# CorrelationTests

##### Correlation Tests

Testing the independence of two numeric variables.

- Keywords
- htest

##### Usage

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

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

# S3 method for formula
koziol_test(formula, data, subset = NULL, weights = NULL, …)
# S3 method for 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
- 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
H<U+00E1>jek, <U+0160>id<U+00E1>k 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 H<U+00E1>jek,
<U+0160>id<U+00E1>k 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

##### References

H<U+00E1>jek, J., <U+0160>id<U+00E1>k, 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 Cram<U+00E9>r-von Mises
type statistic for testing bivariate independence. *The Canadian Journal
of Statistics* **7**(1), 43--52. 10.2307/3315014

##### Examples

```
# NOT RUN {
## Asymptotic Spearman test
spearman_test(CONT ~ INTG, data = USJudgeRatings)
## Asymptotic Fisher-Yates test
fisyat_test(CONT ~ INTG, data = USJudgeRatings)
## Asymptotic quadrant test
quadrant_test(CONT ~ INTG, data = USJudgeRatings)
## Asymptotic Koziol-Nemec test
koziol_test(CONT ~ INTG, data = USJudgeRatings)
# }
```

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