This is pretty much standard. I'm quite sure that other stats packages do likewise and I wouldn't know who "everyone" is. It is not unheard of that textbook authors give suboptimal formulas in order not to confuse students, though.

The basic point is that the t transformation gives the exact distribution under the null. Fisher's Z is only approximately normally distributed.

The t transformation works because if beta is the regression coefficient of y on x, beta==0 iff rho==0, and we have exact theory for testing beta==0 by a t-test.

Off-null, the t-approach does not readily transfer, so confidence intervals tend to be based on the Z-transformation.

-Peter D.

On 17 Oct 2014, at 02:20 , Joshua Wiley <

[hidden email]> wrote:

> Hi Jeremy,

>

> I don't know about references, but this around. See for example:

>

http://afni.nimh.nih.gov/sscc/gangc/tr.html>

> the relevant line in cor.test is:

>

> STATISTIC <- c(t = sqrt(df) * r/sqrt(1 - r^2))

>

> You can convert *t*s to *r*s and vice versa.

>

> Best,

>

> Josh

>

>

>

> On Fri, Oct 17, 2014 at 10:32 AM, Jeremy Miles <

[hidden email]>

> wrote:

>

>> 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

>>

>> ______________________________________________

>>

[hidden email] 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.

>>

>

>

>

> --

> Joshua F. Wiley

> Ph.D. Student, UCLA Department of Psychology

>

http://joshuawiley.com/> Senior Analyst, Elkhart Group Ltd.

>

http://elkhartgroup.com> Office: 260.673.5518

>

> [[alternative HTML version deleted]]

>

> ______________________________________________

>

[hidden email] 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.

--

Peter Dalgaard, Professor,

Center for Statistics, Copenhagen Business School

Solbjerg Plads 3, 2000 Frederiksberg, Denmark

Phone: (+45)38153501

Email:

[hidden email] Priv:

[hidden email]
______________________________________________

[hidden email] mailing list

https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide

http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.