. I read some of Cumming/Finch/Belia's discussion of error bars earlier, and find it both interesting and useful. $\endgroup$ – joelostblom Oct 31 '14 at 23:08

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