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

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?

Answer 1

[Prasanna]

Hi Rahul,

To check whether the partial correlations are significant at the 5% significance level, you can compare each p-value in your 3-D matrix to the significance level (0.05). If a p-value is less than 0.05, the corresponding partial correlation is considered significant.

For the same, in the code you have included, you can iterate through the 3D matrix of p-values and print each partial correlation to check if it is significant or not. A sample code to perform the same is given below assuming the ‘alldata’ variable refers to the table present in the ‘Dataset.xlsx’ file:

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); 
            
            % Check if the p-value is less than 0.05 
            if pval(i, j, k) < 0.05 
                fprintf('Partial correlation between variables %d, %d, and %d is significant (p = %.4f)\n', i, j, k, pval(i, j, k)); 
            else 
                fprintf('Partial correlation between variables %d, %d, and %d is not significant (p = %.4f)\n', i, j, k, pval(i, j, k)); 
            end 
        end 
    end 
end    

For more information regarding ‘partialcorri’, you can refer the following documentation: https://www.mathworks.com/help/releases/r2023a/stats/partialcorri.html

Hope this helps!