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 |
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 |
object |
an object of class |
alternative |
a character, the alternative hypothesis must be
one of |
distribution |
a character, the null distribution of the test statistic
can be computed |
ties.method |
a character, two methods are available to adjust scores for ties,
either the score generating function is applied to |
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)