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Start with the data scale
A sample standard deviation summarizes dispersion in the observed measurements around their sample mean. It remains in the measurements’ units. A fictional transaction sample might have a mean processing time of 12 minutes and sample standard deviation of 6 minutes.
Identify the estimate being assessed
If n = 36 independent observations are used to estimate a common mean, the usual estimated standard error is 6/√36 = 1 minute. That 1-minute number concerns variation of the mean estimator under the model, rather than the spread of individual transactions.
Keep labels on a comparison
| Report | Describes |
|---|---|
| Mean 12, SD 6 minutes | Location and observation dispersion |
| Mean 12, estimated SE 1 minute | Location and estimated mean uncertainty |
| A transaction will fall within 12 ± 1 minutes | Not implied by either report |
Ask what makes observations independent
Repeated measurements on the same subject or measurements clustered by day can contain dependence. An estimated SE that assumes independence may understate uncertainty. Identify the sampling unit before replacing n with a count of every stored row.