0
$\begingroup$

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.

Improve this question
$\endgroup$
2
  • $\begingroup$ Why would you expect higher n when the correlation is stronger (further from the null value of 0)? $\endgroup$ – mark999 Oct 18 '17 at 9:52
  • $\begingroup$ 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. $\endgroup$ – Kamaldeep Singh Oct 18 '17 at 9:55
3
$\begingroup$

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.

More info here.

Improve this answer
$\endgroup$
2
  • $\begingroup$ Sorry i don't get this part - why would a cor of 0.7 be more harder to detect than 0.9 ? Assuming we are sampling our data set , its possible to sample in such a way so as to achieve a weak correlation between 2 variables which is false positive. If we need a strong cor. which is significant enough, you need more samples. The same is case when you do a t-test . The more sig and power you choose the higher your N . $\endgroup$ – Kamaldeep Singh Oct 18 '17 at 13:05
  • 1
    $\begingroup$ Sorry, I do not follow you.... In a t-test, a difference of 1 is harder to detect than a difference of 10000. Likewise, a correlation of 0.7 is harder to detect than a correlation of 0.9. $\endgroup$ – ocram Oct 18 '17 at 13:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.