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Compare correlations using Fisher's Z transformation

PURPOSE:

This program uses Fisher's Z transformation to compare the correlations in one matrix with those correlations in a second matrix. A test statistic and p-value are computed for each pair of correlations testing the hypothesis that the sample correlations estimate the same population correlation value.

REQUIREMENTS:

BASE SAS Software, Release 6.08 or later.

USAGE:

Follow the instructions in the Downloads tab of this sample to save the %COMPCORR macro definition. Replace the text within quotes in the following statement with the location of the %COMPCORR macro definition file on your system. In your SAS program or in the SAS editor window, specify this statement to define the %COMPCORR macro and make it available for use:

   %inc "<location of your file containing the COMPCORR macro>";

Following this statement, you may call the %COMPCORR macro. See the Results tab for an example.

The parameters of the macro are described below. All parameters are required and must be specified.

SET1=

SAS data set which contains the original data used as input to PROC CORR.

CORR1=

SAS data set of TYPE='CORR'. Most often this is an OUTP= data set generated by PROC CORR.

SET2=

SAS data set which contains the original data used as input to PROC CORR.

CORR2=

SAS data set of TYPE='CORR'. Most often this is an OUTP= data set generated by PROC CORR.

OUT=

SAS data set which contains 12 variables:

• 2 variables (VAR1_1, VAR1_2) which indicate the variable names for the first correlation.
• 2 variables (VAR1_1, VAR1_2) which indicate the variable names for the second correlation.
• 2 variables (CORR1, CORR2) for the two correlations.
• 2 variables (N1, N2) for the number of observations used to compute the two correlations.
• 4 variables (D, SIGD, Z0 and PVAL) for the test statistics and p-value.

DETAILS:

The method used is described in Snedecor & Cochran (1980).

The method is not appropriate for two comparing two dependent correlations. Consequently, this program will not compare correlations which involve a shared variable from a shared data set. That is, if SET1=SET2 and if the two correlation coefficients share at least one of the variables, then the test isn't output, since the correlations aren't independent. User should be aware of other possible violations in independence.

Small p-values indicate strong evidence that the correlations estimate different rho values.

MISSING VALUES:

Missing values are handled on a pairwise basis for each correlation.

SEE ALSO:

The %CORRCI macro (defined and used within the %COMPCORR macro) computes 95% confidence limits for correlation coefficients using Fisher's Z. The %CORRPVAL macro restructures the output data set from PROC CORR to include p-values and the number of observations used along with the correlation estimates.

REFERENCES:

Snedecor & Cochran (1980), Statistical Methods, Iowa State University Press, pages 185-188.

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These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.

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These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.

EXAMPLE:

The following example generates some random data and uses the %COMPCORR macro to compare the correlations among variables X1, X2, and X3 with the correlations among X4, X5, and X6.

     data one;  * generate artificial dataset ;
         do i=1 to 100;
          x1=normal(529);
          x2=normal(529);
          x3=normal(529);
          x4=normal(529);
          x5=normal(529);
          x6=normal(529);
          output;
         end;
        run;

        PROC CORR outp=two DATA=one;
         VAR  x1-x3  ;
        RUN;

        PROC CORR outp=three DATA=one;
         VAR  x4-x6  ;
        RUN;

        /* Define the COMPCORR and CORRCI macros */
        %inc "<location of your file containing the COMPCORR macro>";
        %compcorr(set1=one, corr1=two, set2=one, corr2=three, out=four);

        proc print data=four noobs;
            var var1_1 var1_2 corr1 n1 var2_1 var2_2 corr2 n2 d sigd z0 pval;
        run;

RESULTS:

The %COMPCORR macro produces only an output data set. Following is the OUT= data set from %COMPCORR in the example above. The first observation is interpreted as follows: The Pearson correlation between variables X1 and X2 is -0.04267 (computed from a sample of 100 (X1, X2) pairs of values). The Pearson correlation between variables X4 and X5 is 0.022997 (computed from a sample of 100 (X4, X5) pairs of values). Fisher's Z is computed for both correlations. The difference between these is D=-0.06570 and its standard deviation is SIGD=0.14359. The ratio Z0=-0.45753 has a p-value of PVAL=0.64729. Since this p-value is not small, we conclude that the data do not present strong evidence that these two Pearson correlations are estimating different population correlation coefficients.

 var1_1 var1_2   corr1   n1 var2_1 var2_2   corr2   n2     d      sigd     z0      pval

   x1     x2   -0.04267 100   x4     x5   0.022997 100 -0.06570 0.14359 -0.45753 0.64729
   x1     x2   -0.04267 100   x4     x6   0.049712 100 -0.09245 0.14359 -0.64383 0.51969
   x1     x2   -0.04267 100   x5     x6   0.064155 100 -0.10694 0.14359 -0.74474 0.45643
   x1     x3   -0.03804 100   x4     x5   0.022997 100 -0.06106 0.14359 -0.42522 0.67067
   x1     x3   -0.03804 100   x4     x6   0.049712 100 -0.08781 0.14359 -0.61153 0.54085
   x1     x3   -0.03804 100   x5     x6   0.064155 100 -0.10230 0.14359 -0.71244 0.47619
   x2     x3    0.18332 100   x4     x5   0.022997 100  0.16241 0.14359  1.13107 0.25803
   x2     x3    0.18332 100   x4     x6   0.049712 100  0.13566 0.14359  0.94477 0.34478
   x2     x3    0.18332 100   x5     x6   0.064155 100  0.12117 0.14359  0.84385 0.39875

Right-click on the link below and select Save to save the %COMPCORR macro definition to a file. It is recommended that you name the file compcorr.sas.

Download and save compcorr.sas

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