R/tau.R

In musto101/wilcox_R: What the package does (short line)

tau <-
function(x,y=NULL,alpha=.05){
#
#   Compute Kendall's tau plus a 1-alpha confidence interval
#   using the method recommended by Long and Cliff (1997).
#
#   y=NULL, assume x is a matrix with two columsn
#
if(is.null(y))m=elimna(x) 
if(!is.null(y))m=elimna(cbind(x,y)) # casewise deletion of missing values.
x=m[,1]
y=m[,2]
xdif<-outer(x,x,FUN="-")
ydif<-outer(y,y,FUN="-")
tv<-sign(xdif)*sign(ydif)
dbar<-apply(tv,1,mean)
n<-length(x)
tau<-sum(tv)/(n*(n-1))
A<-sum((dbar-tau)^2)/(n-1)
B<-(n*(n-1)*(-1)*tau^2+sum(tv^2))/(n^2-n-1)
C<-(4*(n-2)*A+2*B)/(n*(n-1))
crit<-qnorm(alpha/2)
cilow<-tau+crit*sqrt(C)
cihi<-tau-crit*sqrt(C)
test<-tau/sqrt((2*(2*n+5))/(9*n*(n-1)))
siglevel<-2*(1-pnorm(abs(test)))
list(cor=tau,ci=c(cilow,cihi),p.value=siglevel)
}