# SignTest: Sign Test In DescTools: Tools for Descriptive Statistics

## Description

Performs one- and two-sample sign tests on vectors of data.

## Usage

 ```1 2 3 4 5 6 7 8``` ```SignTest(x, ...) ## Default S3 method: SignTest(x, y = NULL, alternative = c("two.sided", "less", "greater"), mu = 0, conf.level = 0.95, ... ) ## S3 method for class 'formula' SignTest(formula, data, subset, na.action, ...) ```

## Arguments

 `x` numeric vector of data values. Non-finite (e.g. infinite or missing) values will be omitted. `y` an optional numeric vector of data values: as with x non-finite values will be omitted. `mu` a number specifying an optional parameter used to form the null hypothesis. See Details. `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. `formula` a formula of the form `lhs ~ rhs` where `lhs` gives the data values and rhs the corresponding groups. `data` an optional matrix or data frame (or similar: see `model.frame`) containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`. `subset` an optional vector specifying a subset of observations to be used. `na.action` a function which indicates what should happen when the data contain NAs. Defaults to `getOption("na.action")`. `...` further arguments to be passed to or from methods.

## Details

The formula interface is only applicable for the 2-sample test.

`SignTest` computes a “Dependent-samples Sign-Test” if both `x` and `y` are provided. If only `x` is provided, the “One-sample Sign-Test” will be computed.

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

The confidence levels are exact.

## Value

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

 `statistic` the S-statistic (the number of positive differences between the data and the hypothesized median), with names attribute “S”. `parameter` the total number of valid differences. `p.value` the p-value for the test. `null.value` is the value of the median specified by the null hypothesis. This equals the input argument `mu`. `alternative` a character string describing the alternative hypothesis. `method` the type of test applied. `data.name` a character string giving the names of the data. `conf.int` a confidence interval for the median. `estimate` the sample median.

## Author(s)

Andri Signorell <andri@signorell.net>

## 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.

`t.test`, `wilcox.test`, `ZTest`, `binom.test`, `SIGN.test` in the package BSDA (reporting approximative confidence intervals).

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35``` ```x <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30) y <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29) SignTest(x, y) wilcox.test(x, y, paired = TRUE) d.light <- data.frame( black = c(25.85,28.84,32.05,25.74,20.89,41.05,25.01,24.96,27.47), white <- c(18.23,20.84,22.96,19.68,19.5,24.98,16.61,16.07,24.59), d <- c(7.62,8,9.09,6.06,1.39,16.07,8.4,8.89,2.88) ) d <- d.light\$d SignTest(x=d, mu = 4) wilcox.test(x=d, mu = 4, conf.int = TRUE) SignTest(x=d, mu = 4, alternative="less") wilcox.test(x=d, mu = 4, conf.int = TRUE, alternative="less") SignTest(x=d, mu = 4, alternative="greater") wilcox.test(x=d, mu = 4, conf.int = TRUE, alternative="greater") # test die interfaces x <- runif(10) y <- runif(10) g <- rep(1:2, each=10) xx <- c(x, y) SignTest(x ~ group, data=data.frame(x=xx, group=g )) SignTest(xx ~ g) SignTest(x, y) SignTest(x - y) ```

### Example output

```	Dependent-samples Sign-Test

data:  x and y
S = 7, number of differences = 9, p-value = 0.1797
alternative hypothesis: true median difference is not equal to 0
96.1 percent confidence interval:
-0.080  0.952
sample estimates:
median of the differences
0.49

Wilcoxon signed rank test

data:  x and y
V = 40, p-value = 0.03906
alternative hypothesis: true location shift is not equal to 0

One-sample Sign-Test

data:  d
S = 7, number of differences = 9, p-value = 0.1797
alternative hypothesis: true median is not equal to 4
96.1 percent confidence interval:
2.88 9.09
sample estimates:
median of the differences
8

Wilcoxon signed rank test

data:  d
V = 41, p-value = 0.02734
alternative hypothesis: true location is not equal to 4
95 percent confidence interval:
4.505 11.845
sample estimates:
(pseudo)median
7.81

One-sample Sign-Test

data:  d
S = 7, number of differences = 9, p-value = 0.9805
alternative hypothesis: true median is less than 4
98 percent confidence interval:
-Inf 8.89
sample estimates:
median of the differences
8

Wilcoxon signed rank test

data:  d
V = 41, p-value = 0.9902
alternative hypothesis: true location is less than 4
95 percent confidence interval:
-Inf 9.09
sample estimates:
(pseudo)median
7.81

One-sample Sign-Test

data:  d
S = 7, number of differences = 9, p-value = 0.08984
alternative hypothesis: true median is greater than 4
98 percent confidence interval:
2.88  Inf
sample estimates:
median of the differences
8

Wilcoxon signed rank test

data:  d
V = 41, p-value = 0.01367
alternative hypothesis: true location is greater than 4
95 percent confidence interval:
5.14  Inf
sample estimates:
(pseudo)median
7.81

Dependent-samples Sign-Test

data:  x by group
S = 5, number of differences = 10, p-value = 1
alternative hypothesis: true median difference is not equal to 0
97.9 percent confidence interval:
-0.2695244  0.8241343
sample estimates:
median of the differences
0.0388419

Dependent-samples Sign-Test

data:  xx by g
S = 5, number of differences = 10, p-value = 1
alternative hypothesis: true median difference is not equal to 0
97.9 percent confidence interval:
-0.2695244  0.8241343
sample estimates:
median of the differences
0.0388419

Dependent-samples Sign-Test

data:  x and y
S = 5, number of differences = 10, p-value = 1
alternative hypothesis: true median difference is not equal to 0
97.9 percent confidence interval:
-0.2695244  0.8241343
sample estimates:
median of the differences
0.0388419

One-sample Sign-Test

data:  x - y
S = 5, number of differences = 10, p-value = 1
alternative hypothesis: true median is not equal to 0
97.9 percent confidence interval:
-0.2695244  0.8241343
sample estimates:
median of the differences
0.0388419
```

DescTools documentation built on June 17, 2021, 5:12 p.m.