Tamhane-Dunnett Many-to-One Comparison Test
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 ≤ j ≤ n_0) and X_{ij} the j-the realization in the i-th treatment group (1 ≤ i ≤ k). Furthermore, the total sample size is N = n_0 + ∑_{i=1}^k n_i. A total of m = k hypotheses can be tested: The null hypothesis is H_{i}: μ_i = μ_0 is tested against the alternative A_{i}: μ_i \ne μ_0 (two-tailed). Tamhane-Dunnett's test statistics are given by
SEE PDF
The null hypothesis is rejected if |t_{i}| > T_{kv_{i}ρ_{ij}α} (two-tailed), with
SEE PDF
degree of freedom and the correlation
SEE PDF
The p-values are computed from the multivariate-t
distribution as implemented in the function
pmvt distribution.
tamhaneDunnettTest(x, ...)
## Default S3 method:
tamhaneDunnettTest(x, g, alternative = c("two.sided", "greater", "less"), ...)
## S3 method for class 'formula'
tamhaneDunnettTest(
formula,
data,
subset,
na.action,
alternative = c("two.sided", "greater", "less"),
...
)
## S3 method for class 'aov'
tamhaneDunnettTest(x, alternative = c("two.sided", "greater", "less"), ...)x |
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. |
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 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.
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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