Difference of sample means
= Difference of sample means
{title2=$\overline X-\overline Y$}
= Differences of sample means
{synonym}
For independent samples of sizes $n,m$ from populations with <means> $\mu_X,\mu_Y$ and finite <variances> $\sigma_X^2,\sigma_Y^2$, the difference of their <sample means> has <expected value> $\mu_X-\mu_Y$ and <variance> $\sigma_X^2/n+\sigma_Y^2/m$. This uses independence between and within the samples. With dependent samples, a <covariance> term is required instead.