Take the 2-minute tour ×
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It's 100% free, no registration required.

I want to test the hypothesis that correlation coefficient between X and Y is 0 with a bootstrap, however I don't know which is a correct way to construct bootstrap samples. I have several ideas, which may be wrong:

1) randomly permute Y among X's as in permutation test, but sample Y with replacement

2) permute Y among X's without replacement and sample pairs (X,Y) with replacement

Could you please tell me the right way to do bootstrapping in this case and justify it? Thank a lot!

share|improve this question
add comment

2 Answers 2

up vote 2 down vote accepted

Just sample pairs (X,Y) with replacement. You should not be permuting anything.

share|improve this answer
1  
As I understand then I will get the sampling distribution of correlation coefficient centered around the value (e.g. 0.2), which I observe in the original sample. And to test H_0 I need to take p-value, which is a proportion of bootstrapped correlations less than 0? But then it doesn't look like a p-value –  user2575760 Jun 13 at 10:52
    
Yes. How does that not look like a p-value? –  zkurtz Jun 13 at 11:42
    
Caveat 1: if H_0 is that the true proportion = 0, then you want a 2-sided test, which I believe means that you would just multiply the above-described p-value by 2. –  zkurtz Jun 13 at 11:45
    
Caveat 2: If your sample is small (not sure what small means), I suspect the p-value estimate will be a little biased, and corrections for this may exist -- just something to watch out for. –  zkurtz Jun 13 at 11:47
add comment

If you sample pairs of (X,Y) with replacement, then you are bootstrapping and it will give you the variance (or other measure of spread) of the correlation. You can use this to test your hypothesis.

If you permute either, then you are doing a permutation test and it will tell you how a correlation as large as the one you got occurs. This is not a bootstrap (at least, as I understand the term) but it will give you a p-value directly.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.