# IndependenceTestStatistic-class

##### Class `"IndependenceTestStatistic"`

and its subclasses

Objects of class `"IndependenceTestStatistic"`

and its subclasses
`"MaxTypeIndependenceTestStatistic"`

,
`"QuadTypeIndependenceTestStatistic"`

and
`"ScalarIndependenceTestStatistic"`

represent the test statistic, the
linear statistic, and the transformed and original data structures
corresponding to an independence problem.

- Keywords
- classes

##### Objects from the Class

Class `"IndependenceTestStatistic"`

is a *virtual* class, so objects
cannot be created from it directly.

Objects can be created by calls of the form

new("MaxTypeIndependenceTestStatistic", object, alternative = c("two.sided", "less", "greater"), \dots),new("QuadTypeIndependenceTestStatistic", object, paired = FALSE, \dots)

and

new("ScalarIndependenceTestStatistic", object, alternative = c("two.sided", "less", "greater"), paired = FALSE, \dots)

where `object`

is an object of class
`"IndependenceLinearStatistic"`

, `alternative`

is a character
specifying the direction of the alternative hypothesis and `paired`

is a
logical indicating that paired data have been transformed in such a way that
the (unstandardized) linear statistic is the sum of the absolute values of the
positive differences between the paired observations.

##### Slots

For objects of classes `"IndependenceTestStatistic"`

,
`"MaxTypeIndependenceTestStatistic"`

,
`"QuadTypeIndependenceTestStatistic"`

or
`"ScalarIndependenceTestStatistic"`

:

`teststatistic`

:Object of class

`"numeric"`

. The test statistic.`standardizedlinearstatistic`

:Object of class

`"numeric"`

. The standardized linear statistic.`linearstatistic`

:Object of class

`"numeric"`

. The linear statistic.`expectation`

:Object of class

`"numeric"`

. The expectation of the linear statistic.`covariance`

:Object of class

`"'>VarCovar"`

. The covariance or variance of the linear statistic.`xtrans`

:Object of class

`"matrix"`

. The transformed`x`

.`ytrans`

:Object of class

`"matrix"`

. The transformed`y`

.`xtrafo`

:Object of class

`"function"`

. The regression function for`x`

.`ytrafo`

:Object of class

`"function"`

. The influence function for`y`

.`x`

:Object of class

`"data.frame"`

. The variables`x`

.`y`

:Object of class

`"data.frame"`

. The variables`y`

.`block`

:Object of class

`"factor"`

. The block structure.`weights`

:Object of class

`"numeric"`

. The case weights.

Additionally, for objects of classes `"MaxTypeIndependenceTest"`

or
`"ScalarIndependenceTest"`

:

`alternative`

:Object of class

`"character"`

. The direction of the alternative hypothesis.

Additionally, for objects of class `"QuadTypeIndependenceTest"`

:

`covarianceplus`

:Object of class

`"matrix"`

. The Moore-Penrose inverse of the covariance matrix.`df`

:Object of class

`"numeric"`

. The rank of the covariance matrix.

Additionally, for objects of classes `"QuadTypeIndependenceTest"`

or
`"ScalarIndependenceTest"`

:

`paired`

:Object of class

`"logical"`

. The indicator for paired test statistics.

##### Extends

For objects of class `"IndependenceTestStatistic"`

:
Class `"'>IndependenceLinearStatistic"`

, directly.
Class `"'>IndependenceTestProblem"`

, by class
`"'>IndependenceLinearStatistic"`

, distance 2.
Class `"'>IndependenceProblem"`

, by class
`"'>IndependenceLinearStatistic"`

, distance 3.

For objects of classes `"MaxTypeIndependenceTestStatistic"`

,
`"QuadTypeIndependenceTestStatistic"`

or
`"ScalarIndependenceTestStatistic"`

:
Class `"'>IndependenceTestStatistic"`

, directly.
Class `"'>IndependenceLinearStatistic"`

, by class
`"'>IndependenceTestStatistic"`

, distance 2.
Class `"'>IndependenceTestProblem"`

, by class
`"'>IndependenceTestStatistic"`

, distance 3.
Class `"'>IndependenceProblem"`

, by class
`"'>IndependenceTestStatistic"`

, distance 4.

##### Known Subclasses

For objects of class `"IndependenceTestStatistic"`

:
Class `"MaxTypeIndependenceTestStatistic"`

, directly.
Class `"QuadTypeIndependenceTestStatistic"`

, directly.
Class `"ScalarIndependenceTestStatistic"`

, directly.

##### Methods

- ApproxNullDistribution
`signature(object = "MaxTypeIndependenceTestStatistic")`

: See the documentation for`ApproxNullDistribution`

for details.- ApproxNullDistribution
`signature(object = "QuadTypeIndependenceTestStatistic")`

: See the documentation for`ApproxNullDistribution`

for details.- ApproxNullDistribution
`signature(object = "ScalarIndependenceTestStatistic")`

: See the documentation for`ApproxNullDistribution`

for details.- AsymptNullDistribution
`signature(object = "MaxTypeIndependenceTestStatistic")`

: See the documentation for`AsymptNullDistribution`

for details.- AsymptNullDistribution
`signature(object = "QuadTypeIndependenceTestStatistic")`

: See the documentation for`AsymptNullDistribution`

for details.- AsymptNullDistribution
`signature(object = "ScalarIndependenceTestStatistic")`

: See the documentation for`AsymptNullDistribution`

for details.- ExactNullDistribution
`signature(object = "QuadTypeIndependenceTestStatistic")`

: See the documentation for`ExactNullDistribution`

for details.- ExactNullDistribution
`signature(object = "ScalarIndependenceTestStatistic")`

: See the documentation for`ExactNullDistribution`

for details.- initialize
`signature(.Object = "MaxTypeIndependenceTestStatistic")`

: See the documentation for`initialize`

(in package methods) for details.- initialize
`signature(.Object = "QuadTypeIndependenceTestStatistic")`

: See the documentation for`initialize`

(in package methods) for details.- initialize
`signature(.Object = "ScalarIndependenceTestStatistic")`

: See the documentation for`initialize`

(in package methods) for details.- statistic
`signature(object = "IndependenceTestStatistic")`

: See the documentation for`statistic`

for details.

*Documentation reproduced from package coin, version 1.3-1, License: GPL-2*