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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
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