## General Instructions

To do each example, just click the Submit

button.
You do not have to type in any R instructions or specify a dataset.
That's already done for you.

## Kendall's Tau

### Hypothesis Test

### Example 8.1 in Hollander and Wolfe.

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).

### Point Estimate

### Example 8.1 in Hollander and Wolfe.

Same thing, except that we don't have to bother with the
`alternative = "greater"`

.

### Confidence Interval

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).

## Spearman's Rho

### Hypothesis Test

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.

### Example 8.5 in Hollander and Wolfe.

### Point Estimate and Confidence Interval

Spearman's rho doesn't actually estimate any population quantity of interest.

It does estimate φ defined on p. 405 in Hollander and Wolfe, but that's not a very interesting quantity.

Hence we don't consider it an estimator of anything and the question of confidence intervals is moot.