## Sign Tests

### Upper-Tailed Tests

There is no R function to do a sign test. We have to do it by hand

,
but this is easy. Suppose we want to do an upper-tailed test with null
hypothesis `H`_{0} θ = θ_{0}.

In the particular examples we do, we will use θ_{0} = 0,
but we will allow for general θ_{0} in the code.

This can also be done loading the data from a URL

### Lower-Tailed Tests

Here is the corresponding lower-tailed test

### Two-Tailed Tests

Here is the corresponding two-tailed test

## Confidence Interval Associated with the Sign Test

Select a `k`, get a confidence interval.

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

## Hodges-Lehmann Estimator Associated with the Sign Test

This is just a long-winded name for the sample 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.