Don’t make errors in your error bars

Comparing averages should be one of the easiest kinds of information to show, but they are surprisingly tricky.Most people know that when they show an average, there should be an indication of how much smear there is in the data. It makes a huge difference to your interpretation of the information, particularly when glancing at the figure.For instance, I’m willing to bet most people looking at this...

Would say, “Wow, the treatment is making a big difference compared to the control!”I’m likewise willing to bet most people looking at this (which plots the same averages)...

Would say, “There’s so much overlap in the data, there might not be any real difference between the control and the treatments.”The problem is that error bars can represent at least three different measurements (Cumming et al. 2007).

• Standard deviation

• Standard error

• Confidence interval

Sadly, there is no convention for which of the three one should add to a graph. There is no graphical convention to distinguish these three values, either. Here’s a nice example of how different these three measures look (Figure 4 from Cumming et al. 2007), and how they change with sample size:

I often see graphs with no indication of which of those three things the error bars are showing! And the moral of the story is: Identify your error bars! Put in the Y axis or in the caption for the graph.

ReferenceCumming G, Fidler F, Vaux D 2007. Error bars in experimental biology The Journal of Cell Biology 177(1): 7-11. DOI: 10.1083/jcb.200611141A different problem with error bars is here.