Error bars on error bars? Inspired by my recent attendance at an environmental toxicology conference, I have the following question about error bars:
Let's say that I'm drawing samples from some unknown distribution, with finite mean and variance. I want to present the sample mean, and add some error bars. Since I don't know much about the underlying distribution, I just add error bars showing +/- the standard devaition of the samples.
My question is, is there any way I could meaningfully indicate how certain I am of those error bars? Adding error bars to the error bars, so to speak.
As as example, I have drawn 5 samples from some distribution, and I have repeated this 5 times. The sample means, and error bars of +/- the sample standard deviations, are shown below.

We can see that by chance, these sample means and error bars look quite different, and not really mutually compatible. Of course 5 samples isn't very much, but if my samples are obtained via some convoluted experimental procedure (capturing a wild animal and taking a blood sample, for example), it might not be an easy option to get more samples.
Update:
Just to add some notes on how I was thinking:
Coming from a computational physics background myself, I'm used to Monte Carlo methods, and the $1/\sqrt{N}$-error which follows from the central limit theorem. So just like the error in the sample mean has an expected distribution, I thought perhaps it would make sense to ask about the expected error in the sample standard deviation. Of course, the problem is that the distribution of the error in the sample mean is expressed in terms of the (unknown) variance of the underlying distribution, and hence I am left taking the standard deviation of the sample, or something along those lines.
But still, I thought there ought to be some way of indicating that my sample standard deviation is itself quite uncertain, due to the small $N$. But perhaps the only way is simply to list $N$, and be explicit about what the error bars show.

The objects we use to make inferences (e.g., estimates, confidence intervals, error bars, test statistics, p-values, etc.) are statistics, meaning that they are functions of the observed data.  Since they are already functions of the observed data, these objects do not have any uncertainty in them --- they represent inferences about uncertain values, but there no uncertainty in the statistics themselves.  We do not form error bars on error bars because there is no uncertainty in the error bars to begin with, because they are formed as a function of the observed data.
As a minor point, it is generally suboptimal practice to use error bars to show a deviation of plus/minus one (estimated) standard deviation.  Usually you are better off using these values and other statistics to form an appropriate confidence interval for the uncertain value of interest, and using the error bars to show the confidence interval.  In either case you should label your plot appropriately so that the reader understands what the error bars represent.
