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If you create a graph with error bars, or create a table with plus/minus values, you need to decide whether to show the SD, the SEM, or something else. Consider these points:
| • | Why show error bars? Consider showing the raw data in a scatter plot. This lets you show more information in the same amount of space. |
| • | If the scatter is due to biological variation, show either raw data or the SD. |
| • | If you don't want to show the scatter, but instead want to show how precisely you have determined the mean, then show the 95% confidence interval of the mean. If all the scatter is due to experimental imprecision (and not biological variation), you can justify putting the focus on the mean, and how precisely it has been determined, and not on the scatter among replicates. |
| • | An alternative way to indicate the precision of a mean (or some other value) is to show the standard error instead of the confidence interval. I prefer confidence intervals, as they are much more straightforward to interpret. But showing the SE in graphs (as error bars) or tables is conventional in many fields of science. |
| • | If in doubt, show raw data. |
| • | If in doubt, but you really want to show an error bar, choose the SD. |
| • | Always state whether your error bars are SD or SEM (or something else) in figure legends or in the methods section of a paper. |
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When you are trying to emphasize small and unimportant differences in your data, show your error bars as standard errors and hope that your readers think they are standard deviations.
When you are trying to cover-up large differences, show the error bars as standard deviations and hope that your readers think they are standard errors.
Steve Simon (in jest)
http://www.childrens-mercy.org/stats/weblog2005/standarderror.asp
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