Compute Kendall rank correlation coefficient between two objects. Kendall is a coefficient used in statistics to measure the ordinal association between two measured quantities. A tau test is a non-parametric hypothesis test for statistical dependence based on the tau coefficient. The 'kendallTau' function applies the "kendall" method from 'stats::cor' with some previous treatment in the data, such as converting floating numbers into ranks (from the higher being the first and negative being the last) and the possibility to remove zeros from incomplete ranks
Perform a pairwise permutation test to assess statistical differences in Kendall's Tau correlation between two or more groups.
kendallTau(x, y, null.rm = TRUE, average = TRUE, na.omit = FALSE, ...)
# Default S3 method
kendallTau(x, y, null.rm = TRUE, ...)
# S3 method for class 'matrix'
kendallTau(x, y, null.rm = TRUE, average = TRUE, na.omit = FALSE, ...)
# S3 method for class 'rankings'
kendallTau(x, y, ...)
# S3 method for class 'grouped_rankings'
kendallTau(x, y, ...)
# S3 method for class 'paircomp'
kendallTau(x, y, ...)
kendallTau_bootstrap(x, y, nboot = 100, seed = NULL, ...)
kendallTau_permute(x, y, split, n.permutations = 500)a numeric vector, matrix or data frame
a vector, matrix or data frame with compatible dimensions to x
logical, to remove zeros from x and y
logical, if FALSE returns the kendall and N-effective for each entry
logical, if TRUE ignores entries with kendall = NA
when computing the average
further arguments affecting the Kendall tau produced. See details
integer, the size of the bootstrap sample
integer, the seed for random number generation. If NULL (the default), gosset will set the seed randomly
a vector indicating the splitting rule for the test
an integer, the number of permutations to perform
The Kendall correlation coefficient and the Effective N, which is the equivalent N needed if all items were compared to all items. Used for significance testing.
A data.frame containing:
observed absolute differences in Kendall's tau for all group pairs.
p-values from the permutation test for all group pairs.
Kendall M. G. (1938). Biometrika, 30(1–2), 81–93. doi:10.1093/biomet/30.1-2.81
# Vector based example same as stats::cor(x, y, method = "kendall")
# but showing N-effective
x = c(1, 2, 3, 4, 5)
y = c(1, 1, 3, 2, NA)
w = c(1, 1, 3, 2, 5)
kendallTau(x, y)
kendallTau(x, w)
# Matrix and PlacketLuce ranking example
library("PlackettLuce")
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)
kendallTau(R, preds)
# Also returns raw values (no average)
kendallTau(R, preds, average = FALSE)
# Choose to ignore entries with NA
R2 = matrix(c(1, 2, 4, 3,
1, 4, 2, 3,
NA, NA, NA, NA,
1, 2, 4, 3,
1, 3, 4, 2,
1, 4, 3, 2), nrow = 6, byrow = TRUE)
kendallTau(R, R2, average = FALSE)
kendallTau(R, R2, average = TRUE)
kendallTau(R, R2, average = TRUE, na.omit = TRUE)
if (FALSE) { # interactive()
set.seed(42)
x = rnorm(100)
y = rnorm(100)
split = rep(c("Group1", "Group2", "Group3"), length.out = 100)
kendallTau_permute(x, y, split)
data("breadwheat", package = "gosset")
x = rank_tricot(breadwheat,
items = paste0("variety_", letters[1:3]),
input = c("yield_best", "yield_worst"),
validate.rankings = TRUE)
y = rank_tricot(breadwheat,
items = paste0("variety_", letters[1:3]),
input = c("overall_best", "overall_worst"),
validate.rankings = TRUE)
kendallTau_permute(x, y,
split = rep(c("Group1", "Group2", "Group3"), length.out = nrow(breadwheat)),
n.permutations = 100)
}