ansari.test(x, ...)
"ansari.test"(x, y, alternative = c("two.sided", "less", "greater"), exact = NULL, conf.int = FALSE, conf.level = 0.95, ...)
"ansari.test"(formula, data, subset, na.action, ...)
"two.sided"
, "greater"
or "less"
. You
can specify just the initial letter.lhs ~ rhs
where lhs
is a numeric variable giving the data values and rhs
a factor
with two levels giving the corresponding groups.model.frame
) containing the variables in the
formula formula
. By default the variables are taken from
environment(formula)
.NA
s. Defaults to
getOption("na.action")
."htest"
containing the following components:
"Ansari-Bradley test"
.conf.int = TRUE
.)conf.int = TRUE
.)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
$s$, the ratio of scales, 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 $s != 1$ (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 and an estimator for $s$ are computed. If exact p-values are available, an exact confidence interval is obtained by the algorithm described in Bauer (1972), and the Hodges-Lehmann estimator is employed. Otherwise, the returned confidence interval and point estimate are based on normal approximations.
Note that mid-ranks are used in the case of ties rather than average scores as employed in Hollander & Wolfe (1973). See, e.g., Hajek, Sidak and Sen (1999), pages 131ff, for more information.
Jaroslav Hajek, Zbynek Sidak and Pranab K. Sen (1999), Theory of Rank Tests. San Diego, London: Academic Press.
Myles Hollander and Douglas A. Wolfe (1973), Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 83--92.
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. ansari_test
in package \href{https://CRAN.R-project.org/package=#1}{\pkg{#1}}coincoin
for exact and approximate conditional p-values for the
Ansari-Bradley test, as well as different methods for handling ties.
## 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)
## try more points - failed in 2.4.1
ansari.test(rnorm(100), rnorm(100, 0, 2), conf.int = TRUE)
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