tamhaneDunnettTest {PMCMRplus}

Tamhane-Dunnett Many-to-One Comparison Test

Description

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.

Usage

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"), ...)

Arguments

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 "x". Ignored with a warning if "x" is a list.

alternative

the alternative hypothesis. Defaults to "two.sided".

formula

a formula of the form response ~ group where response gives the data values and group a vector or factor of the corresponding groups.

data

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).

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 NAs. Defaults to getOption("na.action").

Value

A list with class "PMCMR" 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

lower-triangle matrix of the estimated quantiles of the pairwise test statistics.

p.value

lower-triangle matrix of the p-values for the pairwise tests.

alternative

a character string describing the alternative hypothesis.

p.adjust.method

a character string describing the method for p-value adjustment.

model

a data frame of the input data.

dist

a string that denotes the test distribution.

References

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.

See Also

pmvt, welchManyOneTTest

Examples

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"))