The distribution of rho…

March 21, 2010
By

(This article was first published on Stats raving mad » R, and kindly contributed to R-bloggers)

There was a post here about obtaining non-standard p-values for testing the correlation coefficient. The R-library

SuppDists

deals with this problem efficiently.

library(SuppDists)

plot(function(x)dPearson(x,N=23,rho=0.7),-1,1,ylim=c(0,10),ylab="density")
plot(function(x)dPearson(x,N=23,rho=0),-1,1,add=TRUE,col="steelblue")
plot(function(x)dPearson(x,N=23,rho=-.2),-1,1,add=TRUE,col="green")
plot(function(x)dPearson(x,N=23,rho=.9),-1,1,add=TRUE,col="red");grid()

legend("topleft", col=c("black","steelblue","red","green"),lty=1,
		legend=c("rho=0.7","rho=0","rho=-.2","rho=.9"))</pre>

This is how it looks like,


Now, let’s construct a table of critical values for some arbitrary or not significance levels.

q=c(.025,.05,.075,.1,.15,.2)
xtabs(qPearson(p=q, N=23, rho = 0, lower.tail = FALSE, log.p = FALSE) ~ q )
# q
#     0.025      0.05     0.075       0.1      0.15       0.2
# 0.4130710 0.3514298 0.3099236 0.2773518 0.2258566 0.1842217

We can calculate p-values as usual too…

1-pPearson(.41307,N=23,rho=0)
# [1] 0.0250003

To leave a comment for the author, please follow the link and comment on his blog: Stats raving mad » R.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Tags: , , , , , , ,

Comments are closed.