Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 2 3 4 5 6 7 8 |

`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 |

`conf.level` |
confidence level for the returned confidence interval, restricted to lie between zero and one. |

`formula` |
a formula of the form |

`data` |
an optional matrix or data frame (or similar: see |

`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 |

`...` |
further arguments to be passed to or from methods. |

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.

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 |

`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. |

Andri Signorell <andri@signorell.net>

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).

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)
``` |

```
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
```

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