# statistic-methods: Extraction of the Test Statistic and the Linear Statistic In coin: Conditional Inference Procedures in a Permutation Test Framework

## Description

Methods for extraction of the test statistic and the linear statistic.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```## S4 method for signature 'IndependenceLinearStatistic' statistic(object, type = c("test", "linear", "centered", "standardized"), partial = FALSE, ...) ## S4 method for signature 'IndependenceTestStatistic' statistic(object, type = c("test", "linear", "centered", "standardized"), partial = FALSE, ...) ## S4 method for signature 'IndependenceTest' statistic(object, type = c("test", "linear", "centered", "standardized"), partial = FALSE, ...) ```

## Arguments

 `object` an object from which the test statistic or the linear statistic can be extracted. `type` a character string indicating the type of statistic: either `"test"` (default) for the test statistic, `"linear"` for the unstandardized linear statistic, `"centered"` for the centered linear statistic or `"standardized"` for the standardized linear statistic. `partial` a logical indicating that the partial linear statistic for each block should be extracted. Defaults to `FALSE`. `...` further arguments (currently ignored).

## Details

The method `statistic` extracts the univariate test statistic or the, possibly multivariate, linear statistic in its unstandardized, centered or standardized form.

The test statistic (`type = "test"`) is returned by default. The unstandardized, centered or standardized linear statistic is obtained by setting `type` to `"linear"`, `"centered"` or `"standardized"`, respectively. For tests of conditional independence within blocks, the partial linear statistic for each block is obtained by setting `partial = TRUE`.

## Value

The test statistic or the unstandardized, centered or standardized linear statistic extracted from `object`. A numeric vector, matrix or array.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ```## Example data dta <- data.frame( y = gl(4, 5), x = gl(5, 4) ) ## Asymptotic Cochran-Mantel-Haenszel Test ct <- cmh_test(y ~ x, data = dta) ## Test statistic statistic(ct) ## The unstandardized linear statistic... statistic(ct, type = "linear") ## ...is identical to the contingency table xtabs(~ x + y, data = dta) ## The centered linear statistic... statistic(ct, type = "centered") ## ...is identical to statistic(ct, type = "linear") - expectation(ct) ## The standardized linear statistic, illustrating departures from the null ## hypothesis of independence... statistic(ct, type = "standardized") ## ...is identical to (statistic(ct, type = "linear") - expectation(ct)) / sqrt(variance(ct)) ```

### Example output

```Loading required package: survival
 38
1 2 3 4
1 4 0 0 0
2 1 3 0 0
3 0 2 2 0
4 0 0 3 1
5 0 0 0 4
y
x   1 2 3 4
1 4 0 0 0
2 1 3 0 0
3 0 2 2 0
4 0 0 3 1
5 0 0 0 4
1  2  3  4
1  3 -1 -1 -1
2  0  2 -1 -1
3 -1  1  1 -1
4 -1 -1  2  0
5 -1 -1 -1  3
1  2  3  4
1  3 -1 -1 -1
2  0  2 -1 -1
3 -1  1  1 -1
4 -1 -1  2  0
5 -1 -1 -1  3
1         2         3         4
1  3.774917 -1.258306 -1.258306 -1.258306
2  0.000000  2.516611 -1.258306 -1.258306
3 -1.258306  1.258306  1.258306 -1.258306
4 -1.258306 -1.258306  2.516611  0.000000
5 -1.258306 -1.258306 -1.258306  3.774917
1         2         3         4
1  3.774917 -1.258306 -1.258306 -1.258306
2  0.000000  2.516611 -1.258306 -1.258306
3 -1.258306  1.258306  1.258306 -1.258306
4 -1.258306 -1.258306  2.516611  0.000000
5 -1.258306 -1.258306 -1.258306  3.774917
```

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