Testing Several Treatments With One Control
Performs Fligner-Wolfe non-parametric test for simultaneous testing of several locations of treatment groups against the location of the control group.
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"),
...
)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 |
For a one-factorial layout with non-normally distributed residuals the Fligner-Wolfe test can be used.
Let there be k-1-treatment groups and one control group, then the null hypothesis, H_0: θ_i - θ_c = 0 ~ (1 ≤ i ≤ k-1) is tested against the alternative (greater), A_1: θ_i - θ_c > 0 ~ (1 ≤ i ≤ k-1), with at least one inequality being strict.
Let n_c denote the sample size of the control group, N^t = ∑_{i=1}^{k-1} n_i the sum of all treatment sample sizes and N = N^t + n_c. The test statistic without taken ties into account is
SEE PDF
with r_{ij} the rank of variable x_{ij}. The null hypothesis is rejected, if W > W_{α,m,n} with m = N^t and n = n_c.
In the presence of ties, the statistic is
SEE PDF
where
SEE PDF
with g the number of tied groups and t_j the number of tied values in the jth group. The null hypothesis is rejected, if \hat{z} > z_α (as cited in EPA 2006).
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.
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.
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.