How to appropriately show a small error bar?

Question

Error bars are graphical representations of the variability of data and used on graphs to indicate the error or uncertainty in a reported measurement.

However, sometimes error bars are really short and even smaller than the size of the markers on my plot. In a scientific paper in the experimental sciences, it is still expected to include such error bars on the graphs. Thus, I got an ugly figure like:

Obviously, I'm not an experimentalist, and my questions are:

(1) Are there some convention about such an issue in practice;

(2) If the lengths of error bars are the same for all measuring points with the same marker. Can I just explain in the caption that I have used the size of markers (such as the diameter of a circle and side length of a square) to represent the error bar instead of plotting the error bars actually? If not, could you please suggest me how should I present such a figure better to show the statistic property.

Answer 1

It depends on the area, but in general, the appropriate choice for displaying the error depends on the specific purpose of the plot. Here are some examples:

• When the errors are obtained from a quantity such as the standard deviation $\sigma$, it's possible to the define them instead at $3\sigma$ ($99.7\%$ confidence).

• In some circumstances, e.g., when the errors are being used to judge a fit, depicting the residuals instead is usually the best option.

• When it's important to show the relative sizes (for different data points) of the error bars, they can be multiplied by an arbitrary common factor in order to become visible.

• And when the too-small error bars don't play an important role in the plot, it's very usual to simply point out that the "error bars are smaller than the symbol size".

Answer 2

Science writing is for effectively communicating results. You don't need error bars, you just need to communicate your error. If your error bars are too small to be visible in your graph, then the graph is an ineffective way to communicate your measurement error. If the error bars are all smaller than your data point symbol, it may be sufficient to simply state as much and elaborate in the caption or text. If you really need to communicate the variability of the error across data points, there may be other ways to do this. If it's important, perhaps it warrants a separate plot (or an inset). On the other hand, over-communicating useless detail about your measurement error can detract from the presentation. What is the story you want to tell?

Science writing is an ever-evolving discipline that has developed organically. The only rule is, and has ever been, to communicate your results effectively.