The CORR Procedure
- Overview
- Getting Started
-
Syntax
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DetailsPearson Product-Moment CorrelationSpearman Rank-Order CorrelationKendall’s Tau-b Correlation CoefficientHoeffding Dependence CoefficientPartial CorrelationFisher’s z TransformationPolychoric CorrelationPolyserial CorrelationCronbach’s Coefficient AlphaConfidence and Prediction EllipsesMissing ValuesIn-Database ComputationOutput TablesOutput Data SetsODS Table NamesODS Graphics
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ExamplesComputing Four Measures of AssociationComputing Correlations between Two Sets of VariablesAnalysis Using Fisher’s z TransformationApplications of Fisher’s z TransformationComputing Polyserial CorrelationsComputing Cronbach’s Coefficient AlphaSaving Correlations in an Output Data SetCreating Scatter PlotsComputing Partial Correlations
- References
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.
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
| 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.