SIGN.test {BSDA}  R Documentation 
Sign Test
Description
This function will test a hypothesis based on the sign test and reports linearly interpolated confidence intervals for one sample problems.
Usage
SIGN.test(
x,
y = NULL,
md = 0,
alternative = "two.sided",
conf.level = 0.95,
...
)
Arguments
x 
numeric vector; 
y 
optional numeric vector; 
md 
a single number representing the value of the population median specified by the null hypothesis 
alternative 
is a character string, one of 
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 “Dependentsamples SignTest” if both x
and
y
are provided. If only x
is provided, computes the
“SignTest”.
Value
A list of class htest_S
, containing the following components:
statistic 
the Sstatistic (the number of positive differences between the data and the hypothesized median), with names attribute “S”. 
p.value 
the pvalue 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

estimate 
is avector of length 1, giving the sample median; this
estimates the corresponding population parameter. Component 
null.value 
is the value of the median specified by the null hypothesis.
This equals the input argument 
alternative 
records the value of the input argument alternative:

data.name 
a character string (vector of length 1)
containing the actual name of the input vector 
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 onesample signtest, the null hypothesis
is that the median of the population from which x
is drawn is
md
. For the twosample 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"
.)
Note
The reported confidence interval is based on linear interpolation. The lower and upper confidence levels are exact.
Author(s)
Alan T. Arnholt
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.
See Also
Examples
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)
# Computes twosided signtest 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")
# Data from Example 6.11 page 330 of Kitchens BSDA.
# Computes onesided signtest 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.