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I'm a statistically incompetent social scientist who is very much out of my depth...

I'm using R to analyse a data set, which is a 1% sample of a population showing cancer rates across 20 regions. There are parameters for male and female rates.

If I have to calculate 95% credible intervals for the mean based on the two sexes, am I better off using an arithmetic calculation or bootstrapping? I've searched high and low for something comprehensible but I'm struggling. I think I'm right in saying that bootstrapping is better when the data isn't normally distributed (this, however, very much is) and sample size is small (which this is).

On the basis of the sample size, am I justified in going down the bootstrapping route?

Any advice much appreciated!

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    $\begingroup$ How "small" is your dataset? 1% of a population of say 100,000 is actually quite large and inference on a mean can often be done arithmetically. $\endgroup$ – P Schnell Mar 9 '14 at 17:52
  • $\begingroup$ Oh right, shows how little I know then! Population is 81 million. Makes sense when I think about it... $\endgroup$ – blobcow Mar 9 '14 at 19:08
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Bootstrapping is not so great when a sample size is actually small (less than 50 say, though it depends somewhat on exactly what you're doing); it works fine in large samples.

Bootstrapping works fine on normal data. You seem to be asserting that your data is normal -- on what basis do you say that?

If your sample size is 810,000 (as your comment seems to suggest), then you can pretty safely assume the mean is normal, and generally, reasonably safely apply Slutsky as well, so you can construct normal theory intervals for means with relatively little concern about the original distribution.

Note that a credible interval is an interval from a Bayesian analysis. If you're going to bootstrap, you need to be clear about how any bootstrap you use relates to that.

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