The CORR Procedure
Example 1.3 Analysis Using Fisher’s z Transformation
The following statements request Pearson correlation statistics by using Fisher’s z 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 1.3.1.
Output 1.3.1: Pearson Correlations
| Pearson Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight | Oxygen | RunTime | ||||||||||
| Weight |
|
|
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| Oxygen |
|
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| RunTime |
|
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| |||||||||
Using the FISHER option, the CORR procedure displays correlation statistics by using Fisher’s z transformation in Output 1.3.2.
Output 1.3.2: Correlation Statistics Using Fisher’s z 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 p-value for the default null hypothesis 
. See the section Fisher’s z Transformation for details on Fisher’s z transformation.
The following statements request one-sided hypothesis tests and confidence limits for the correlations using Fisher’s z 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 1.3.3 displays correlation statistics by using Fisher’s z transformation.
Output 1.3.3: One-Sided Correlation Analysis Using Fisher’s z Transformation
| 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 p-value for the test of the one-sided hypothesis 
against the alternative hypothesis 
. Here Fisher’s z, 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 p-values are computed.