| ansari.test {ctest} | R Documentation |
Ansari-Bradley Test
Description
Performs the Ansari-Bradley two-sample test for a difference in scale parameters.
Usage
ansari.test(x, y, alternative = c("two.sided", "less", "greater"),
exact = NULL, conf.int = TRUE, conf.level = 0.95)
Arguments
x |
numeric vector of data values. |
y |
numeric vector of data values. |
alternative |
indicates the alternative hypothesis and must be
one of |
exact |
a logical indicating whether an exact p-value should be computed. |
conf.int |
a logical,indicating whether a confidence interval should be computed. |
conf.level |
confidence level of the interval. |
Details
Suppose that x and y are independent samples from
distributions with densities f((t-m)/s)/s and f(t-m),
respectively, where m is an unknown nuisance parameter and
s is the parameter of interest. The Ansari-Bradley test is used
for testing the null that s equals 1, the two-sided alternative
being that s \ne 1 (the distributions differ only in
variance), and the one-sided alternatives being s > 1 (the
distribution underlying x has a larger variance,
"greater") or s < 1 ("less").
By default (if exact is not specified), an exact p-value is
computed if both samples contain less than 50 finite values and there
are no ties. Otherwise, a normal approximation is used.
Optionally, a nonparametric confidence interval for s is
computed. If exact p-values are available, an exact confidence
interval is obtained by the algorithm described in Bauer (1972).
Otherwise, an asymptotic confidence interval is returned.
Value
A list with class "htest" containing the following components:
statistic |
the value of the Ansari-Bradley test statistic. |
p.value |
the p-value of the test. |
alternative |
a character string describing the alternative hypothesis. |
method |
the string |
data.name |
a character string giving the names of the data. |
conf.int |
a confidence interval for the scale parameter.
(Only present if argument |
References
Myles Hollander & Douglas A. Wolfe (1973), Nonparametric statistical inference. New York: John Wiley & Sons. Pages 83–92.
David F. Bauer (1972), Constructing confidence sets using rank statistics. Journal of the American Statistical Association 67, 687–690.
See Also
fligner.test for a rank-based (nonparametric) k-sample
test for homogeneity of variances;
mood.test for another rank-based two-sample test for a
difference in scale parameters;
var.test and bartlett.test for parametric
tests for the homogeneity in variance.
Examples
## Hollander & Wolfe (1973, p. 86f):
## Serum iron determination using Hyland control sera
ramsay <- c(111, 107, 100, 99, 102, 106, 109, 108, 104, 99,
101, 96, 97, 102, 107, 113, 116, 113, 110, 98)
jung.parekh <- c(107, 108, 106, 98, 105, 103, 110, 105, 104,
100, 96, 108, 103, 104, 114, 114, 113, 108, 106, 99)
ansari.test(ramsay, jung.parekh)
ansari.test(rnorm(10), rnorm(10, 0, 2), conf.int = TRUE)