Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!
Get Started for Free

dunnettTest

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 ≤ 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.

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

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"))

PMCMRplus

Calculate Pairwise Multiple Comparisons of Mean Rank Sums Extended

v1.9.0
GPL (>= 3)
Authors
Thorsten Pohlert [aut, cre] (<https://orcid.org/0000-0003-3855-3025>)
Initial release
2021-01-12

We don't support your browser anymore

Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.