In many plots there are the group means and +/- 1 SD. Does it make sense to use the +/- 2*SD for making a simple, rough and quick visual comparison of the means?
For example, in this plot are 10 independent groups. We can see the mean and +/- 1 SD (we don't have standard error). Then, while I am presenting this plot in a meeting someone asks if the last group could be different compared to 1st group (comparison of these two groups only, we don't care for the rest). Does it make sense to say, look the 2SD of 1st group and the 2SD of the last group are not overlapping so yes, the chances to be different is high. Is this thought somehow valid? or the response should be something like.. we can not make this conclusion from this plot?