# The CORR Procedure

### Example 2.3 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 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 z transformation in Output 2.3.2.

Output 2.3.2: 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 2.3.3 displays correlation statistics by using Fisher’s z transformation.

Output 2.3.3: One-Sided Correlation Analysis Using Fisher’s z 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 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.