Finding critical values for the Pearson correlation coefficient

Question

I'd like to use R to find the critical values for the Pearson correlation coefficient.

This has proved difficult to find in search engines since the standard variable for the Pearson correlation coefficient is itself r. In turn, I'm finding a lot of r critical value tables (rather than how to find this by using the statistical package R).

I'm looking for a function that will provide output like the following:

I'm comfortable finding the correlation with:

cor(x,y)

However, I'd also like to find the critical values.

Is there a function I can use to enter n (or degrees of freedom) as well as alpha in order to find the critical value?

Answer 1

The significance of a correlation coefficient, r, is determined by converting r to a t-statistic and then finding the significance of that t-value at the degrees of freedom that correspond to the sample size, n. So, you can use R to find the critical t-value and then convert that value back to a correlation coefficient to find the critical correlation coefficient.

critical.r <- function( n, alpha = .05 ) {
  df <- n - 2
  critical.t <- qt(alpha/2, df, lower.tail = F)
  critical.r <- sqrt( (critical.t^2) / ( (critical.t^2) + df ) )
  return(critical.r)
}
# Example usage: Critical correlation coefficient at sample size of n = 100
critical.r( 100 )