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There is data $x$ and $y$ which does not come from two dimensional normal distribution. However I would like to perform correlation coefficient test. For this purpose I have created the bootstrap distribution of correlation coefficient $\rho$ of $x$ and $y$. How do I test null hypothesis $H_0: \rho=0$ ?

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In a strict sense the answer is that you don't. For a bootstrap test you need to resample from a transformed version of the data, which is changed in such a way that the null-hypothesis is true. This does not seem to be what you have done.

However, you can create a confidence interval (the easiest version would be to look at the 2.5th and 97.5th percentiles for the 95% confidence interval) and see if that confidence interval includes 0.

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  • $\begingroup$ Thank you very much. It is what I have done, but wasn;t sure if that is proper thing to do. $\endgroup$
    – Misery
    Oct 29, 2014 at 12:36

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