In this article , equation (8) is incorrect because it omitted the covariance terms. Let h denote the number of strata, so s = 1,2,...,h. Let T denote transpose, • denote matrix product, and Diagonal Matrix [vector] denote a matrix of all 0's except for vector on the diagonal. The correct formula is
In our example, the effect of the correction was negligible; the corrected estimated standard error was the same to two significant digits as the incorrect value.
Also for clarification, we note that in the sentence after (11), it is an assumption that, within stratum s, the difference, Δs, does not depend on the unobserved covariate x.