Effective sample size of correlated observations

Question

You have n = 200 observations, each correlated with every other at common correlation \rho = 0.05. What is the effective sample size, the number of independent observations that would give the same precision?

Accepted Answer

Correlated observations carry overlapping information, so 200 of them are worth fewer than 200 independent ones. The effective sample size answers "how many independent points would match this precision?" Starting from the variance of a correlated average, the effective sample size works out to n{	ext{eff}} = \frac{n}{1 + (n-1)ho}. The denominator is the same bracket that inflates the variance; here it deflates the count. Plug in n = 200, ho = 0.05: n{	ext{eff}} = \frac{200}{1 + 199 	imes 0.05} = \frac{200}{1 + 9.95} = \frac{200}{10.95} \approx 18.3. So your 200 correlated observations…

Effective sample size of correlated observations

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