# IndependenceTestStatistic-class: Class '"IndependenceTestStatistic"' and Its Subclasses In coin: Conditional Inference Procedures in a Permutation Test Framework

## Description

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.

## 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

 ```1 2 3 4``` ``` new("MaxTypeIndependenceTestStatistic", object, alternative = c("two.sided", "less", "greater"), \dots), new("QuadTypeIndependenceTestStatistic", object, paired = FALSE, \dots) ```

and

 ```1 2``` ``` 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 `"matrix"`. The linear statistic for each block.

`expectation`:

Object of class `"matrix"`. The expectation of the linear statistic for each block.

`covariance`:

Object of class `"matrix"`. The lower triangular elements of the covariance of the linear statistic for each block.

`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 `"numeric"`. The lower triangular elements of the Moore-Penrose inverse of the covariance of the linear statistic.

`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.

covariance

`signature(object = "QuadTypeIndependenceTestStatistic")`: See the documentation for `covariance` for details.

initialize

`signature(.Object = "IndependenceTestStatistic")`: See the documentation for `initialize` (in package methods) 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.

coin documentation built on Oct. 8, 2021, 9:07 a.m.