3.2.5 Examining the standard error formula

The formula for the standard error of the difference in two means is similar to the formula for other standard errors. Recall that the standard error of a single mean, ${\overline{x}}_1$, can be approximated by

where $s_1$ and $n_1$ represent the sample standard deviation and sample size.

The standard error of the difference of two sample means can be constructed from the standard errors of the separate sample means:

This special relationship follows from probability theory.