Testing against Ordered Alternatives (Jonckheere-Terpstra Test)
Performs the Jonckheere-Terpstra test for testing against ordered alternatives.
jonckheereTest(x, ...)
## Default S3 method:
jonckheereTest(
x,
g,
alternative = c("two.sided", "greater", "less"),
continuity = FALSE,
...
)
## S3 method for class 'formula'
jonckheereTest(
formula,
data,
subset,
na.action,
alternative = c("two.sided", "greater", "less"),
continuity = FALSE,
...
)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 |
continuity |
logical indicator whether a continuity correction
shall be performed. 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.
The p-values are estimated from the standard normal 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 code for the computation of the standard deviation
for the Jonckheere-Terpstra test in the presence of ties was taken from:
Kloke, J., McKean, J. (2016) npsm: Package for Nonparametric Statistical Methods using R. R package version 0.5. https://CRAN.R-project.org/package=npsm
jonckheereTest(x, g, alternative = "two.sided", continuity = TRUE) is
equivalent to
cor.test(x, as.numeric(g), method = "kendall", alternative = "two.sided", continuity = TRUE)
Jonckheere, A. R. (1954) A distribution-free k-sample test against ordered alternatives. Biometrica 41, 133–145.
Kloke, J., McKean, J. W. (2015) Nonparametric statistical methods using R. Boca Raton, FL: Chapman & Hall/CRC.
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.