ansari.test {stats} | R Documentation |

Performs the Ansari-Bradley two-sample test for a difference in scale parameters.

ansari.test(x, ...) ## Default S3 method: ansari.test(x, y, alternative = c("two.sided", "less", "greater"), exact = NULL, conf.int = FALSE, conf.level = 0.95, ...) ## S3 method for class 'formula': ansari.test(formula, data, subset, na.action, ...)

`x` |
numeric vector of data values. |

`y` |
numeric vector of data values. |

`alternative` |
indicates the alternative hypothesis and must be
one of `"two.sided"` , `"greater"` or `"less"` . You
can specify just the initial letter. |

`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. |

`formula` |
a formula of the form `lhs ~ rhs` where `lhs`
is a numeric variable giving the data values and `rhs` a factor
with two levels giving the corresponding groups. |

`data` |
an optional matrix or data frame (or similar: see
`model.frame` ) containing the variables in the
formula `formula` . By default the variables are taken from
`environment(formula)` . |

`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 `NA` s. Defaults to
`getOption("na.action")` . |

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

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*, 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.

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. |

`null.value` |
the ratio of scales s under the null, 1. |

`alternative` |
a character string describing the alternative hypothesis. |

`method` |
the string `"Ansari-Bradley test"` . |

`data.name` |
a character string giving the names of the data. |

`conf.int` |
a confidence interval for the scale parameter.
(Only present if argument `conf.int = TRUE` .) |

`estimate` |
an estimate of the ratio of scales.
(Only present if argument `conf.int = TRUE` .) |

To compare results of the Ansari-Bradley test to those of the F test
to compare two variances (under the assumption of normality), observe
that *s* is the ratio of scales and hence *s^2* is the ratio
of variances (provided they exist), whereas for the F test the ratio
of variances itself is the parameter of interest. In particular,
confidence intervals are for *s* in the Ansari-Bradley test but
for *s^2* in the F test.

David F. Bauer (1972),
Constructing confidence sets using rank statistics.
*Journal of the American Statistical Association*
**67**, 687–690.

Jaroslav Hajek, Zbynek Sidak & Pranab K. Sen (1999),
*Theory of Rank Tests*.
San Diego, London: Academic Press.

Myles Hollander & Douglas A. Wolfe (1973),
*Nonparametric statistical inference*.
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 **coin** 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)

[Package *stats* version 2.5.0 Index]