How to check whether partial correlation is significant or not at 5% significance level?

I have to check check whether partial correlation is significant or not at 5% significance level. I have calculated the partial correlation by using the predefined command in Matlab "partialcorri''. Which gave me R values and P values. I have attached my code below:

Kindly suggest me whethe it is right or not??

alldata=xlsread('Dataset',1,'A2:H68');

datainput1=alldata(:,1);

for j=2:8

datainput2=alldata(:,j);

[rho(j),pval(j)] = partialcorri(datainput1,datainput2);

lprctl(j)=prctile(pval(:,j),2.5);

uprctl(j)=prctile(pval(:,j),97.5);

if (pval(j)<lprctl(j) || pval(j)>uprctl(j))

fprintf('input %d is significant\n',j)

else

fprintf('input %d is not significant\n',j)

end

end

I want to check the significant partial correlation of Data 1 (which is the 1st column in the Dataset) with other Data at 5% significance level.

Answer 1

[MarKf]

A partial correlation means you are controlling or "partialing out" some variance that is explained by -usually- another (3rd) variable or a series of factors. The function partialcorri does take only 2 inputs, but then there should be some addtional variables (as columns I'm guessing) in x, for which the function is controlling for. So, since with your code both x and y have one column and the same n of values (67), then you are doing a simple correlation ([rho(j),pval(j)]=corr(datainput1,datainput2); would give the same results; btw y is datainput1).

After that there is no need to take a percentile of pval, that's already significant if <0.05 (by convention). So the above (normal, non partial) correlations are all significant, tho some much more. You may want to control for multiple comparisons (7 above) so maybe (conservatively) accept only pval<(0.05/7). Maybe you meant to include more variables to your partial correlation, something like this:

alldata = xlsread(websave('rd', "https://nl.mathworks.com/matlabcentral/answers/uploaded_files/1372129/Dataset.xlsx"),1,'A2:H68');
datainput1=alldata(:,1);
datainput2=alldata(:,2:5);
[rho,pval] = partialcorri(datainput1,datainput2); 

pval = 1×4

0.0000 0.0770 0.8403 0.5945

log10(pval)

ans = 1×4

-12.1243 -1.1137 -0.0756 -0.2258

Which means the correlation between column 2 (x) and column 1 (y) after controlling for the effects of columns 3 to 5 has pval<10e-12.

% for j=2:8
%     datainput2=alldata(:,j);
% [rho(j),pval(j)] = partialcorri(datainput1,datainput2);
% end

Answer 2

[Rahul Verma]

I tried this approach:

for i=1:6

datainput1=alldata(:,i);

for j=i+1:7

datainput2=alldata(:,j);

for k=i+2:8

datainput3=alldata(:,k);

[rho(i,j,k),pval(i,j,k)] = partialcorri(datainput1,datainput2,datainput3);

end

end

end

But this gave me a 3-D matrix of P values.

No how can I check for significant or not?