spearmanTest {PMCMRplus} | R Documentation |
Testing against Ordered Alternatives (Spearman Test)
Description
Performs a Spearman type test for testing against ordered alternatives.
Usage
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"),
...
)
Arguments
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 |
Details
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 with the increasing
order number
of the treatment levels (Kloke and McKean 2015).
More precisely,
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
.
The following expected mid-value ranks are
for
.
The corresponding number of tied values for the
th group is
. #
The sum of squared residuals is
.
Consequently, Spearman's rank correlation coefficient can be calculated as:
with
and the number of ties of the
th group of ties.
Spearman's rank correlation coefficient can be tested for
significance with a
-test.
For a one-tailed test the null hypothesis of
is rejected and the alternative
is accepted if
with degree of freedom.
Value
A list with class "htest"
containing the following components:
- method
a character string indicating what type of test was performed.
- data.name
a character string giving the name(s) of the data.
- statistic
the estimated quantile of the test statistic.
- p.value
the p-value for the test.
- parameter
the parameters of the test statistic, if any.
- alternative
a character string describing the alternative hypothesis.
- estimates
the estimates, if any.
- null.value
the estimate under the null hypothesis, if any.
Note
Factor labels for g
must be assigned in such a way,
that they can be increasingly ordered from zero-dose
control to the highest dose level, e.g. integers
{0, 1, 2, ..., k} or letters {a, b, c, ...}.
Otherwise the function may not select the correct values
for intended zero-dose control.
It is safer, to i) label the factor levels as given above,
and to ii) sort the data according to increasing dose-levels
prior to call the function (see order
, factor
).
References
Kloke, J., McKean, J. W. (2015) Nonparametric statistical methods using R. Boca Raton, FL: Chapman & Hall/CRC.
See Also
kruskalTest
and shirleyWilliamsTest
of the package PMCMRplus,
kruskal.test
of the library stats.
Examples
## 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)