Update ESS.Rd

[felixthoemmes]

Hello Noah, I may have found a very small typo in the help file on the ESS function.

Formula was missing an "n" in denominator, as per reference Shook-Sa et al. (2020)

[ngreifer]

Hi Felix,

Shook-Sa and Hudgens don't actually describe the ESS; they describe the design effect (deff), which is

deff = \frac{n \sum w^2}{(\sum{w})^2}

The ESS is

ESS = \frac{(\sum{w})^2}{\sum w^2}

So, we have that

deff = \frac{n}{ESS}

The expression in the documentation for the ESS is correct.

[felixthoemmes]

Argh, my mistake. Yes, indeed that's correct. Apologies for the pre-mature and unnecessary pull request.

On Sat, Jan 21, 2023, 2:39 PM Noah Greifer @.***> wrote:

Hi Felix,

Shook-Sa and Hudgens don't actually describe the ESS; they describe the design effect (deff), which is $$deff = \frac{n \sum w^2}{(\sum{w})^2}$$

The ESS is $$ESS = \frac{(\sum{w})^2}{\sum w^2}$$

So, we have that $$deff = \frac{n}{ESS}$$

The expression in the documentation for the ESS is correct.

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