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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.

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  • $\begingroup$ 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
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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.

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  • $\begingroup$ 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
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    $\begingroup$ 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

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