CorrelationTests {coin} R Documentation

## Correlation Tests

### Description

Testing the independence of two numeric variables.

### Usage

```## S3 method for class 'formula'
spearman_test(formula, data, subset = NULL, weights = NULL, ...)
## S3 method for class 'IndependenceProblem'
spearman_test(object, distribution = c("asymptotic", "approximate", "none"), ...)

## S3 method for class 'formula'
fisyat_test(formula, data, subset = NULL, weights = NULL, ...)
## S3 method for class 'IndependenceProblem'
fisyat_test(object, distribution = c("asymptotic", "approximate", "none"),
ties.method = c("mid-ranks", "average-scores"), ...)

## S3 method for class 'formula'
quadrant_test(formula, data, subset = NULL, weights = NULL, ...)
## S3 method for class 'IndependenceProblem'
quadrant_test(object, distribution = c("asymptotic", "approximate", "none"),
mid.score = c("0", "0.5", "1"), ...)

## S3 method for class 'formula'
koziol_test(formula, data, subset = NULL, weights = NULL, ...)
## S3 method for class 'IndependenceProblem'
koziol_test(object, distribution = c("asymptotic", "approximate", "none"),
ties.method = c("mid-ranks", "average-scores"), ...)
```

### Arguments

 `formula` a formula of the form `y ~ x | block` where `y` and `x` are numeric variables and `block` is an optional factor for stratification. `data` an optional data frame containing the variables in the model formula. `subset` an optional vector specifying a subset of observations to be used. Defaults to `NULL`. `weights` an optional formula of the form `~ w` defining integer valued case weights for each observation. Defaults to `NULL`, implying equal weight for all observations. `object` an object inheriting from class `"IndependenceProblem"`. `distribution` a character, the conditional null distribution of the test statistic can be approximated by its asymptotic distribution (`"asymptotic"`, default) or via Monte Carlo resampling (`"approximate"`). Alternatively, the functions `asymptotic` or `approximate` can be used. Computation of the null distribution can be suppressed by specifying `"none"`. `ties.method` a character, the method used to handle ties: the score generating function either uses mid-ranks (`"mid-ranks"`, default) or averages the scores of randomly broken ties (`"average-scores"`). `mid.score` a character, the score assigned to observations exactly equal to the median: either 0 (`"0"`, default), 0.5 (`"0.5"`) or 1 (`"1"`); see `median_test`. `...` further arguments to be passed to `independence_test`.

### Details

`spearman_test`, `fisyat_test`, `quadrant_test` and `koziol_test` provide the Spearman correlation test, the Fisher-Yates correlation test using van der Waerden scores, the quadrant test and the Koziol-Nemec test. A general description of these methods is given by Hájek, Šidák and Sen (1999, Sec. 4.6). The Koziol-Nemec test was suggested by Koziol and Nemec (1979). For the adjustment of scores for tied values see Hájek, Šidák and Sen (1999, pp. 133–135).

The null hypothesis of independence, or conditional independence given `block`, between `y` and `x` is tested.

The conditional null distribution of the test statistic is used to obtain p-values and an asymptotic approximation of the exact distribution is used by default (`distribution = "asymptotic"`). Alternatively, the distribution can be approximated via Monte Carlo resampling by setting `distribution` to `"approximate"`. See `asymptotic` and `approximate` for details.

### Value

An object inheriting from class `"IndependenceTest"`.

### References

Hájek, J., Šidák, Z. and Sen, P. K. (1999). Theory of Rank Tests, Second Edition. San Diego: Academic Press.

Koziol, J. A. and Nemec, A. F. (1979). On a Cramér-von Mises type statistic for testing bivariate independence. The Canadian Journal of Statistics 7(1), 43–52. doi: 10.2307/3315014

### Examples

```## Asymptotic Spearman test
spearman_test(CONT ~ INTG, data = USJudgeRatings)

## Asymptotic Fisher-Yates test
fisyat_test(CONT ~ INTG, data = USJudgeRatings)