For comparison, the second line gives the usual parametric analysis
based on assumption of population normality and using Pearson's
product-moment correlation coefficient (what many textbooks
just call correlation with no qualifying adjectives).

Unfortunately, cor.test doesn't do confidence intervals
for Kendall's tau, so we have to do by hand in R.

Example 8.1 in Hollander and Wolfe.

For comparison, the second analysis (below the blank line) gives the usual
parametric analysis based on assumption of population normality and using
Pearson's product-moment correlation coefficient (what many textbooks
just call correlation with no qualifying adjectives). A reference
is Lindgren Statistical Theory, 4th ed., p. 427.

Unfortunately, the Spearman mode of the cor.test
function doesn't do the right thing in the presence of ties.
The cited reference for the algorithm it uses doesn't have any
adjustment for ties.

Hollander and Wolfe give a very bizarre correction for ties that
actually changes the point estimate (not just its estimated asymptotic
variance) for no reason they explain. Rather than do that, we will
do a Monte Carlo test.