**StATS: ****Tests of hypothesis and confidence intervals involving a correlation coefficient (January
18, 2007)**

Suppose you compute a correlation coefficient from a sample of patients. Can you test a hypothesis about this correlation? Can you place confidence limits around this correlation? Yes, you can, but there are a wide array of approaches that you could use.

If you are testing the hypothesis that the correlation is equal to zero, you can compute a test statistic.

You would compare this test statistic with a t distribution with n-2 degrees of freedom. Someone asked me for a table of critical values for r. When the observed correlation is larger than the critical value, you would reject the null hypothesis. You can get the formula for the critical value:

through simple algebra. I programmed a spreadsheet

to perform these calculations.

If you want to compute a confidence interval for the correlation coefficient, you can't necessarily assume that the population correlation is equal to zero. Instead, you use the Fisher's Z transformation. I'll write up some details about this transformation and work up some examples soon.

This work is licensed under a Creative Commons Attribution 3.0 United States License. It was written by Steve Simon.

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Linear regression.