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,
...
)numeric vector; NAs and Infs are allowed but will be
removed.
optional numeric vector; NAs and Infs are allowed but
will be removed.
a single number representing the value of the population median specified by the null hypothesis
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.
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:
the S-statistic (the number of positive differences between the data and the hypothesized median), with names attribute “S”.
the p-value for the test
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.
is avector of length 1, giving the sample median; this
estimates the corresponding population parameter. Component estimate
has a names attribute describing its elements.
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.
records the value of the input argument alternative:
"greater", "less", or "two.sided"
a character string (vector of length 1)
containing the actual name of the input vector x
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".)
The median test assumes the parent population is continuous.
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.
with(data = PHONE, SIGN.test(call.time, md = 2.1))
#>
#> One-sample Sign-Test
#>
#> data: call.time
#> s = 11, p-value = 1
#> alternative hypothesis: true median is not equal to 2.1
#> 95 percent confidence interval:
#> 0.7261939 5.4952244
#> sample estimates:
#> median of x
#> 2.1
#>
#> Achieved and Interpolated Confidence Intervals:
#>
#> Conf.Level L.E.pt U.E.pt
#> Lower Achieved CI 0.9069 0.8000 5.2000
#> Interpolated CI 0.9500 0.7262 5.4952
#> Upper Achieved CI 0.9653 0.7000 5.6000
#>
# 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.