## Signed Rank Tests

The R function `wilcox.test`

(on-line
help) does signed rank tests and confidence intervals.

## Confidence Interval Associated with the Signed Rank Test

### Using the R Function

The R function `wilcox.test`

also does confidence intervals,
if asked.

### By Hand

Select a`k`, get a confidence interval.

This prints the interval and its actual confidence level (in percent).

The R function `outer`

(on-line
help) does outer products

of matrices and analogous operations
using operators other than multiplication. Here the result is an
`n` × `n` matrix whose `i`,j
element is `x``i` −
`x``j`.

The R function `lower.tri`

(on-line
help) produces the indices of the lower triangle of a matrix. These
can be use with subscripting to extract the lower triangle.

The R function `psignrank`

(on-line
help) calculates the distribution function (DF) of the distribution
under `H`_{0} of the test statistic of the signed rank test.

## Hodges-Lehmann Estimator Associated with the Signed Rank Test

This is just a long-winded name for the median of the Walsh averages.

The median of the Walsh averages is printed as the (pseudo)median

.

## Fuzzy Test

There is an R contributed package `fuzzyRankTests`

that does
the corresponding fuzzy procedures.

do the lower-tailed test, the upper-tailed test, and the two-tailed test, respectively.

## Fuzzy Confidence Intervals

The R contributed package `fuzzyRankTests`

also does
fuzzy confidence intervals.