R: Dunn's Test of Multiple Comparisons

DunnTest {DescTools} | R Documentation

## Dunn's Test of Multiple Comparisons

### Description

Performs Dunn's test of multiple comparisons using rank sums.

### Usage

    DunnTest(x, ...)

    ## Default S3 method:
    DunnTest(x, g,
             method = c("holm", "hochberg", "hommel", "bonferroni", "BH",
                        "BY", "fdr", "none"),
             alternative = c("two.sided", "less", "greater"),
             out.list = TRUE, ...)

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

    ## S3 method for class 'DunnTest'
    print(x, digits = getOption("digits", 3), ...)

### Arguments

`x` | a numeric vector of data values, or a list of numeric data vectors.
`g` | a vector or factor object giving the group for the corresponding elements of `x`. Ignored if `x` is a list.
`method` | the method for adjusting p-values for multiple comparisons. The function is calling `p.adjust` and this parameter is directly passed through.
`alternative` | a character string specifying the alternative hypothesis, must be one of `"two.sided"` (default), `"greater"` or `"less"`. You can specify just the initial letter.
`out.list` | logical, indicating if the results should be printed in list mode or as a square matrix. Default is list (TRUE).
`formula` | a formula of the form `lhs ~ rhs` where `lhs` gives the data values and `rhs` 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")`.
`digits` | controls the number of fixed digits to print.
`...` | further arguments to be passed to or from methods.

### Details

`DunnTest` performs the post hoc pairwise multiple comparisons procedure appropriate to follow the rejection of a Kruskal-Wallis test. The Kruskal-Wallis test, being a non-parametric analog of the one-way ANOVA, is an omnibus test of the null hypothesis that none of k groups stochastically dominate one another. Dunn's test is constructed in part by summing jointly ranked data. The rank sum test, itself a non-parametric analog of the unpaired t-test, is possibly intuitive, but inappropriate as a post hoc pairwise test, because (1) it fails to retain the dependent ranking that produced the Kruskal-Wallis test statistic, and (2) it does not incorporate the pooled variance estimate implied by the null hypothesis of the Kruskal-Wallis test.

If `x` is a list, its elements are taken as the samples to be compared, and hence have to be numeric data vectors. In this case, `g` is ignored, and one can simply use `DunnTest(x)` to perform the test. If the samples are not yet contained in a list, use `DunnTest(list(x, ...))`.

Otherwise, `x` must be a numeric data vector, and `g` must be a vector or factor object of the same length as `x` giving the group for the corresponding elements of `x`.

### Value

A list with class `"DunnTest"` containing the following components:

`res` | an array containing the mean rank differencens and the according p-values

### Author(s)

Andri Signorell <andri@signorell.net>, the interface is based on R-Core code

### References

Dunn, O. J. (1961) Multiple comparisons among means Journal of the American Statistical Association, 56(293):52-64.

Dunn, O. J. (1964) Multiple comparisons using rank sums Technometrics, 6(3):241-252.

### See Also

`kruskal.test`, `wilcox.test`, `p.adjust`

### Examples

    ## Hollander & Wolfe (1973), 116.
    ## Mucociliary efficiency from the rate of removal of dust in normal
    ##  subjects, subjects with obstructive airway disease, and subjects
    ##  with asbestosis.
    x <- c(2.9, 3.0, 2.5, 2.6, 3.2) # normal subjects
    y <- c(3.8, 2.7, 4.0, 2.4)      # with obstructive airway disease
    z <- c(2.8, 3.4, 3.7, 2.2, 2.0) # with asbestosis
    DunnTest(list(x, y, z))

    ## Equivalently,
    x <- c(x, y, z)
    g <- factor(rep(1:3, c(5, 4, 5)),
                labels = c("Normal subjects",
                           "Subjects with obstructive airway disease",
                           "Subjects with asbestosis"))

    # do the kruskal.test first
    kruskal.test(x, g)

    # ...and the pairwise test afterwards
    DunnTest(x, g)

    ## Formula interface.
    boxplot(Ozone ~ Month, data = airquality)
    DunnTest(Ozone ~ Month, data = airquality)

[Package DescTools version 0.99.25 Index]