kendall.w <- function(x)
{
nv <- ncol(x)
nc <- nrow(x)
o <- apply(x, 2, rank)
t <- apply(o, 2, tabulate)
s1 <- apply(o, 1, sum)
w <- 12*sum((s1-sum(s1)/nc)^2)/(nv^2*(nc^3-nc)-nv*sum(sapply(1:nv, function(i) {sum(t[[i]]^3-t[[i]])})))
p <- 1-pchisq((chi <- nv*(nc-1)*w), nc-1)
result <- c(w, chi, nc-1, p)
names(result) <- c("Kendall W", "chi sq.", "d.f.", "P value")
result
}
x <- matrix(c(6,6,2,2,5,4, 1,5,5,4,2,3, 6,3,2,5,4,4), ncol=3)
rownames(x) <- paste("object", 1:6, sep="")
colnames(x) <- paste("rater", 1:3, sep="")
kendall.w(x)
# rater1 rater2 rater3
# object1 6 1 6
# object2 6 5 3
# object3 2 5 2
# object4 2 4 5
# object5 5 2 4
# object6 4 3 4
# result
# Kendall W chi sq. d.f. P value
# 0.1221122 1.8316832 5.0000000 0.8719100