Standard Deviation vs Standard Error

The standard deviation (SD) describes how spread out individual observations are around their mean; the standard error (SE) of the mean describes how precisely the sample mean estimates the population mean. They answer different questions and should not be used interchangeably.

Definitions

• SD: a measure of variability in the data. It does not shrink as the sample grows.
• SE of the mean: SD divided by the square root of the sample size, SE = SD/√n. It gets smaller as the sample gets larger.

When to use each

• Describe a sample (for example in Table 1): report mean and SD (or median and IQR for skewed data).
• Show precision of an estimate: report a confidence interval, which is built from the SE. A 95% confidence interval for a mean is roughly mean ± 1.96 × SE for large samples.

Illustrative example with worked numbers

Invented for teaching. Systolic blood pressure in 25 patients has a mean of 130 mm Hg and an SD of 10 mm Hg. SE = 10/√25 = 2 mm Hg. An approximate 95% CI is 130 ± 1.96 × 2 = 126.1 to 133.9 mm Hg (for small samples a t-based interval is slightly wider). The SD tells us that most patients' values lie within about 110 to 150 mm Hg if the data are roughly normal; the SE tells us how well the mean is estimated.

Why mixing them up misleads

Reporting SE instead of SD makes the data look less variable than they are, because SE is smaller. Journals and guidelines recommend using SD to describe data and confidence intervals to describe precision.

Common pitfalls

• Error bars labelled "SEM" in figures with no description of what they mean.
• Using SE to describe variability of individuals.

Key takeaways

• SD = spread of data; SE = precision of an estimate.
• Prefer SD for description and confidence intervals for estimation.

This page is general educational information about research methods. It is not medical, legal or regulatory advice; follow your institution's ethics board and your target journal's instructions.