gosset (version 1.4)

kendallTau: Kendall rank correlation coefficient

Description

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.

Usage

kendallTau(x, y, null.rm = TRUE, average = TRUE, na.omit = FALSE, ...)
# S3 method for default
kendallTau(x, y, null.rm = TRUE, ...)
# S3 method for matrix
kendallTau(x, y, null.rm = TRUE, average = TRUE, na.omit = FALSE, ...)
# S3 method for rankings
kendallTau(x, y, ...)
# S3 method for grouped_rankings
kendallTau(x, y, ...)
# S3 method for paircomp
kendallTau(x, y, ...)
kendallTau_bootstrap(x, y, nboot = 100, seed = NULL, ...)
kendallTau_permute(x, y, split, n.permutations = 500)

Value

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_diff

observed absolute differences in Kendall's tau for all group pairs.

p_values

p-values from the permutation test for all group pairs.

Arguments

x

a numeric vector, matrix or data frame

y

a vector, matrix or data frame with compatible dimensions to x

null.rm

logical, to remove zeros from x and y

average

logical, if FALSE returns the kendall and N-effective for each entry

na.omit

logical, if TRUE ignores entries with kendall = NA when computing the average

...

further arguments affecting the Kendall tau produced. See details

nboot

integer, the size of the bootstrap sample

seed

integer, the seed for random number generation. If NULL (the default), gosset will set the seed randomly

split

a vector indicating the splitting rule for the test

n.permutations

an integer, the number of permutations to perform

Author

Kauê de Sousa and Jacob van Etten

Kauê de Sousa

References

Kendall M. G. (1938). Biometrika, 30(1–2), 81–93. tools:::Rd_expr_doi("https://doi.org/10.1093/biomet/30.1-2.81")

See Also

cor

kendallTau

Other goodness-of-fit functions: kendallW(), pseudoR2()

Examples

# 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)
                
}