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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

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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