Testing against Ordered Alternatives (Chacko's Test)
Performs Chacko's test for testing against ordered alternatives.
chackoTest(x, ...)
## Default S3 method:
chackoTest(x, g, alternative = c("greater", "less"), ...)
## S3 method for class 'formula'
chackoTest(formula, data, subset, na.action, alternative = alternative, ...)x |
a numeric vector of data values, or a list of numeric data vectors. |
... |
further arguments to be passed to or from methods. |
g |
a vector or factor object giving the group for the
corresponding elements of |
alternative |
the alternative hypothesis. Defaults to |
formula |
a formula of the form |
data |
an optional matrix or data frame (or similar: see
|
subset |
an optional vector specifying a subset of observations to be used. |
na.action |
a function which indicates what should happen when
the data contain |
The null hypothesis, H_0: θ_1 = θ_2 = … = θ_k is tested against a simple order hypothesis, H_\mathrm{A}: θ_1 ≤ θ_2 ≤ … ≤ θ_k,~θ_1 < θ_k.
Let R_{ij} be the rank of X_{ij}, where X_{ij} is jointly ranked from ≤ft\{1, 2, …, N \right\}, ~~ N = ∑_{i=1}^k n_i, then the test statistic is calculated as
SEE PDF
where \bar{R^*}_i is the isotonic mean of the i-th group and σ_R^2 = N ≤ft(N + 1\right) / 12 the expected variance (without ties). H_0 is rejected, if H > χ^2_{v,α} with v = k -1 degree of freedom. The p-values are estimated from the chi-square distribution.
A list with class "htest" containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
the estimated quantile of the test statistic.
the p-value for the test.
the parameters of the test statistic, if any.
a character string describing the alternative hypothesis.
the estimates, if any.
the estimate under the null hypothesis, if any.
The source code for the application of the pool adjacent violators
theorem to calculate the isotonic means
was taken from the file "pava.f", which is included in the
package Iso:
Rolf Turner (2015). Iso: Functions to Perform Isotonic Regression. R package version 0.0-17. https://CRAN.R-project.org/package=Iso.
The file "pava.f" is a Ratfor modification of Algorithm AS 206.1:
Bril, G., Dykstra, R., Pillers, C., Robertson, T. (1984) Statistical Algorithms: Algorithm AS 206: Isotonic Regression in Two Independent Variables, Appl Statist 34, 352–357.
The Algorith AS 206 is available from StatLib http://lib.stat.cmu.edu/apstat/. The Royal Statistical Society holds the copyright to these routines, but has given its permission for their distribution provided that no fee is charged.
The function does neither check nor correct for ties.
Chacko, V. J. (1963) Testing homogeneity against ordered alternatives, Ann Math Statist 34, 945–956.
kruskalTest and shirleyWilliamsTest
of the package PMCMRplus,
kruskal.test of the library stats.
## Example from Sachs (1997, p. 402)
x <- c(106, 114, 116, 127, 145,
110, 125, 143, 148, 151,
136, 139, 149, 160, 174)
g <- gl(3,5)
levels(g) <- c("A", "B", "C")
## Chacko's test
chackoTest(x, g)
## Cuzick's test
cuzickTest(x, g)
## Johnson-Mehrotra test
johnsonTest(x, g)
## Jonckheere-Terpstra test
jonckheereTest(x, g)
## Le's test
leTest(x, g)
## Spearman type test
spearmanTest(x, g)
## Murakami's BWS trend test
bwsTrendTest(x, g)
## Fligner-Wolfe test
flignerWolfeTest(x, g)
## Shan-Young-Kang test
shanTest(x, g)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.