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

```
SIGN.test(
x,
y = NULL,
md = 0,
alternative = "two.sided",
conf.level = 0.95,
...
)
```

- 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

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

Computes a “Dependent-samples Sign-Test” if both `x`

and
`y`

are provided. If only `x`

is provided, computes the
“Sign-Test”.

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

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"`

.)

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.

```
x <- c(7.8, 6.6, 6.5, 7.4, 7.3, 7., 6.4, 7.1, 6.7, 7.6, 6.8)
SIGN.test(x, md = 6.5)
#>
#> One-sample Sign-Test
#>
#> data: x
#> s = 9, p-value = 0.02148
#> alternative hypothesis: true median is not equal to 6.5
#> 95 percent confidence interval:
#> 6.571273 7.457455
#> sample estimates:
#> median of x
#> 7
#>
#> Achieved and Interpolated Confidence Intervals:
#>
#> Conf.Level L.E.pt U.E.pt
#> Lower Achieved CI 0.9346 6.6000 7.4000
#> Interpolated CI 0.9500 6.5713 7.4575
#> Upper Achieved CI 0.9883 6.5000 7.6000
#>
# Computes two-sided sign-test for the null hypothesis
# that the population median for 'x' is 6.5. The alternative
# hypothesis is that the median is not 6.5. An interpolated 95%
# confidence interval for the population median will be computed.
reaction <- c(14.3, 13.7, 15.4, 14.7, 12.4, 13.1, 9.2, 14.2,
14.4, 15.8, 11.3, 15.0)
SIGN.test(reaction, md = 15, alternative = "less")
#>
#> One-sample Sign-Test
#>
#> data: reaction
#> s = 2, p-value = 0.03271
#> alternative hypothesis: true median is less than 15
#> 95 percent confidence interval:
#> -Inf 14.82845
#> sample estimates:
#> median of x
#> 14.25
#>
#> Achieved and Interpolated Confidence Intervals:
#>
#> Conf.Level L.E.pt U.E.pt
#> Lower Achieved CI 0.9270 -Inf 14.7000
#> Interpolated CI 0.9500 -Inf 14.8285
#> Upper Achieved CI 0.9807 -Inf 15.0000
#>
# Data from Example 6.11 page 330 of Kitchens BSDA.
# Computes one-sided sign-test for the null hypothesis
# that the population median is 15. The alternative
# hypothesis is that the median is less than 15.
# An interpolated upper 95% upper bound for the population
# median will be computed.
```