dev/kendallTau-with-z-value.R

In agrobioinfoservices/gosset: Tools for Data Analysis in Experimental Agriculture

library("PlackettLuce")
library("gosset")
library('DescTools')


R = matrix(c(1, 2, 4, 3,
             1, 4, 2, 3,
             1, 2, NA, 3,
             1, 2, 4, 3,
             1, 3, 4, 2,
             1, 4, 3, 2), nrow = 6, byrow = TRUE)
colnames(R) = LETTERS[1:4]

G = group(as.rankings(R), 1:6)

mod = pltree(G ~ 1, data = G)

preds = predict(mod, type = "rank")

k = kendallTau(R, preds)

k

tau = k[1,1]
n = k[1,2]

# calculate z-value using n effective
z = (3 * tau * sqrt(n*(n-1))) / sqrt(2 * (2*n + 5))

z

# then p-value
p = pnorm(z, lower.tail = F)
p = formatC(p, format = "e", digits = 2)
p


KendallTauB(x = R[1, ], y = preds[1, ], conf.level = 0.95)

kendallTau(x = R[1, ], y = preds[1, ])


# now example with ties
x = c(1, 1, 2, 3)

y = c(1, 2, 2, 3)

kendallTau(x, y)

KendallTauB(x, y, conf.level = 0.95)