The distribution of the statistic $ndf * r^2 / (1-r^2)$ with the true value $\rho = zero$ follows an $F(1,ndf)$ distribution. So the t-test is the correct test for $\rho=0$. Fisher's z is an asymptotically normal transformation for any value of $\rho$. Thus Fisher's z is better for testing $\rho= \rho_0 $ or $\rho_1 = \rho_2$. The two statistics will not be equivalent at $\rho=0$ because the statistics are based on different assumptions.
Jeremy Miles <jeremy.mi...@gmail.com> Sent by: r-help-boun...@r-project.org 10/16/2014 07:32 PM To r-help <r-help@r-project.org>, cc Subject [R] Difference betweeen cor.test() and formula everyone says to use I'm trying to understand how cor.test() is calculating the p-value of a correlation. It gives a p-value based on t, but every text I've ever seen gives the calculation based on z. For example: > data(cars) > with(cars[1:10, ], cor.test(speed, dist)) Pearson's product-moment correlation data: speed and dist t = 2.3893, df = 8, p-value = 0.04391 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0.02641348 0.90658582 sample estimates: cor 0.6453079 But when I use the regular formula: > r <- cor(cars[1:10, ])[1, 2] > r.z <- fisherz(r) > se <- se <- 1/sqrt(10 - 3) > z <- r.z / se > (1 - pnorm(z))*2 [1] 0.04237039 My p-value is different. The help file for cor.test doesn't (seem to) have any reference to this, and I can see in the source code that it is doing something different. I'm just not sure what. Thanks, Jeremy ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.