1. estimate r 2. do the z transformation - z is a simple function of r - z has an approximate standard normal distribution. 3. use the normal distribution tables to decide on the significance of z or of differences between two z's.
I don't see the need for packages. John C Frain 3 Aranleigh Park Rathfarnham Dublin 14 Ireland www.tcd.ie/Economics/staff/frainj/home.html https://jcfrain.wordpress.com/ https://jcfraincv19.wordpress.com/ mailto:fra...@tcd.ie mailto:fra...@gmail.com On Thu, 23 Mar 2023 at 09:30, Luigi Marongiu <marongiu.lu...@gmail.com> wrote: > Thank you, but this now sounds more difficult: what would be the point > in having these ready-made functions if I have to do it manually? > Anyway, How would I implement the last part? > > On Thu, Mar 23, 2023 at 1:23 AM Ebert,Timothy Aaron <teb...@ufl.edu> > wrote: > > > > If you are open to other options: > > The null hypothesis is that there is no difference. > > If I have two equations y=x and y=z and there is no difference then > it would not matter if an observation was from x or z. > > Randomize the x and z observations. For each randomization calculate > a correlation for y=x and for y=z. > > At each iteration calculate the absolute value of the difference in > the correlations. > > Generate a frequency distribution from 100,000+ randomizations. > > Find the observed difference in the frequency from random > distributions. > > What proportion of observations are as large or larger than the > observed. This is your p-value. > > > > Tim > > > > -----Original Message----- > > From: R-help <r-help-boun...@r-project.org> On Behalf Of Luigi Marongiu > > Sent: Wednesday, March 22, 2023 5:12 PM > > To: r-help <r-help@r-project.org> > > Subject: [R] How to test the difference between paired correlations? > > > > [External Email] > > > > Hello, > > I have three numerical variables and I would like to test if their > correlation is significantly different. > > I have seen that there is a package that "Test the difference between > two (paired or unpaired) correlations". > > [ > https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.personality-project.org%2Fr%2Fhtml%2Fpaired.r.html&data=05%7C01%7Ctebert%40ufl.edu%7C35f2e7d6d9e844553c6408db2b1a337f%7C0d4da0f84a314d76ace60a62331e1b84%7C0%7C0%7C638151163767327230%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=S5T%2F1r%2BotV2BeL7S8bQFR0Avi4jDOuRX8N7LxACA6jg%3D&reserved=0 > ] > > However, there is the need to convert the correlations to "z scores > using the Fisher r-z transform". I have seen that there is another package > that does that [ > https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fsearch.r-project.org%2FCRAN%2Frefmans%2FDescTools%2Fhtml%2FFisherZ.html&data=05%7C01%7Ctebert%40ufl.edu%7C35f2e7d6d9e844553c6408db2b1a337f%7C0d4da0f84a314d76ace60a62331e1b84%7C0%7C0%7C638151163767327230%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=gI3vIHV5UnFbPSmeMyuCVvg9hpFCdF33qNgAXmOQOXU%3D&reserved=0 > ]. > > Yet, I do not understand how to process the data. Shall I pass the raw > data or the correlations directly? > > > > I have made the following working example: > > ``` > > # define data > > v1 <- c(62.480, 59.492, 74.060, 88.519, 91.417, 53.907, 64.202, > 62.426, > > 54.406, 88.117) > > v2 <- c(56.814, 42.005, 56.074, 65.990, 81.572, 53.855, 50.335, 63.537, > 41.713, > > 78.265) > > v3 <- c(54.170, 64.224, 57.569, 85.089, 104.056, 48.713, 61.239, > 60.290, > > 67.308, 71.179) > > # visual exploration > > par(mfrow=c(2, 1)) > > plot(v2~v1, ylim=c(min(c(v1,v2,v3)), max(c(v1,v2,v3))), > > xlim=c(min(c(v1,v2,v3)), max(c(v1,v2,v3))), > > main="V1 vs V2") > > abline(lm(v2~v1)) > > plot(v3~v1, ylim=c(min(c(v1,v2,v3)), max(c(v1,v2,v3))), > > xlim=c(min(c(v1,v2,v3)), max(c(v1,v2,v3))), > > main="V1 vs V3") > > abline(lm(v3~v1)) > > ## test differences in correlation > > # convert raw data into z-scores > > library(psych) > > library(DescTools) > > FisherZ(v1) # I cannot convert the raw data into z scores (same for the > other variables): > > > [1] NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Warning message: > > > In log((1 + rho)/(1 - rho)) : NaNs produced > > # convert correlations into z scores > > # (the correlation score of 0.79 has been converted into 1.08; is this > correct?) > > FisherZ(lm(v2~v1)$coefficients[2]) > > > v1 > > > 1.081667 > > lm(v2~v1)$coefficients[2] > > > v1 > > > 0.7938164 > > # apply test > > v1_v2 = FisherZ(lm(v2~v1)$coefficients[2]) > > v1_v3 = FisherZ(lm(v3~v1)$coefficients[2]) > > paired.r(v1_v2, v1_v3, yz=NULL, length(v1), n2=NULL, twotailed=TRUE) > > > Call: paired.r(xy = v1_v2, xz = v1_v3, yz = NULL, n = length(v1), n2 = > NULL, > > > twotailed = TRUE) > > > [1] "test of difference between two independent correlations" > > > z = NaN With probability = NaNWarning messages: > > > 1: In log((1 + xy)/(1 - xy)) : NaNs produced > > > 2: In log((1 + xz)/(1 - xz)) : NaNs produced > > ``` > > > > What is the right way to run this test? > > Shall I apply also yz? > > Thank you > > > > -- > > Best regards, > > Luigi > > > > ______________________________________________ > > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > > > https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fstat.ethz.ch%2Fmailman%2Flistinfo%2Fr-help&data=05%7C01%7Ctebert%40ufl.edu%7C35f2e7d6d9e844553c6408db2b1a337f%7C0d4da0f84a314d76ace60a62331e1b84%7C0%7C0%7C638151163767327230%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=C%2FnA51iGPdivPDSPOktAvvb7r%2BjACQCqvcAc5jVMPew%3D&reserved=0 > > PLEASE do read the posting guide > https://nam10.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.r-project.org%2Fposting-guide.html&data=05%7C01%7Ctebert%40ufl.edu%7C35f2e7d6d9e844553c6408db2b1a337f%7C0d4da0f84a314d76ace60a62331e1b84%7C0%7C0%7C638151163767327230%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=wKr4mBr%2ByPybzuj1xUzD1a75yfLHQ9uagaUfrE%2F6JDk%3D&reserved=0 > > and provide commented, minimal, self-contained, reproducible code. > > > > -- > Best regards, > Luigi > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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 -- To UNSUBSCRIBE and more, see 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.