Compare two distribution of correlation coefficient

[nadra]

Hi,

I would compare two distributions of correlation coefficient A and B (two sample of correlation coefficients). I want to know if B came from the same population as A. A and B are not independent. (so KS test not applicable)

How can I do this?


best regards,

[Ksharp]

It looks like you are perform t-test by useing correlation coefficient statistic estimator ?
If it is, you do not need to calculate the correlation coefficient separately.
proc ttest has do it for you automatically.


Ksharp

[nadra]

> It looks like you are perform t-test by useing
> correlation coefficient statistic estimator ?
> If it is, you do not need to calculate the
> correlation coefficient separately.
> proc ttest has do it for you automatically.
>
>
> Ksharp

Hi Ksharp, thanks for answering!

A ttest will be based only on mean comparison, so it is not my objective. I want to compare a distribution of correlation coefficient to another one distribution of coorelation coefficient .

Say if A is a distribution of (1000) correlation coefficient obtained from corrlation between average scores on a population N and B another distribution of (1000) correlation coefficient obtained from correlation between average scores on a population n (nЄN).

a ttest reject the equality of A and B even if mean A =0.98 and mean B= 0.97?!!

nadra

[Ksharp]

Hi.
How about Wilcox Rank Sum test ? It is assuming A and B both from the same distribution. And it is non-parameter method , which is much robust.


Ksharp

[nadra]

> Hi.
> How about Wilcox Rank Sum test ? It is assuming A and
> B both from the same distribution. And it is
> non-parameter method , which is much robust.
>
>
> Ksharp

Hi,

I used the test also but what I see is that these tests are very sensitive. As I mentionned above even if the two distribution have the same shapes, same means, the test tend to reject the hypothesis of the equality if the two distribution.

Does a quantile test exists? something that compares paired quantiles ?

Thanks,

[Ksharp]

Hi.
If you want to compare paired quantiles.
You can make another 'difference' variable ( dif = A -B ),then test whether its mean equal zero.
But I am not quit sure this method's power, since you want some exact distribution test.


Ksharp

[SPR]

Hello Nadra,

I still do not understand why you can not use KS. A null hypothesis for KS is that both samples are drawn from the same distribution. Is not it your purpose?

Sincerely,
SPR

[nadra]

> Hello Nadra,
>
> I still do not understand why you can not use KS. A
> null hypothesis for KS is that both samples are drawn
> from the same distribution. Is not it your purpose?
>
> Sincerely,
> SPR

Hi,

Indeed, my purpose is is that both samples are drawn from the same distribution but KS assumption suppose that A and B are independent which is not the case here

Thanks

[Dale]

You can use the GLIMMIX procedure to test hypotheses about correlations in dependent data. Below is code to generate variables Y1, Y2, and Y3 with a specified correlation structure. After generating the data, PROC CORR is run to show that the specified correlation structure was actually generated. The data are then written in a form suitable for the GLIMMIX procedure and then the GLIMMIX procedure is invoked with a COVTEST statement to test equality of two of the correlations.

/***********************************/
/* Construct variables Y1, Y2, Y3 */
/* which have covariance structure */
/* */
/* 1 rho12 rho13 */
/* rho12 1 rho23 */
/* rho13 rho23 1 */
/***********************************/
data test;
  rho12 = 0.6;
  rho13 = 0.6;
  rho23 = 0.3;
  a11 = 1;
  a21 = rho12;
  a31 = rho13;
  a22 = sqrt(1 - a21**2);
  a32 = (rho23 - a31*a21)/a22;
  a33 = sqrt(1 - a31**2 - a32**2);
  do subject=1 to 10000;
      x1 = rannor(1234579);
      x2 = rannor(1234579);
      x3 = rannor(1234579);
      y1 = a11*x1;
      y2 = a21*x1 + a22*x2;
      y3 = a31*x1 + a32*x2 + a33*x3;
      output;
  end;
  drop rho: a: x:;
run;

/* Compute correlations between Ys */
proc corr data=test;
  var y:;
run;


/* Write the data in long form */
/* for use in GLIMMIX procedure */
data test_long;
  set test;
  y = y1; response=1; output;
  y = y2; response=2; output;
  y = y3; response=3; output;
run;


/* Obtain correlations using the GLIMMIX procedure */
/* and test whether the rho12=rho13. */
proc glimmix data=test_long;
  class subject response;
  model y =;
  random response / subject=subject residual type=unr;
  covtest general 0 0 0 -1 1 0;
run;


Feel free to modify the code to change the correlations. You might also want to change the sample size. I used a very large sample size to demonstrate that the assumed correlations were actually generated.