Re: [R] Difference betweeen cor.test() and formula everyone says to use
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 jwiley.ps...@gmail.com 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 jeremy.mi...@gmail.com 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 __ 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. -- 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]] __ 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. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd@cbs.dk Priv: pda...@gmail.com __ 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.
Re: [R] Difference betweeen cor.test() and formula everyone says to use
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.
[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.
Re: [R] Difference betweeen cor.test() and formula everyone says to use
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 jeremy.mi...@gmail.com 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 __ 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. -- 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]] __ 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.
