I was working on stratified sampling for variance reduction for monte carlo estimation, and I found an odd statement from this website (link posted below).

The first line on his site is, "Intuitively, smaller samples have less variance."

I don't find this intuitive at all, especially when looking at the sample variance formula:

$$s^2 = \frac{1}{n-1} \, \sum_{i=1}^n \, \Big(X_i - \overline{X}\Big)$$

Maybe I'm missing some context for this quote, so feel free to check out his site. If someone wouldn't mind explaining what the author might have intended, that would be great.

Link: https://am207.github.io/2017/wiki/stratification.html#why-does-stratification-decrease-variance

  • $\begingroup$ Intuitively, I would say that it does not change with sample size if estimator is unbiased. Is the estimator you showed unbiased in your case? $\endgroup$ – user1420303 Apr 28 '18 at 13:43
  • $\begingroup$ That link does not work anymore! $\endgroup$ – kjetil b halvorsen Jun 21 at 18:56

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