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I'd like to ask you something about the bootstrap method. If I understood correctly, I can use this method when the size of a sample is small, in order to extract more information. For example, applying a Cox model I noticed that when I had a bigger sample (n=1050), I found several significant small effects and a big significant effect for only one variable. When I reduced the sample size (n=300), all small effects disappeared, remaining only the variable with big effect as significant variable. Can I use a bootstrap method on this sample (n=321) and realize many Cox models (for example generating 1000 samples) in order to make stronger the effects of the variables with small effects?

Thank you for your attention.

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No. Bootstrap is a method of estimating the possible uncertainty of your estimate. It has nothing to do with "extracting more information" from the data. Since you are re-sampling your data, it will contain nothing more then before the bootstrap (if you have a jar of sweets and you randomly sample from this jar, than by doing so you obviously won't be able to generate any sweets that were absent in the jar).

It has also nothing to do with making insignificant effects significant! When using bootstrap, you sample with replacement $N$ observations out of sample of size $N$, you do not sample more or less observations than you have seen initially. If you sampled more values then you had initially, you would possibly hack the $p$-values, in fact if you sampled a huge number of observations from your data you may find that every effect in your dataset to be "significant", since $p$-values depend on sample size. So if your aim is to lie with statistics, then this is a very easy and effective way of hacking your $p$-values.

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    $\begingroup$ +1 for directly answer the user!. good luck on the election! $\endgroup$ – Haitao Du Aug 10 '17 at 13:49
  • $\begingroup$ you explained what bootstrap is not about, but can you explain more on what it can do? I remember we had some good discussions somewhere, can you give me the link? $\endgroup$ – Haitao Du Aug 10 '17 at 13:51
  • $\begingroup$ @hxd1011 there is a brief explanation in the first link and lots of related answers in other questions tagged as bootstrap (best: sorted by votes), so there is probably no need to duplicate them. $\endgroup$ – Tim Aug 10 '17 at 13:57

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