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The CORR Procedure

Example 2.3 Analysis Using Fisher’s z Transformation

The following statements request Pearson correlation statistics by using Fisher’s transformation for the data set Fitness:

proc corr data=Fitness nosimple fisher;
   var weight oxygen runtime;
run;

The NOSIMPLE option suppresses the table of univariate descriptive statistics. By default, PROC CORR displays the "Pearson Correlation Coefficients" table in Output 2.3.1.

Output 2.3.1 Pearson Correlations
The CORR Procedure

Pearson Correlation Coefficients
Prob > |r| under H0: Rho=0
Number of Observations
  Weight Oxygen RunTime
Weight
1.00000
 
31
-0.15358
0.4264
29
0.20072
0.2965
29
Oxygen
-0.15358
0.4264
29
1.00000
 
29
-0.86843
<.0001
28
RunTime
0.20072
0.2965
29
-0.86843
<.0001
28
1.00000
 
29

Using the FISHER option, the CORR procedure displays correlation statistics by using Fisher’s transformation in Output 2.3.2.

Output 2.3.2 Correlation Statistics Using Fisher’s Transformation
Pearson Correlation Statistics (Fisher's z Transformation)
Variable With Variable N Sample Correlation Fisher's z Bias Adjustment Correlation Estimate 95% Confidence Limits p Value for
H0:Rho=0
Weight Oxygen 29 -0.15358 -0.15480 -0.00274 -0.15090 -0.490289 0.228229 0.4299
Weight RunTime 29 0.20072 0.20348 0.00358 0.19727 -0.182422 0.525765 0.2995
Oxygen RunTime 28 -0.86843 -1.32665 -0.01608 -0.86442 -0.935728 -0.725221 <.0001

The table also displays confidence limits and a -value for the default null hypothesis . See the section Fisher’s z Transformation for details on Fisher’s transformation.

The following statements request one-sided hypothesis tests and confidence limits for the correlations using Fisher’s transformation:

proc corr data=Fitness nosimple nocorr fisher (type=lower);
   var weight oxygen runtime;
run;

The NOSIMPLE option suppresses the "Simple Statistics" table, and the NOCORR option suppresses the "Pearson Correlation Coefficients" table.

Output 2.3.3 displays correlation statistics by using Fisher’s transformation.

Output 2.3.3 One-Sided Correlation Analysis Using Fisher’s Transformation
The CORR Procedure

Pearson Correlation Statistics (Fisher's z Transformation)
Variable With Variable N Sample Correlation Fisher's z Bias Adjustment Correlation Estimate Lower 95% CL p Value for
H0:Rho<=0
Weight Oxygen 29 -0.15358 -0.15480 -0.00274 -0.15090 -0.441943 0.7850
Weight RunTime 29 0.20072 0.20348 0.00358 0.19727 -0.122077 0.1497
Oxygen RunTime 28 -0.86843 -1.32665 -0.01608 -0.86442 -0.927408 1.0000

The FISHER(TYPE=LOWER) option requests a lower confidence limit and a -value for the test of the one-sided hypothesis against the alternative hypothesis . Here Fisher’s , the bias adjustment, and the estimate of the correlation are the same as for the two-sided alternative. However, because TYPE=LOWER is specified, only a lower confidence limit is computed for each correlation, and one-sided -values are computed.


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