Confidence interval for correlation coefficient

When we perform the correlation analysis, we typically calculate the correlation coefficient and then test if this correlation coefficient is statistically significant or not. We will then judge the degree of the correlation based on the numerical value of the correlation coefficient. Sometimes, we may want to calculate the confidence interval for correlation coefficient to see if the correlation coefficient has reasonable precision.

The easy way to calculate the confidence interval for correlation coefficient is to use FISHER option in SAS procedure. FISHER option is available after SAS version 9. FISHER option specifies the Fisher's z transformation to estimate 95% confidence intervals for a correlation.

• Stan Brown has a nice description of the Fisher's z transformation
• SAS Provided an explanation for Applications of Fisher’s z Transformation
• A SUGI paper by David Shen provide the SAS codes

When we use the confidence interval to make a judgment about the procision, we need to be aware that this is largely related to the sample size used in the calculation of the correlation coefficient. The larger the sample size, the narrower the confidence interval.