coin (version 1.1-0)

CorrelationTests: Correlation Tests

Description

Testing the independence of two numeric variables.

Usage

## S3 method for class 'formula':
spearman_test(formula, data, subset = NULL, weights = NULL, \dots)
## 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, \dots)
## 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, \dots)
## 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, \dots)
## 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 functi

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.

Value

• An object inheriting from class "IndependenceTest".

concept

• Spearman correlation test
• Fisher-Yates correlation test
• Quadrant test
• Koziol-Nemec test

encoding

UTF-8

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{Hajek}, Šidák{Sidak} 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{Hajek}, Šidák{Sidak} 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.

References

Hájek{Hajek}, J., Šidák{Sidak}, 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{Cramer}-von Mises type statistic for testing bivariate independence. The Canadian Journal of Statistics 7(1), 43--52.

Examples

## 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)