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 | blockwhereyandxare numeric variables andblockis 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
~ wdefining integer valued case weights for each observation. Defaults toNULL, 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 functionsasymptoticorapproximatecan 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"); seemedian_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)
# }