I am trying to understand what N represents when calculating confidence intervals under bootstrap?

In this scenario, I have a sample with 188 values, so the sample size, SS, is 188. I am interested in the mean of these 188 values.

I bootstrap from this one sample 100 times so the number of bootstrap samples, NS, is 100. So I end up with 100 bootstrap sample means (I calculate the mean of each sample of size 188)

I want to calculate a 95% confidence interval on the mean of the samples (of the 188 values in the sample).

Using the formula:

bootstrap_CI_upper = mean(1000 means of each bootstrap sample) + 1.96*sd(1000 means of each bootstrap sample)/sqrt(N),

what is N here? Is it the number of bootstrap samples (100) or the size of each sample (188)?

I think N here is 188 (the size of each sample) but I want to confirm it.

Thank you! p.s. Since I'm new to bootstrapping, please let me know if you know of a good resource to learn about applying the bootstrapping method.

  • 1
    $\begingroup$ You might be able to answer this yourself by comparing this formula to a standard formula for a (Normal-theory) upper confidence limit, or even by looking at formulas for the standard error of the mean. $\endgroup$ – whuber Aug 6 '15 at 16:26
  • $\begingroup$ Thank you for your comment, but I'm not sure I know enough about this type of statistics to answer it myself. I think N here is 188 (the size of each sample) but I want to confirm it. $\endgroup$ – dvaaaaaaaalllllll111111111llll Aug 6 '15 at 16:35
  • $\begingroup$ Another hint: what will happen with the two intervals in question if you simply increase the number of replications from 100 to 1'000'000? $\endgroup$ – Michael M Aug 6 '15 at 17:47
  • $\begingroup$ It will shrink the more bootstraps i take. So N is the number of bootstraps then? $\endgroup$ – dvaaaaaaaalllllll111111111llll Aug 6 '15 at 18:03
  • $\begingroup$ I think from my study of your helpful comments and links that N is the number of bootstraps (and not the size of the sample). Could you confirm this please? I just want to be sure. Thank you to all of you for your help! $\endgroup$ – dvaaaaaaaalllllll111111111llll Aug 11 '15 at 20:10

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