Zbicyclist writes:

Doug Rivers’s discussion about weighting and bias reminds me of a common trick I don’t see very much, and that is using effective sample size as a planning/tracking tool. ESS is (Sum of the weights)^2 / Sum of (weights^2).

If all n cases are weighted equally, ESS is n. Otherwise, ESSKish, Leslie (1992) Weighting for unequal Pi. Journal of Official Statistics, 8, 183-200, which makes sense, since I pulled the ESS formula from my class notes from when I took sampling from Kish.

My question is this: given that this is such a simple tracking and planning metric, why does it seem so hard to find in the literature?

My reply: I dunno. I use this formula all the time, but I usually just derive it myself from scratch when I need it. In general, survey sampling books are weak on this stuff. The other thing is that this formula in general overestimates the sampling variance, I think. It’s a formula for variance with unequal-probability sampling (as indicated by the title of the Kish article). When weights are constructed using poststratification (as is standard, see for example any of my many articles on the topic), the sampling variance will be lower.