How to calculate correlation p-value?

I have a correlation matrix and have performed some filtering on it. Now I want to calculate the p-value of the filtered correlation matrix. Can anyone help we with the code. [R,P]=corrcoef(A) returns both the correlation matrix as well as the p-value matrix, but I already have the correlation matrix, and just want to calculate the p-value matrix.

Thank you in advance. Ritankar.

Answer 1

[Gregory Pelletier]

Here is how to calculate the p-values the same way that matlab does in corrcoef if you only know the correlation coefficient matrix R and the number of samples N (see p_check below for the manual calculation of the p-value compared with p from corrcoef):

load hospital
X = [hospital.Weight hospital.BloodPressure];
[R, p] = corrcoef(X) 
N = size(X,1);
t = sqrt(N-2).*R./sqrt(1-R.^2);
s = tcdf(t,N-2);
p_check = 2 * min(s,1-s)
% R =
   % 1.0000e+00   1.5579e-01   2.2269e-01
   % 1.5579e-01   1.0000e+00   5.1184e-01
   % 2.2269e-01   5.1184e-01   1.0000e+00
% p =
   % 1.0000e+00   1.2168e-01   2.5953e-02
   % 1.2168e-01   1.0000e+00   5.2460e-08
   % 2.5953e-02   5.2460e-08   1.0000e+00
% p_check =
            % 0   1.2168e-01   2.5953e-02
   % 1.2168e-01            0   5.2460e-08
   % 2.5953e-02   5.2460e-08            0

Answer 2

[the cyclist]

You cannot calculate a P-value from only a correlation matrix. You need the underlying data. The reason why is pretty easy to understand ... The correlation matrix could have come from a dataset with maybe N=10 measurements, or perhaps N=100000 measurements. These will (almost certainly) have different P-values.

[Gregory Pelletier]

Here is how to calculate the p-values the same way that matlab does in corrcoef if you only know the correlation coefficient matrix R and the number of samples N (see p_check below for the manual calculation of the p-value compared with p from corrcoef):

load hospital
X = [hospital.Weight hospital.BloodPressure];
[R, p] = corrcoef(X) 
N = size(X,1);
t = sqrt(N-2).*R./sqrt(1-R.^2);
s = tcdf(t,N-2);
p_check = 2 * min(s,1-s)
% R =
   % 1.0000e+00   1.5579e-01   2.2269e-01
   % 1.5579e-01   1.0000e+00   5.1184e-01
   % 2.2269e-01   5.1184e-01   1.0000e+00
% p =
   % 1.0000e+00   1.2168e-01   2.5953e-02
   % 1.2168e-01   1.0000e+00   5.2460e-08
   % 2.5953e-02   5.2460e-08   1.0000e+00
% p_check =
            % 0   1.2168e-01   2.5953e-02
   % 1.2168e-01            0   5.2460e-08
   % 2.5953e-02   5.2460e-08            0

Answer 3

[Anil Kamat]

Lets say

N --> no.of the observations / data points

r --> assumed corr.coef

t = r*sqrt((N-2)/(1-r^2)); % find t-statistics

p1 = 1 - tcdf(t,(N-2)) % find pvalue using Student's t cumulative distribution function for one sample test.

https://www.mathworks.com/help/stats/tcdf.html

[the cyclist]

Can you help me understand that your formula is correct? Here is a correlation coefficient calculated from a randome dataset, and then your calculation. (I modified your formula only to make meaningful variable names.)

rng default

N = 1000;

x = randn(N,2);

[correlationMatrix,pMatrix] = corrcoef(x);
pValueFromOriginalData = pMatrix(1,2);

correlationCoefficient = correlationMatrix(1,2);


t = correlationCoefficient*sqrt((N-2)/(1-correlationCoefficient^2)); % find t-statistics 
p_from_anil = 1 - tcdf(t,(N-2));  % find pvalue using Student's t cumulative distribution function for  one sample test

sprintf('p-value from original data = %7.4f',pValueFromOriginalData)

ans = 'p-value from original data =  0.7695'

sprintf('p-value from Anil = %7.4f',p_from_anil)

ans = 'p-value from Anil =  0.6153'

They give different results.