flignerWolfeTest {PMCMRplus} | R Documentation |
Testing Several Treatments With One Control
Description
Performs Fligner-Wolfe non-parametric test for simultaneous testing of several locations of treatment groups against the location of the control group.
Usage
flignerWolfeTest(x, ...)
## Default S3 method:
flignerWolfeTest(
x,
g,
alternative = c("greater", "less"),
dist = c("Wilcoxon", "Normal"),
...
)
## S3 method for class 'formula'
flignerWolfeTest(
formula,
data,
subset,
na.action,
alternative = c("greater", "less"),
dist = c("Wilcoxon", "Normal"),
...
)
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 |
dist |
the test distribution. 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
For a one-factorial layout with non-normally distributed residuals the Fligner-Wolfe test can be used.
Let there be -treatment groups and one control group, then
the null hypothesis, H
is tested against the alternative (greater),
A
,
with at least one inequality being strict.
Let denote the sample size of the control group,
the sum of all treatment
sample sizes and
. The test statistic without taken
ties into account is
with the rank of variable
.
The null hypothesis is rejected,
if
with
and
.
In the presence of ties, the statistic is
where
with the number of tied groups and
the number of tied values in the
th group. The null hypothesis
is rejected, if
(as cited in EPA 2006).
If dist = Wilcoxon
, then the -values are estimated from the
Wilcoxon
distribution, else the Normal
distribution is used. The latter can be used,
if ties are present.
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
EPA (2006) Data Quality Assessment: Statistical Methods for Practitioners (Guideline No. EPA QA/G-9S), US-EPA.
Fligner, M.A., Wolfe, D.A. (1982) Distribution-free tests for comparing several treatments with a control. Stat Neerl 36, 119–127.
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)