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Standard error vs standard deviation
Standard deviation measures how much individual values vary around the mean of a sample. Standard error measures how much the sample mean itself would vary if the study were repeated, and equals the standard deviation divided by the square root of the sample size. Use the first to describe data and the second to show precision.
The two are often swapped on posters because the standard error is always smaller and makes results look tidier. Readers then misjudge either the spread of the data or the certainty of the finding, and an error bar that does not say which it shows is close to meaningless.
Indunil Asanka · Co-founder
4 min read · Published
| Standard deviation (SD) | Standard error of the mean (SE) | |
|---|---|---|
| Answers | How spread out are the values | How precisely is the mean estimated |
| Formula | Square root of the average squared distance from the mean, with n minus 1 | SD divided by the square root of n |
| As n grows | Settles near the population value | Keeps shrinking toward zero |
| Example, SD 10 and n 25 | 10 | 2 |
| Example, SD 10 and n 100 | 10 | 1 |
| Report it as | Mean (SD), for example 54 (10) | Usually through a 95% confidence interval, about mean plus or minus 1.96 SE |
What each one describes
Altman and Bland put the distinction in one sentence: the standard deviation describes the variability between individuals in a sample, and the standard error describes the uncertainty of a sample statistic such as a mean. If blood pressure in a group of patients has a standard deviation of 15 mmHg, most individuals sit within about 30 mmHg of the mean. If that group had 100 people, the standard error of the mean is 1.5 mmHg, which says the mean is pinned down closely even though people differ a lot. Neither number is better; they answer different questions, and a poster needs to say which question it is answering.
Why the standard error is not a description of the data
Because the standard error shrinks with the square root of the sample size, a large study can show tiny standard errors around a mean that hides wide individual variation. Reporting mean plus or minus SE in a baseline table makes groups look more uniform than they are. Lee notes that the standard deviation belongs in descriptive statistics and the standard error belongs in inference, and that the clearest way to show inference is the confidence interval built from it. For a two group comparison, the standard error of the difference, and its interval, matters more than either group alone.
What error bars should show
Cumming, Fidler and Vaux list the rules every figure needs: say in the legend whether bars are SD, SE or 95% confidence intervals, give n for each group, and do not draw bars for n of 3 or fewer, where they mislead. SD bars show spread, so they suit describing a sample. SE bars are short and are easily misread as confidence intervals; two SE bars that just fail to overlap do not mean a significant difference. Confidence interval bars are usually the best choice for comparing means, because their width can be read directly as precision.
Common mistakes
Labelling a bar chart with error bars and no legend saying what they are. Switching from SD in the text to SE in the figure without saying so. Calculating the standard error of a skewed variable such as length of stay and reporting it as if the data were symmetric, where a median and interquartile range describe it better. Using the standard error to argue that two groups at baseline were similar. And reporting a mean to more decimal places than the standard deviation supports.
Reporting spread and precision on a poster board
Every poster layout has a figure block and section slots, and three boards carry a table slot, which suits a short baseline table with means and standard deviations. Chart figures take one value per bar or point, so write the spread or the interval in the caption or in the text beside the figure rather than relying on the chart to show it. Key number blocks on 26 boards can carry the headline difference with its 95% interval in the detail line. Put the means, standard deviations, group sizes and the interval in the brief, since the generator uses only the numbers it is given.
Questions people ask
When should I use standard deviation instead of standard error?
Use the standard deviation whenever you describe the people or samples you measured, such as in a baseline characteristics table. Use the standard error, or better the confidence interval built from it, when you estimate a population mean or compare groups. If the poster has room for one, describing the sample with SD and the main result with a 95% interval covers both needs.
Can I convert a standard error back to a standard deviation?
Yes, if you know the sample size: multiply the standard error by the square root of n. A standard error of 2 from 36 people is a standard deviation of 12. Systematic reviewers do this routinely when papers report only standard errors, which is one reason to state n clearly beside every mean.
Is standard error the same as margin of error?
Not quite. The margin of error is usually the standard error multiplied by a critical value, about 1.96 for 95% confidence, so it is roughly twice the standard error. Survey reports often quote the margin of error; scientific papers more often give the confidence interval, which is the estimate plus and minus that margin.
Why is my standard error so small?
Because your sample is large, or the values vary little, or both. The standard error falls with the square root of the sample size, so quadrupling n halves it. A small standard error means the mean is estimated precisely; it does not mean individuals are alike or that the difference you found matters in practice.
Should a poster show standard deviation or confidence interval bars?
For comparing groups, confidence interval bars are usually clearest because a reader can judge precision without extra arithmetic. For showing how varied the measurements are, standard deviation bars or a dot plot of individual values work better. Whichever you choose, say so in the figure caption and give the number in each group.
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