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When presenting results from your experiment, such as treatment means, it is best practice to provide a measure of uncertainty, such as a standard error or a confidence interval (CI). However, a commonly asked is what should be reported: the SD, SEM, SED, or a CI for the mean or the difference between means.
It may seem like a small thing, but presenting an appropriate metric makes a difference to how your results are interpreted. Let’s discover why!
Importantly, each quantity describes something different. In a nutshell:
- The standard deviation (SD) describes the variability in the raw data.
- The standard error of the mean (SEM) describes how precisely a single treatment mean has been estimated.
- The standard error of a difference (SED) describes how precisely two treatment means can be compared.
- A confidence interval for a mean provides a range of plausible values for an individual treatment mean.
- A confidence interval for a difference provides a range of plausible values for the difference between two treatment means.
Consequently, in practice, these quantities answer different questions:
- The SD is useful for understanding the spread of the data, but it does not reflect uncertainty in treatment means.
- The SEM, or CI for the mean, is appropriate when describing the precision of individual means, but it does not directly inform comparisons between treatments.
- The SED, or CI for the difference, is appropriate when the focus is on the difference between a pair of treatment means.
This leads to a simple rule of thumb:
- If you are describing the data, report the SD.
- If you are describing individual treatment means, report the SEM or CI for the mean.
- If you are comparing treatments, report the SED or CI for the difference.
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