Performs Tamhane-Dunnett's multiple comparisons test with one control. For many-to-one comparisons in an one-factorial layout with normally distributed residuals and unequal variances Tamhane-Dunnett's test can be used. Let \(X_{0j}\) denote a continuous random variable with the \(j\)-the realization of the control group (\(1 \le j \le n_0\)) and \(X_{ij}\) the \(j\)-the realization in the \(i\)-th treatment group (\(1 \le i \le k\)). Furthermore, the total sample size is \(N = n_0 + \sum_{i=1}^k n_i\). A total of \(m = k\) hypotheses can be tested: The null hypothesis is H\(_{i}: \mu_i = \mu_0\) is tested against the alternative A\(_{i}: \mu_i \ne \mu_0\) (two-tailed). Tamhane-Dunnett's test statistics are given by
$$ t_{i} \frac{\bar{X}_i - \bar{X_0}} {\left( s^2_0 / n_0 + s^2_i / n_i \right)^{1/2} } ~~ (1 \le i \le k) $$
The null hypothesis is rejected if \(|t_{i}| > T_{kv_{i}\rho_{ij}\alpha}\) (two-tailed), with
$$ v_i = n_0 + n_i - 2 $$
degree of freedom and the correlation
$$ \rho_{ii} = 1, ~ \rho_{ij} = 0 ~ (i \ne j). $$
The p-values are computed from the multivariate-t
distribution as implemented in the function
pmvt distribution.
tamhaneDunnettTest(x, ...)# S3 method for default
tamhaneDunnettTest(x, g, alternative = c("two.sided", "greater", "less"), ...)
# S3 method for formula
tamhaneDunnettTest(
formula,
data,
subset,
na.action,
alternative = c("two.sided", "greater", "less"),
...
)
# S3 method for aov
tamhaneDunnettTest(x, alternative = c("two.sided", "greater", "less"), ...)
a numeric vector of data values, a list of numeric data vectors or a fitted model object, usually an aov fit.
further arguments to be passed to or from methods.
a vector or factor object giving the group for the
corresponding elements of "x".
Ignored with a warning if "x" is a list.
the alternative hypothesis.
Defaults to "two.sided".
a formula of the form response ~ group where
response gives the data values and group a vector or
factor of the corresponding groups.
an optional matrix or data frame (or similar: see
model.frame) containing the variables in the
formula formula. By default the variables are taken from
environment(formula).
an optional vector specifying a subset of observations to be used.
a function which indicates what should happen when
the data contain NAs. Defaults to getOption("na.action").
A list with class "PMCMR" containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
lower-triangle matrix of the estimated quantiles of the pairwise test statistics.
lower-triangle matrix of the p-values for the pairwise tests.
a character string describing the alternative hypothesis.
a character string describing the method for p-value adjustment.
a data frame of the input data.
a string that denotes the test distribution.
OECD (ed. 2006) Current approaches in the statistical analysis of ecotoxicity data: A guidance to application - Annexes. OECD Series on testing and assessment, No. 54.
# NOT RUN {
set.seed(245)
mn <- c(1, 2, 2^2, 2^3, 2^4)
x <- rep(mn, each=5) + rnorm(25)
g <- factor(rep(1:5, each=5))
fit <- aov(x ~ g - 1)
shapiro.test(residuals(fit))
bartlett.test(x ~ g - 1)
anova(fit)
## works with object of class aov
summary(tamhaneDunnettTest(fit, alternative = "greater"))
# }
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