How to test the difference between two Spearman correlations

[Mostafa Harakeh]

Dear members,

I hope you are all doing well.

I have two simple questions:



Question 1:

. spearman u30 u40

Number of obs = 5001
Spearman's rho = -0.1995

Test of Ho: u30 and u40 are independent
Prob > t = 0.0000

. spearman u31 u41

Number of obs = 5803
Spearman's rho = -0.2359

Test of Ho: u31 and u41 are independent
Prob > t = 0.0000

Now I want to test if these two correlations are significantly different. That is, -0.1995 is significantly different from -0.2359.



Question 2:

How to compare two R-square from two regressions using Vuong test.



Thank you very much for your suggestions.

Mustafa

[Matthias Greiff]

Dear Mustafa,

regarding the first question, I think one could use a bootstrap procedure. The following procedure bootstraps the difference between both correlations. As output, you get the bootstrapped difference and the 95% confidence interval.

However, I'm not sure if this is the best way to compare two Spearman correlations, so any suggestions are welcome.

All the best

Matthias


capture prog drop spearmandiff
program define spearmandiff, rclass
spearman var1 var2
local def1=`r(rho)'
spearman var1 var3
local def2=`r(rho)'
return scalar diff = `def1' - `def2'
end
bootstrap diff=r(diff), reps(1000) saving(spearmandiff_bsreps, replace every(1)): spearmandiff

[Mostafa Harakeh]

Dear Matthias,

Thank you very much for providing the bootstrapping code.

I hope this works.

Best wishes,
Mustafa