How to calculate p-value for Kendall Tau correlation coefficients in R?

Question

I have calculated Kendal correlation coefficients using:

corr_test <- cor.test(values, use = "pairwise", method="kendall")
corr_test

but I need the p-value. I cannot find any packages that provide a p-value for the Kendall correlations.

How can I calculate the p-value for Kendall tau correlation coefficients?

The goal of this task is to generate a correlation plot, where colored cells indicate significant correlation coefficients. I am using Kendall tau because there are many ties in my data and one variable is a factor.

`cor.test(iris$Sepal.Length, iris$Sepal.Width, method = "kendall")` ? — Richard Telford, Aug 01 '19 at 14:33
@teunbrand cor.test also seems to take only vector, i have a matrix — Nneka, Aug 01 '19 at 14:50

score 2 · Answer 1 · answered Aug 01 '19 at 16:10

You can simply iterate over the columns (or rows if you so please) of your data to use cor.test() on each combination of columns as follows:

# Use some data
mat <- iris[,1:4]

# Index combinations of columns
# Not very efficient, but it'll do for now
idx <- expand.grid(colnames(mat), colnames(mat))

# Loop over indices, calculate p-value
pvals <- apply(idx, 1, function(i){
  x <- mat[,i[[1]]]
  y <- mat[,i[[2]]]
  cor.test(x, y, method = "kendall")$p.value
})
# Combine indices with pvalues, do some sort of multiple testing correction
# Note that we are testing column combinations twice 
# so we're overcorrecting with the FDR here
pvals <- cbind.data.frame(idx, pvals = p.adjust(pvals, "fdr"))

Next you would have to supplement these with the regular correlation values and combine these with the p-values.

# Calculate basic correlation
cors <- cor(mat, method = "kendall")
cors <- reshape2::melt(cors)

# Indices of correlations and pvalues should be the same, thus can be merged
if (identical(cors[,1:2], pvals[,1:2])) {
  df <- cbind.data.frame(pvals, cor = cors[,3])
}

And plot the data in the following fashion:

# Plot a matrix
ggplot(df, aes(Var1, Var2, fill = ifelse(pvals < 0.05, cor, 0))) +
  geom_raster() +
  scale_fill_gradient2(name = "Significant Correlation", limits = c(-1, 1))

Another option is to use idx <- t(combn(colnames(mat), 2)), in which case multiple testing corrections are appropriate, but you'll have to figure out how to manipulate these values to match up with the correlations again.

How to calculate p-value for Kendall Tau correlation coefficients in R?

1 Answers1