R: Dunnett's T3 Test

dunnettT3Test {PMCMRplus} | R Documentation

## Dunnett's T3 Test

### Description

Performs Dunnett's all-pairs comparison test for normally distributed data with unequal variances.

### Usage

    dunnettT3Test(x, ...)

    ## Default S3 method:
    dunnettT3Test(x, g, ...)

    ## S3 method for class 'formula'
    dunnettT3Test(formula, data, subset, na.action, ...)

    ## S3 method for class 'aov'
    dunnettT3Test(x, ...)

### 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.
`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 `NA`s. Defaults to `getOption("na.action")`.

### Details

For all-pairs comparisons in an one-factorial layout with normally distributed residuals but unequal groups variances the T3 test of Dunnett can be performed. A total of m = k(k-1)/2 hypotheses can be tested. The null hypothesis H_{ij}: μ_i(x) = μ_j(x) is tested in the two-tailed test against the alternative A_{ij}: μ_i(x) \ne μ_j(x), ~~ i \ne j.

The p-values are computed from the studentized maximum modulus distribution that is the equivalent of the multivariate t distribution with ρ = 0. The function `pmvt` is used to calculate the p-values.

### 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

C. W. Dunnett (1980) Pair wise multiple comparisons in the unequal variance case, Journal of the American Statistical Association 75, 796–800.

### See Also

`pmvt`

### Examples

    fit <- aov(weight ~ feed, chickwts)
    shapiro.test(residuals(fit))
    bartlett.test(weight ~ feed, chickwts)
    anova(fit)

    ## also works with fitted objects of class aov
    res <- dunnettT3Test(fit)
    summary(res)
    summaryGroup(res)

[Package PMCMRplus version 1.6.1 Index]