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Exercise: Reliability of balance performance measures
in chronic stroke patients, answer 6

Question 6: Standard deviations relate to populations, samples, and distributions,
standard errors are attached to estimates
Why is the within subject standard deviation also called the standard error of measurement?

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Suggested answer:

A standard error is the standard deviation we would get for repeated estimates
found in the same way.
The observed value of a measurement is an estimate of the true value for that subject.
The within subject standard deviation is the standard deviation of repeated measurements
on the same subject.
Hence it is the standard error of a single measurement taken as the estimate of the
subject's true value.

I warned you it was a difficult one.
(If you thought it was easy, good for you!)

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