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An estimate for the mean of a set of observations is just that - an estimate. Another set of observations will give a different estimates. These estimates for the mean will have a distribution which will have a standard error. If you have two sub-populations, the mean of each sub-population will have a standards error and the se of the difference between the means is a measure of the variability of the estimates of the difference.

A typical school work example: the heights of men and of women. There will be a mean height for men, Hm, with a se for men's heights and a mean height for women, Hw, with its own se. The difference in mean heights is Hm - Hw and which will have an estimated se.

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Q: What does the standard error of the difference between means mean?
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