Testing against Ordered Alternatives (Spearman Test)
Performs a Spearman type test for testing against ordered alternatives.
spearmanTest(x, ...)
## Default S3 method:
spearmanTest(x, g, alternative = c("two.sided", "greater", "less"), ...)
## S3 method for class 'formula'
spearmanTest(
formula,
data,
subset,
na.action,
alternative = c("two.sided", "greater", "less"),
...
)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 |
A one factorial design for dose finding comprises an ordered factor, .e. treatment with increasing treatment levels. The basic idea is to correlate the ranks R_{ij} with the increasing order number 1 ≤ i ≤ k of the treatment levels (Kloke and McKean 2015). More precisely, R_{ij} is correlated with the expected mid-value ranks under the assumption of strictly increasing median responses. Let the expected mid-value rank of the first group denote E_1 = ≤ft(n_1 + 1\right)/2. The following expected mid-value ranks are E_j = n_{j-1} + ≤ft(n_j + 1 \right)/2 for 2 ≤ j ≤ k. The corresponding number of tied values for the ith group is n_i. # The sum of squared residuals is D^2 = ∑_{i=1}^k ∑_{j=1}^{n_i} ≤ft(R_{ij} - E_i \right)^2. Consequently, Spearman's rank correlation coefficient can be calculated as:
SEE PDF
with
SEE PDF
and t_c the number of ties of the cth group of ties. Spearman's rank correlation coefficient can be tested for significance with a t-test. For a one-tailed test the null hypothesis of r_\mathrm{S} ≤ 0 is rejected and the alternative r_\mathrm{S} > 0 is accepted if
SEE PDF
with v = n - 2 degree of freedom.
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.
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.