# Statistics 5601 (Geyer, Fall 2003) Examples: Correlation

## 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

### Example 8.1 in Hollander and Wolfe.

External Data Entry

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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).

### Example 8.1 in Hollander and Wolfe.

External Data Entry

Enter a dataset URL :

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.

External Data Entry

Enter a dataset URL :

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.

## 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.

External Data Entry

Enter a dataset URL :

### 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.