dunnettTest {PMCMRplus}

Dunnett's Many-to-One Comparisons Test

Description

Performs Dunnett's multiple comparisons test with one control.

Usage

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"), ...)

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").

Details

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 \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). Dunnett's test statistics are given by

t_{i} \frac{\bar{X}_i - \bar{X_0}} {s_{\mathrm{in}} \left(1/n_0 + 1/n_i\right)^{1/2}}, ~~ (1 \le i \le k)

with s^2_{\mathrm{in}} the within-group ANOVA variance. The null hypothesis is rejected if |t_{ij}| > |T_{kv\rho\alpha}| (two-tailed), with v = N - k degree of freedom and rho the correlation:

\rho_{ij} = \sqrt{\frac{n_i n_j} {\left(n_i + n_0\right) \left(n_j+ n_0\right)}} ~~ (i \ne j) .

The p-values are computed with the function pDunnett that is a wrapper to the the multivariate-t distribution as implemented in the function pmvt.

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

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.

See Also

pmvt pDunnett

Examples

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"))