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.