Wednesday, March 23, 2016

Error Bar Misinterpretation

Nature Methods published an article fairly recently that explains common misconception surrounding error bars. If you're like me, I thought error bars was something I could easily look at and understand. Don't they just represent the likelihood of variance between my replicate samples? Well, first, what are you using your error bars to represent? Standard deviation, standard error of the mean, or a confidence interval? This article (which provides interactive supplementary data where you can see the raw data used in the discussion as well as make your own data), provides examples of how data can look very different (or even not significant) depending on the way the error bars are represented.

A very common misconception is that a gap between bars means that the data are significant while if the bars overlap they are not significant. That is not the case, and again, it all depends on the type of bars you choose to use. 

An an example, figure 1 (above, n=10) shows how error bars cannot be compared. The left graph shows what happens to the p-value when the error bars from SD, SEM, and 95% CI are adjusted to the same lengths. The right graph shows what happens to the size of the error bars when adjusting to a significant p-value (p=0.05). As you can tell, just because SEM error bars do not overlap does not indicate significance and just because SD error bars do overlap does not mean that the data are not significant. 

When showing data with error bars it is important to be clear about which measure of uncertainty is being represented in order for the reader to be able to interpret the results properly.

Short summary:
SD: represents variation of the data and not the error of your measurements.
SEM: represents uncertaintiy in the mean and its dependency on the sample size.
CI: represents an interval estimate indicating the reliability of a measurement.


  1. I know we touched on this in class, but at the time it did not really sink in. The graphic presented here puts error bars into perspective. Usually when I read papers, I just look to see if it the data was labeled as significant. If the error bars were further apart I would assume it was more significant and if they were close to overlapping I would assume that the data was barley significant.

    However this is not the best interpretation of error bars. I should be looking at what the error bars are representing (SD, SEM, or CI). Each measurement provides different information about the data. I especially like how this post includes a short summery at the end to help keep each measurement straight. Often I think scientists just lump all three of these measurements together as 'error' and forget that each one is telling you something different.

  2. I think this is a really important point to bring up, as I also always assumed that non-overlapping error bars meant that findings were sure to be significant. I know in my field, SEMs are frequently used for error bars, likely because they "look better." It's important that we pay close attention to what is actually being shown, so we don't assume things are significant just becuase they look nice.