| ContingencyTests {coin} | R Documentation |
Testing the independence of two possibly ordered factors, eventually stratified by a third factor.
## S3 method for class 'formula':
cmh_test(formula, data, subset = NULL, weights = NULL, ...)
## S3 method for class 'table':
cmh_test(object, distribution = c("asymptotic", "approximate"), ...)
## S3 method for class 'IndependenceProblem':
cmh_test(object, distribution = c("asymptotic", "approximate"), ...)
## S3 method for class 'formula':
chisq_test(formula, data, subset = NULL, weights = NULL, ...)
## S3 method for class 'table':
chisq_test(object, distribution = c("asymptotic", "approximate"), ...)
## S3 method for class 'IndependenceProblem':
chisq_test(object, distribution = c("asymptotic", "approximate"), ...)
## S3 method for class 'formula':
lbl_test(formula, data, subset = NULL, weights = NULL, ...)
## S3 method for class 'table':
lbl_test(object, distribution = c("asymptotic", "approximate"), ...)
## S3 method for class 'IndependenceProblem':
lbl_test(object, distribution = c("asymptotic", "approximate"), ...)
formula |
a formula of the form y ~ x | block where y
and x are factors (possibly ordered) 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. |
weights |
an optional formula of the form ~ w defining
integer valued weights for the observations. |
object |
an object inheriting from class "IndependenceProblem" or an
object of class table. |
distribution |
a character, the null distribution of the test statistic
can be approximated by its asymptotic distribution ("asymptotic")
or via Monte-Carlo resampling ("approximate").
Alternatively, the functions
approximate or asymptotic can be
used to specify how the exact conditional distribution of the test statistic
should be calculated or approximated. |
... |
further arguments to be passed to or from methods. |
The null hypothesis of the independence of y and x is
tested, block defines an optional factor for stratification.
chisq_test implements Pearson's chi-squared test,
cmh_test the Cochran-Mantel-Haenzsel
test and lbl_test the linear-by-linear association test for ordered
data.
In case either x or y are ordered factors, the
corresponding linear-by-linear association test is performed by all the
procedures.
lbl_test coerces factors to class ordered under any
circumstances. The default scores are 1:nlevels(x) and
1:nlevels(y), respectively. The default scores can be changed
via the scores argument (see independence_test),
for example
scores = list(y = 1:3, x = c(1, 4, 6)) first triggers a coercion
to class ordered of both variables and attaches the list elements
as scores to the corresponding factors. The length of a score vector needs
to be equal the number of levels of the factor of interest.
The authoritative source for details on the documented test procedures is Agresti (2002).
An object inheriting from class IndependenceTest-class with
methods show, statistic, expectation,
covariance and pvalue. The null distribution
can be inspected by pperm, dperm,
qperm and support methods.
Alan Agresti (2002), Categorical Data Analysis. Hoboken, New Jersey: John Wiley & Sons.
### for females only
chisq_test(as.table(jobsatisfaction[,,"Female"]),
distribution = approximate(B = 9999))
### both Income and Job.Satisfaction unordered
cmh_test(jobsatisfaction)
### both Income and Job.Satisfaction ordered, default scores
lbl_test(jobsatisfaction)
### both Income and Job.Satisfaction ordered, alternative scores
lbl_test(jobsatisfaction, scores = list(Job.Satisfaction = c(1, 3, 4, 5),
Income = c(3, 10, 20, 35)))
### the same, null distribution approximated
cmh_test(jobsatisfaction, scores = list(Job.Satisfaction = c(1, 3, 4, 5),
Income = c(3, 10, 20, 35)),
distribution = approximate(B = 10000))
### Smoking and HDL cholesterin status
### (from Jeong, Jhun and Kim, 2005, CSDA 48, 623-631, Table 2)
smokingHDL <- as.table(
matrix(c(15, 8, 11, 5,
3, 4, 6, 1,
6, 7, 15, 11,
1, 2, 3, 5), ncol = 4,
dimnames = list(smoking = c("none", "< 5", "< 10", ">=10"),
HDL = c("normal", "low", "borderline", "abnormal"))
))
### use interval mid-points as scores for smoking
lbl_test(smokingHDL, scores = list(smoking = c(0, 2.5, 7.5, 15)))
### Cochran-Armitage trend test for proportions
### Lung tumors in female mice exposed to 1,2-dichloroethane
### Encyclopedia of Biostatistics (Armitage & Colton, 1998),
### Chapter Trend Test for Counts and Proportions, page 4578, Table 2
lungtumor <- data.frame(dose = rep(c(0, 1, 2), c(40, 50, 48)),
tumor = c(rep(c(0, 1), c(38, 2)),
rep(c(0, 1), c(43, 7)),
rep(c(0, 1), c(33, 15))))
table(lungtumor$dose, lungtumor$tumor)
### Cochran-Armitage test (permutation equivalent to correlation
### between dose and tumor), cf. Table 2 for results
independence_test(tumor ~ dose, data = lungtumor, teststat = "quad")
### linear-by-linear association test with scores 0, 1, 2
### is identical with Cochran-Armitage test
lungtumor$dose <- ordered(lungtumor$dose)
independence_test(tumor ~ dose, data = lungtumor, teststat = "quad",
scores = list(dose = c(0, 1, 2)))