Is it better to use use the standard deviation (SD) or standard error (SE) when plotting error bars? There's a great deal of variability in whether people use the SD or SE when plotting error bars. Why would someone choose one over the other?
 A: Answer re-posted from here:

Is it better to plot graphs with SD or SEM error bars? (Answer: Neither)
There are better alternatives to graphing the mean with SD or SEM.
If you want to show the variation in your data:
If each value represents a different individual, you probably want to
show the variation among values. Even if each value represents a
different lab experiment, it often makes sense to show the variation.
With fewer than 100 or so values, create a scatter plot that shows
every value. What better way to show the variation among values than
to show every value? If your data set has more than 100 or so values,
a scatter plot becomes messy. Alternatives are to show a
box-and-whiskers plot, a frequency distribution (histogram), or a
cumulative frequency distribution. What about plotting mean and SD?
The SD does quantify variability, so this is indeed one way to graph
variability. But a SD is only one value, so is a pretty limited way to
show variation. A graph showing mean and SD error bar is less
informative than any of the other alternatives, but takes no less
space and is no easier to interpret. I see no advantage to plotting a
mean and SD rather than a column scatter graph, box-and-wiskers plot,
or a frequency distribution. Of course, if you do decide to show SD
error bars, be sure to say so in the figure legend so no one will
think it is a SEM.
If you want to show how precisely you have determined the mean:
If your goal is to compare means with a t test or
ANOVA, or to show how closely our data come to the predictions of a
model,  you may be more interested in showing how precisely the data
define the mean than in showing the variability. In this case, the
best approach is to plot the 95% confidence interval of the mean (or
perhaps a 90% or 99% confidence interval). What about the standard
error of the mean (SEM)? Graphing the mean with an SEM error bars is a
commonly used method to show how well you know the mean,  The only
advantage of SEM error bars are that they are shorter, but SEM error
bars are harder to interpret than a  confidence interval. Whatever
error bars you choose to show, be sure to state your choice. Noticing
whether or not the error bars overlap tells you less than you might
guess.
If you want to create persuasive propaganda:
If your goal is to emphasize small and unimportant differences in your data, show your error bars as SEM,  and hope that your readers think they are SD If
our goal is to cover-up large differences, show the error bars as the
standard deviations for the groups, and hope that your readers think
they are a standard errors. This approach was advocated by Steve Simon
in his excellent weblog. Of course he meant it as a joke. If you don't
understand the joke, review  the differences between SD and SEM.

