dunnettTest function

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"), ...)

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").

Returns

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.

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

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:

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.

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"))

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