MATLAB: How to get p-val from correlation coefficient and number of sample

Question

Hi, all!

We know that in MATLAB, [r,p]=corrcoef(A) could return the correlation coefficient and p-val.

But who knows how p-val is calculated, what is the formulas?

Thanks for your help!

Answer 1

The p-value is based on a t statistic

t = r* sqrt((n-2)/(1-r^2))

which has n-2 degrees of freedom.

You can find a discussion of the sampling distribution of r both when the null hypothesis is that r=0 and when you are testing for nonzero values of r here:

http://luna.cas.usf.edu/~mbrannic/files/regression/corr1.html