# SIGN.test: Sign Test In PASWR2: Probability and Statistics with R, Second Edition

## Description

This function will test a hypothesis based on the sign test and reports linearly interpolated confidence intervals for one sample problems.

## Usage

 ```1 2 3 4 5 6 7 8``` ```SIGN.test( x, y = NULL, md = 0, alternative = "two.sided", conf.level = 0.95, ... ) ```

## Arguments

 `x` numeric vector; `NA`s and `Inf`s are allowed but will be removed. `y` optional numeric vector; `NA`s and `Inf`s are allowed but will be removed. `md` a single number representing the value of the population median specified by the null hypothesis `alternative` is a character string, one of `"greater"`, `"less"`, or `"two.sided"`, or the initial letter of each, indicating the specification of the alternative hypothesis. For one-sample tests, `alternative` refers to the true median of the parent population in relation to the hypothesized value of the median. `conf.level` confidence level for the returned confidence interval, restricted to lie between zero and one `...` further arguments to be passed to or from methods

## Details

Computes a “Dependent-samples Sign-Test” if both `x` and `y` are provided. If only `x` is provided, computes the “Sign-Test.”

## Value

A list of class `htest_S`, containing the following components:

 `statistic` the S-statistic (the number of positive differences between the data and the hypothesized median), with names attribute “S”. `p.value` the p-value for the test `conf.int` is a confidence interval (vector of length 2) for the true median based on linear interpolation. The confidence level is recorded in the attribute `conf.level`. When the alternative is not `"two.sided"`, the confidence interval will be half-infinite, to reflect the interpretation of a confidence interval as the set of all values `k` for which one would not reject the null hypothesis that the true mean or difference in means is `k`. Here infinity will be represented by `Inf`. `estimate` is avector of length 1, giving the sample median; this estimates the corresponding population parameter. Component `estimate` has a names attribute describing its elements. `null.value` is the value of the median specified by the null hypothesis. This equals the input argument `md`. Component `null.value` has a names attribute describing its elements. `alternative` records the value of the input argument alternative: `"greater"`, `"less"`, or `"two.sided"` `data.name` a character string (vector of length 1) containing the actual name of the input vector `x` `Confidence.Intervals` a 3 by 3 matrix containing the lower achieved confidence interval, the interpolated confidence interval, and the upper achived confidence interval

## Null Hypothesis

For the one-sample sign-test, the null hypothesis is that the median of the population from which `x` is drawn is `md`. For the two-sample dependent case, the null hypothesis is that the median for the differences of the populations from which `x` and `y` are drawn is `md`. The alternative hypothesis indicates the direction of divergence of the population median for `x` from `md` (i.e., `"greater"`, `"less"`, `"two.sided"`.)

## Assumptions

The median test assumes the parent population is continuous.

## Note

The reported confidence interval is based on linear interpolation. The lower and upper confidence levels are exact.

## Author(s)

Alan T. Arnholt <arnholtat@appstate.edu>

## References

• Gibbons, J.D. and Chakraborti, S. 1992. Nonparametric Statistical Inference. Marcel Dekker Inc., New York.

• Kitchens, L.J. 2003. Basic Statistics and Data Analysis. Duxbury.

• Conover, W. J. 1980. Practical Nonparametric Statistics, 2nd ed. Wiley, New York.

• Lehmann, E. L. 1975. Nonparametrics: Statistical Methods Based on Ranks. Holden and Day, San Francisco.

`z.test`, `zsum.test`, `tsum.test`
 ```1 2 3 4 5``` ```with(data = PHONE, SIGN.test(call.time, md = 2.1)) # Computes two-sided sign-test for the null hypothesis # that the population median is 2.1. The alternative # hypothesis is that the median is not 2.1. An interpolated # upper 95% upper bound for the population median will be computed. ```