Excel Pearson R function

Question

Does anyone know what the confidence level is for the Pearson R values that you get when you run the PEARSON function? 

As an aside, the answers I have gotten to questions I have posted here have been EXTREMELY helpful.

thank you

Answer 1

Ronald wrote:

Does anyone know what the confidence level is for the Pearson R values that you get when you run the PEARSON function?

This is not a statistic that I know much about.  So I googled "pearson confidence interval" (without quotes) and looked at some of the references.

One seems particularly helpful:  http://onlinestatbook.com/2/estimation/correlation_ci.html and the follow-up link to http://onlinestatbook.com/2/sampling_distributions/samp_dist_r.html.  In a nutshell:

"The computation of a confidence interval on the population value of Pearson's correlation (ρ) is complicated by the fact that the sampling distribution of r is not normally distributed."

"Fortunately, the statistician Fisher developed a way to transform r to a variable that is normally distributed with a known standard error. The variable is called z' ".

You can read the cited references for details.  But the following Excel information might be helpful.

For a 95% confidence interval, instead of hardcoding 1.96, an approximation, I would use -NORMSINV((1-C1)/2), where C1 is the confidence level (95%).

However -- and remember, I don't know much about this -- for a small sampling, I would expect to use the Student's t-value, namely TINV(1-C1, N1-1), where N1 is the size of the sample.

Perhaps someone who is more familiar with the Pearson confidence interval per se can explain why we should not use the Student's t-value for this particular calculation.

Answer 2

Regarding confidence level for Pearson R: It depends on the sample size.

It's likely you'll find several approaches from classical statistics if you use Google or Bing to search for "confidence level for Pearson R" (without the quotes).