| ScaleTests {coin} | R Documentation |
Testing the equality of the distributions of a numeric response in two or more independent groups against scale alternatives.
## S3 method for class 'formula':
ansari_test(formula, data, subset = NULL, weights = NULL, ...)
## S3 method for class 'IndependenceProblem':
ansari_test(object,
alternative = c("two.sided", "less", "greater"),
ties.method = c("mid-ranks", "average-scores"),
conf.int = FALSE, conf.level = 0.95, ...)
## S3 method for class 'formula':
fligner_test(formula, data, subset = NULL, weights = NULL, ...)
## S3 method for class 'IndependenceProblem':
fligner_test(object,
ties.method = c("mid-ranks", "average-scores"),
distribution = c("asymptotic", "approximate"),
...)
formula |
a formula of the form y ~ x | block where y
is a numeric variable giving the data values and x a factor
with two or more levels giving the corresponding groups. 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 of class IndependenceProblem. |
alternative |
a character, the alternative hypothesis must be
one of "two.sided" (default), "greater" or
"less". You can specify just the initial letter. |
distribution |
a character, the null distribution of the test statistic
can be computed exactly or can be approximated by its
asymptotic distribution (asymptotic)
or via Monte-Carlo resampling (approximate).
Alternatively, the functions
exact, approximate or asymptotic can be
used to specify how the exact conditional distribution of the test statistic
should be calculated or approximated. |
ties.method |
a character, two methods are available to adjust scores for ties,
either the score generating function is applied to mid-ranks
or the scores computed based on random ranks are averaged for all tied
values (average-scores). |
conf.int |
a logical indicating whether a confidence interval for the difference in location should be computed. |
conf.level |
confidence level of the interval. |
... |
further arguments to be passed to or from methods. |
The null hypothesis of the equality of the distribution of y in
the groups given by x is tested. In particular, the methods
documented here are designed to detect scale alternatives. For a general
description of the test procedures documented here we refer to Hollander &
Wolfe (1999).
The asymptotic null distribution is computed by default for both procedures. Exact p-values may be computed for the Ansari-Bradley test can be approximated via Monte-Carlo for the Fligner-Killeen procedure. Exact p-values are computed either by the shift algorithm (Streitberg & R"ohmel, 1986, 1987) or by the split-up algorithm (van de Wiel, 2001).
The Ansari-Bradley test can be used to test the
two-sided hypothesis var(Y_1) / var(Y_2) = 1, where var(Y_i)
is the variance of the responses in the ith group. Confidence intervals
for the ratio of scales are available for the
Ansari-Bradley test and are computed according to Bauer (1972).
In case alternative = "less", the
null hypothesis var(Y_1) / var(Y_2) >= 1 is tested and
alternative = "greater" corresponds to var(Y_1) / var(Y_2) <= 1.
For the adjustment of scores for tied values see Hajek, Sidak and Sen (1999), page 131ff.
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. Confidence
intervals can be extracted by confint.
Myles Hollander & Douglas A. Wolfe (1999). Nonparametric Statistical Methods, 2nd Edition. New York: John Wiley & Sons.
Bernd Streitberg & Joachim R"ohmel (1986). Exact distributions for permutations and rank tests: An introduction to some recently published algorithms. Statistical Software Newsletter 12(1), 10–17.
Bernd Streitberg & Joachim R"ohmel (1987). Exakte Verteilungen f"ur Rang- und Randomisierungstests im allgemeinen $c$-Stichprobenfall. EDV in Medizin und Biologie 18(1), 12–19.
Mark A. van de Wiel (2001). The split-up algorithm: a fast symbolic method for computing p-values of rank statistics. Computational Statistics 16, 519–538.
David F. Bauer (1972). Constructing confidence sets using rank statistics. Journal of the American Statistical Association 67, 687–690.
Jaroslav Hajek, Zbynek Sidak & Pranab K. Sen (1999). Theory of Rank Tests. San Diego, London: Academic Press.
### Serum Iron Determination Using Hyland Control Sera
### Hollander & Wolfe (1999), page 147
sid <- data.frame(
serum = c(111, 107, 100, 99, 102, 106, 109, 108, 104, 99,
101, 96, 97, 102, 107, 113, 116, 113, 110, 98,
107, 108, 106, 98, 105, 103, 110, 105, 104,
100, 96, 108, 103, 104, 114, 114, 113, 108, 106, 99),
method = factor(gl(2, 20), labels = c("Ramsay", "Jung-Parekh")))
### Ansari-Bradley test, asymptotical p-value
ansari_test(serum ~ method, data = sid)
### exact p-value
ansari_test(serum ~ method, data = sid, distribution = "exact")
### Platelet Counts of Newborn Infants
### Hollander & Wolfe (1999), Table 5.4, page 171
platalet_counts <- data.frame(
counts = c(120, 124, 215, 90, 67, 95, 190, 180, 135, 399,
12, 20, 112, 32, 60, 40),
treatment = factor(c(rep("Prednisone", 10), rep("Control", 6))))
### Lepage test, Hollander & Wolfe (1999), page 172
lt <- independence_test(counts ~ treatment, data = platalet_counts,
ytrafo = function(data) trafo(data, numeric_trafo = function(x)
cbind(rank(x), ansari_trafo(x))),
teststat = "quad", distribution = approximate(B = 9999))
lt
### where did the rejection come from? Use maximum statistic
### instead of a quadratic form
ltmax <- independence_test(counts ~ treatment, data = platalet_counts,
ytrafo = function(data) trafo(data, numeric_trafo = function(x)
matrix(c(rank(x), ansari_trafo(x)), ncol = 2,
dimnames = list(1:length(x), c("Location", "Scale")))),
teststat = "max")
### points to a difference in location
pvalue(ltmax, method = "single-step")
### Funny: We could have used a simple Bonferroni procedure
### since the correlation between the Wilcoxon and Ansari-Bradley
### test statistics is zero
covariance(ltmax)