# Min-max vs. standard deviation when plotting error bars

I am running some experiments in which I plot the values of some variable y (averaged over 4 runs) against some independent variable x. I also compare the effect of z. In other words:

• horizontal axis: x
• vertical axis: y
• plots: one line for each value of z

I would like to know if there are any best practices or rules of thumb to decide whether my error bars should reflect (a) min-max values, or (b) standard deviations. What characteristics of the data set should lead me to prefer one over the other?

Some things that I think might be relevant:

• The raw values of y are integers bounded between 0 and 60.
• I can only perform a small number (e.g. 4-5) replications due to the time cost of generating each raw data point.
• There can be some pretty wild fluctuations, e.g. y could be in the high 50's for 3 of the runs, but 20 in the last one.
• The data does not follow any model
• I don't think this decision should only be based on the characteristics of the data set but also what you want to communicate, along with the expectations of your audience. Error bars based on standard errors of the mean are very common, raw standard deviations less common, and ranges less common still (if you're inclined toward ranges, you might consider boxplots). But with only 4-5 values, why not simply indicate all four or five values? -- Do you have any sample data available? – Glen_b Jun 18 '13 at 2:37
• I agree with Glen_b - if the number of data points is small then just show all of them without error bars. On the more general question of what error bars should represent, my preference is for them to show a 95% confidence interval. But whatever you do, make sure you make it clear what the bars indicate, because a lot of people don't. – markseeto Jun 18 '13 at 2:59
• @Glen_b Showing all the values would certainly be simpler, except that I am already also showing the effect of another variable z, which has 4-5 values of its own (so the horizontal axis is x, the vertical axis is y, and each plot is for a value of z). In this case, I'd end up with ~20 values. Sorry, I should have mentioned that earlier - I'll edit the question. – maditya Jun 18 '13 at 3:38