[R] Hmisc package: deff() command's formula for the design effect

[jjh21]

Hello,

I have been using the Hmisc package's deff() command for some research with
clustered data. I noticed that the formula to calculate the design effect
seems a bit different. The formula for the DE is:

1 + rho*(B - 1)

In most resources I have seen the formula for B to simply be the average
number of observations in a cluster: n/k if n is the total sample size and k
is the number of clusters.

However, the deff() command calculates B as: sum(number of observations in
each cluster^2)/n. 

That is a bit hard to write without the Sigma operator. In English it is
"squaring the number of observations in each cluster, adding all those up,
and dividing that total by n."

Which formula is correct? Thank you!
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