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If we are dealing with the full population instead of some sample, would we need to use Bootstrap resampling?

Tim
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user23899
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  • Do we need it..? – Tim Mar 17 '17 at 21:05
  • @Tim Yeah, do we need to use Bootstrap resampling if we're working with the whole population instead of a sample of the population? – user23899 Mar 17 '17 at 21:05
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    In the context of a finite population, if you've done a census then there's no uncertainty left. Your 'sample' statistics are the true population values so you don't need to do any inference at all. – jld Mar 17 '17 at 21:08
  • @Chaconne Does the same go for any other tests, e.g. hypothesis testing? – user23899 Mar 17 '17 at 21:18
  • @user23899 yes, because there's nothing to test. You actually know the results. If you know $\mu$, you don't need to gather evidence against $H_0: \mu = 0$. You can just look at $\mu$ and see if it's $0$ or not. But be sure to read the answer that Tim linked to: there may be superpopulations involved where you don't know everything. – jld Mar 17 '17 at 21:30
  • @Chaconne Now, what if we did take a sample, and saw that the difference in proportions for some event was 0 for that sample. Can we make a conclusion straight from there without doing a hypothesis test? – user23899 Mar 17 '17 at 21:36
  • @user23899 please check the thread linked in my answer. – Tim Mar 18 '17 at 09:57

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The general idea of bootstrap is that by sampling from your data you re-create the sampling process that happened when sampling your sample from the population. Following this logic, if you have whole-population data, for bootstrap you should also take the whole population (unchanged). Obviously this would lead bootstrap-based standard errors estimates to be equal to zero, but indeed they are zero since if you estimate the population parameter on population data, you obtain the exact estimate, since there is no sampling error.

See also the Statistical inference when the sample "is" the population thread.

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Tim
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  • So basically there is no point? – user23899 Mar 17 '17 at 21:11
  • @user23899 Ask yourself, what exactly would you estimate using it? It would be variation of what exactly? I'd say that it would make any sense only if you had doubts if you indeed sampled the whole population correctly and there was some possible sampling error. There is no sampling error, so there is nothing to estimate. – Tim Mar 17 '17 at 21:14
  • So, my thinking is that you're not estimating anything. Everything you collect is for the whole population. – user23899 Mar 17 '17 at 21:15
  • @user23899 sorry, but I do understand what you meant by your comment. – Tim Mar 18 '17 at 09:57