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Dunn's Test for Pairwise Rank Comparisons After a Kruskal–Wallis Test

Source: R/dunnTest.R
dunnTest.Rd

A nonparametric post hoc test for multiple pairwise comparisons following a significant Kruskal-Wallis test, based on rank sums with adjustment for multiple testing.

Usage

dunnTest(x, ...)

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

# Default S3 method
dunnTest(
  x,
  g,
  method = p.adjust.methods,
  alternative = c("two.sided", "less", "greater"),
  output = c("list", "matrix"),
  alpha = 0.05,
  ...
)

Arguments

x

a numeric vector of observations or a list of numeric vectors.

...

further arguments passed to methods.

formula

a formula of the form response ~ group.

data

an optional data frame containing the variables in formula.

subset

an optional expression specifying a subset of observations.

na.action

a function indicating how missing values should be handled.

g

a grouping variable corresponding to x; ignored when x is a list.

method

the method used to adjust the p-values for multiple comparisons, one of p.adjust.methods (default is "holm"). Passed directly to p.adjust().

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "less" or "greater". See the Details for the direction convention.

output

the output format:

  • "list" pairwise comparison table.

  • "matrix" lower-triangular matrix of adjusted p-values.

alpha

the significance level used to compile the groups flagged as significantly different in the label attribute of the p-value matrix (default is 0.05).

Value

An object of class "rankTest" containing:

res

pairwise comparison results. Depending on output, either a table of mean-rank differences and adjusted p-values or a lower-triangular p-value matrix.

pmat

symmetric matrix of adjusted p-values.

Details

dunnTest performs the post hoc pairwise multiple-comparison procedure appropriate after rejection of the Kruskal-Wallis null hypothesis. In contrast to performing separate Wilcoxon rank-sum tests, Dunn's procedure preserves the pooled ranking and variance estimate underlying the Kruskal-Wallis test. It is intended as a post hoc procedure following a significant Kruskal-Wallis test, i.e. typically for three or more groups.

If x is a list, its elements are taken as the samples to be compared and must be numeric vectors. In this case g is ignored. Otherwise, x must be a numeric vector and g a grouping variable of the same length.

Each pairwise comparison is labeled "B-A", where A precedes B in the ordering of the group levels, and reports the mean rank difference \(\bar{R}_B - \bar{R}_A\). For one-sided alternatives, "greater" tests whether B tends to have larger observations than A (upper tail), and "less" tests the reverse (lower tail).

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()

Other test.posthoc: conoverTest(), dscfTest(), dunnettTest(), gamesHowellTest(), nemenyiTest(), plot.PostHocTest(), postHoc, scheffeTest(), signifDiff(), steelTest()

Examples

## Hollander & Wolfe (1973), p. 116
x <- c(2.9, 3.0, 2.5, 2.6, 3.2)
y <- c(3.8, 2.7, 4.0, 2.4)
z <- c(2.8, 3.4, 3.7, 2.2, 2.0)

dunnTest(list(x, y, z))
#> 
#>  Dunn's test of multiple comparisons using rank sums : holm 
#> 
#>     mean.rank.diff   pval    
#> 2-1            1.8 1.0000    
#> 3-1           -0.6 1.0000    
#> 3-2           -2.4 1.0000    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 

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"
  )
)

kruskal.test(x, g)
#> 
#> 	Kruskal-Wallis rank sum test
#> 
#> data:  x and g
#> Kruskal-Wallis chi-squared = 0.77143, df = 2, p-value = 0.68
#> 
dunnTest(x, g)
#> 
#>  Dunn's test of multiple comparisons using rank sums : holm 
#> 
#>                                                                   mean.rank.diff
#> Subjects with obstructive airway disease-Normal subjects                     1.8
#> Subjects with asbestosis-Normal subjects                                    -0.6
#> Subjects with asbestosis-Subjects with obstructive airway disease           -2.4
#>                                                                     pval    
#> Subjects with obstructive airway disease-Normal subjects          1.0000    
#> Subjects with asbestosis-Normal subjects                          1.0000    
#> Subjects with asbestosis-Subjects with obstructive airway disease 1.0000    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 

## Formula interface
dunnTest(Ozone ~ factor(Month), data = airquality)
#> 
#>  Dunn's test of multiple comparisons using rank sums : holm 
#> 
#>     mean.rank.diff    pval    
#> 6-5    12.02991453 1.00000    
#> 7-5    41.21153846 9.9e-05 ***
#> 8-5    38.53846154 0.00032 ***
#> 9-5    11.99734748 0.74574    
#> 7-6    29.18162393 0.14891    
#> 8-6    26.50854701 0.20743    
#> 9-6    -0.03256705 1.00000    
#> 8-7    -2.67307692 1.00000    
#> 9-7   -29.21419098 0.01036 *  
#> 9-8   -26.54111406 0.02428 *  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>