The CORR Procedure
- Overview
- Getting Started
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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
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
| Pearson Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations |
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Weight | Oxygen | RunTime | ||||||||||
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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 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
| 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.