Dunnett's Many-to-One Comparisons Test
Performs Dunnett's multiple comparisons test with one control.
dunnettTest(x, ...) ## Default S3 method: dunnettTest(x, g, alternative = c("two.sided", "greater", "less"), ...) ## S3 method for class 'formula' dunnettTest( formula, data, subset, na.action, alternative = c("two.sided", "greater", "less"), ... ) ## S3 method for class 'aov' dunnettTest(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 |
For many-to-one comparisons in an one-factorial layout with normally distributed residuals 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). Dunnett's test statistics are given by
SEE PDF
with s^2_{\mathrm{in}} the within-group ANOVA variance. The null hypothesis is rejected if |t_{ij}| > |T_{kvρα}| (two-tailed), with v = N - k degree of freedom and rho the correlation:
SEE PDF
The p-values are computed
from the multivariate-t distribution as implemented in the function
pmvt
distribution.
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.
Dunnett, C. W. (1955) A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association 50, 1096–1121.
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.
fit <- aov(Y ~ DOSE, data = trout) shapiro.test(residuals(fit)) bartlett.test(Y ~ DOSE, data = trout) ## works with fitted object of class aov summary(dunnettTest(fit, alternative = "less"))
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