= Equal-cell replication variance formula
{title2=$\operatorname{Cov}(\widehat\mu)=\sigma^2I/m$}
Suppose a <normal linear model> gives an unrestricted mean to each cell and has $m$ <independent> observations per cell, with common error <variance> $\sigma^2$. Each fitted cell mean is its <sample mean>, with <variance> $\sigma^2/m$; different fitted cell means are <independent>. Estimate $\sigma^2$ by the pooled within-cell <residual sum of squares> divided by $n-q$, where $q$ is the number of cells. Thus a cell mean has <standard error> $s/\sqrt m$, a difference of two cell means has <standard error> $s\sqrt{2/m}$, and a two-by-two difference-of-differences has <standard error> $2s/\sqrt m$.
// Target: probability-and-statistics.bigb
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