Overview: CORR Procedure

The CORR procedure computes Pearson correlation coefficients, three nonparametric measures of association, and the probabilities associated with these statistics. The correlation statistics include the following:

• Pearson product-moment correlation

• Spearman rank-order correlation

• Kendall’s tau-b coefficient

• Hoeffding’s measure of dependence,

• Pearson, Spearman, and Kendall partial correlation

Pearson product-moment correlation is a parametric measure of a linear relationship between two variables. For nonparametric measures of association, Spearman rank-order correlation uses the ranks of the data values and Kendall’s tau-b uses the number of concordances and discordances in paired observations. Hoeffding’s measure of dependence is another nonparametric measure of association that detects more general departures from independence. A partial correlation provides a measure of the correlation between two variables after controlling the effects of other variables.

With only one set of analysis variables specified, the default correlation analysis includes descriptive statistics for each analysis variable and Pearson correlation statistics for these variables. You can also compute Cronbach’s coefficient alpha for estimating reliability.

With two sets of analysis variables specified, the default correlation analysis includes descriptive statistics for each analysis variable and Pearson correlation statistics between these two sets of variables.

For a Pearson or Spearman correlation, the Fisher’s transformation can be used to derive its confidence limits and a -value under a specified null hypothesis . Either a one-sided or a two-sided alternative is used for these statistics.

You can save the correlation statistics in a SAS data set for use with other statistical and reporting procedures.

When the relationship between two variables is nonlinear or when outliers are present, the correlation coefficient might incorrectly estimate the strength of the relationship. Plotting the data enables you to verify the linear relationship and to identify the potential outliers. If the ODS GRAPHICS ON statement is specified, scatter plots and a scatter plot matrix can be created via the Output Delivery System (ODS). Confidence and prediction ellipses can also be added to the scatter plot. See the section Confidence and Prediction Ellipses for a detailed description of the ellipses.