# Shouldn't the pwr.r.test on correlation estimate higher n for a higher rho value?

The pwr.r.test in R which uses the arctanh transformation (Fisher's $z$ transformation) relates inversely with the correlation coefficient. That is, if $r$ is high then $n$ is low.

pwr.r.test(n=NULL, r=.7, sig.level=0.01, power=0.99, alternative="two.sided")


gives n = 34.4932. Whereas,

pwr.r.test(n=NULL, r=.9, sig.level=0.01, power=0.99, alternative="two.sided")


gives n = 13.84951.

Isn't that counterintuitive? For a higher correlation value, I'd expect more samples. Thus higher $n$ to say that the correlation is significant.

• Why would you expect higher n when the correlation is stronger (further from the null value of 0)? – mark999 Oct 18 '17 at 9:52
• Well I'm trying to measure the sig. of the cor. , thus I put n==NULL in the pwr.t.test , I would expect higher n since the strong cor. might be a false pos. The stronger the cor. , the more samples should be needed to ascertain the sig. – Kamaldeep Singh Oct 18 '17 at 9:55

pwr.r.test performs sample size calculation for a correlation test (H0: true correlation = 0). The question is: how many samples do I need to detect the anticipated correlation (r argument) ? Well, it is harder to detect a correlation of 0.7 than a correlation of 0.9. Hence the larger sample size in the former case.