Performs Dunn's (1964) test of multiple comparisons following a significant Kruskal-Wallis test, possibly with a correction to control the experimentwise error rate. This is largely a wrapper for the dunn.test function in dunn.test. Please see and cite that package.
Usage
dunnTest(x, ...)
# S3 method for default
dunnTest(
x,
g,
method = dunn.test::p.adjustment.methods[c(4, 2:3, 5:8, 1)],
two.sided = TRUE,
altp = two.sided,
...
)
# S3 method for formula
dunnTest(
x,
data = NULL,
method = dunn.test::p.adjustment.methods[c(4, 2:3, 5:8, 1)],
two.sided = TRUE,
altp = two.sided,
...
)
# S3 method for dunnTest
print(x, dunn.test.results = FALSE, ...)Arguments
- x
A numeric vector of data values or a formula of the form x~g.
- ...
Not yet used.
- g
A factor vector or a (non-numeric) vector that can be coerced to a factor vector.
- method
A single string that identifies the method used to control the experimentwise error rate. See the list of methods in
p.adjustment.methods(documented withdunn.test) in dunn.test.- two.sided
A single logical that indicates whether a two-sided p-value should be returned (
TRUE; default) or not. See details.- altp
Same as
two.sided. Allows similar code with thedunn.testfunction in dunn.test.two.sidedis maintained because it pre-datesaltp.- data
A data.frame that minimally contains
xandg.- dunn.test.results
A single logical that indicates whether the results that would have been printed by
dunn.testfunction in dunn.test are shown.
Value
A list with three items -- method is the long name of the method used to control the experimentwise error rate, dtres is the strings that would have been printed by the dunn.test function in dunn.test, and res is a data.frame with the following variables:
Comparison: Labels for each pairwise comparison.
Z: Values for the Z test statistic for each comparison.
P.unadj: Unadjusted p-values for each comparison.
P.adj: Adjusted p-values for each comparison.
Details
This function performs “Dunn's” test of multiple comparisons following a Kruskal-Wallis test. Unadjusted one- or two-sided p-values for each pairwise comparison among groups are computed following Dunn's description as implemented in the dunn.test function from dunn.test. These p-values may be adjusted using methods in the p.adjustment.methods function in dunn.test.
This function is largely a wrapper for the dunn.test function in dunn.test. Changes here are the possible use of formula notation, results not printed by the main function (but are printed in a more useful format (in my opinion) by the print function), the p-values are adjusted by default with the “holm” method, and two-sided p-values are returned by default. See dunn.test function in dunn.test for more details underlying these computations.
Note
The data.frame will be reduced to only those rows that are complete cases for x and g. In other words, rows with missing data for either x or g are removed from the analysis and a warning will be issued.
There are a number of functions in other packages that do similar analyses.
The results from DunnTest match the results (in a different format) from the dunn.test function from dunn.test.
The pairw.kw function from the asbio package performs the Dunn test with the Bonferroni correction. The pairw.kw also provides a confidence interval for the difference in mean ranks between pairs of groups. The p-value results from DunnTest match the results from pairw.kw.
The posthoc.kruskal.nemenyi.test function from the PMCMR package uses the “Nemenyi” (1963) method of multiple comparisons.
The kruskalmc function from the pgirmess package uses the method described by Siegel and Castellan (1988).
It is not clear which method kruskal from the agricolae package uses. It does not seem to output p-values but it does allow for a wide variety of methods to control the experimentwise error rate.
See also
See kruskal.test, dunn.test in dunn.test, posthoc.kruskal.nemenyi.test in PMCMR, kruskalmc in pgirmess, and kruskal in agricolae.
Author
Derek H. Ogle, DerekOgle51@gmail.com, but this is largely a wrapper (see details) for dunn.test in dunn.test written by Alexis Dinno.
Examples
## pH in four ponds data from Zar (2010)
ponds <- data.frame(pond=as.factor(rep(1:4,each=8)),
pH=c(7.68,7.69,7.70,7.70,7.72,7.73,7.73,7.76,
7.71,7.73,7.74,7.74,7.78,7.78,7.80,7.81,
7.74,7.75,7.77,7.78,7.80,7.81,7.84,NA,
7.71,7.71,7.74,7.79,7.81,7.85,7.87,7.91))
ponds2 <- ponds[complete.cases(ponds),]
# non-formula usage (default "holm" method)
dunnTest(ponds2$pH,ponds2$pond)
#> Dunn (1964) Kruskal-Wallis multiple comparison
#> p-values adjusted with the Holm method.
#> Comparison Z P.unadj P.adj
#> 1 1 - 2 -2.13700630 0.032597479 0.13038992
#> 2 1 - 3 -2.94934889 0.003184443 0.01592221
#> 3 2 - 3 -0.88480467 0.376261991 1.00000000
#> 4 1 - 4 -2.99180882 0.002773299 0.01663979
#> 5 2 - 4 -0.85480252 0.392660483 0.78532097
#> 6 3 - 4 0.05898698 0.952962480 0.95296248
# formula usage (default "holm" method)
dunnTest(pH~pond,data=ponds2)
#> Dunn (1964) Kruskal-Wallis multiple comparison
#> p-values adjusted with the Holm method.
#> Comparison Z P.unadj P.adj
#> 1 1 - 2 -2.13700630 0.032597479 0.13038992
#> 2 1 - 3 -2.94934889 0.003184443 0.01592221
#> 3 2 - 3 -0.88480467 0.376261991 1.00000000
#> 4 1 - 4 -2.99180882 0.002773299 0.01663979
#> 5 2 - 4 -0.85480252 0.392660483 0.78532097
#> 6 3 - 4 0.05898698 0.952962480 0.95296248
# other methods
dunnTest(pH~pond,data=ponds2,method="bonferroni")
#> Dunn (1964) Kruskal-Wallis multiple comparison
#> p-values adjusted with the Bonferroni method.
#> Comparison Z P.unadj P.adj
#> 1 1 - 2 -2.13700630 0.032597479 0.19558488
#> 2 1 - 3 -2.94934889 0.003184443 0.01910666
#> 3 2 - 3 -0.88480467 0.376261991 1.00000000
#> 4 1 - 4 -2.99180882 0.002773299 0.01663979
#> 5 2 - 4 -0.85480252 0.392660483 1.00000000
#> 6 3 - 4 0.05898698 0.952962480 1.00000000
dunnTest(pH~pond,data=ponds2,method="bh")
#> Dunn (1964) Kruskal-Wallis multiple comparison
#> p-values adjusted with the Benjamini-Hochberg method.
#> Comparison Z P.unadj P.adj
#> 1 1 - 2 -2.13700630 0.032597479 0.065194958
#> 2 1 - 3 -2.94934889 0.003184443 0.009553328
#> 3 2 - 3 -0.88480467 0.376261991 0.564392987
#> 4 1 - 4 -2.99180882 0.002773299 0.016639793
#> 5 2 - 4 -0.85480252 0.392660483 0.471192580
#> 6 3 - 4 0.05898698 0.952962480 0.952962480
dunnTest(pH~pond,data=ponds2,method="none")
#> Dunn (1964) Kruskal-Wallis multiple comparison
#> with no adjustment for p-values.
#> Comparison Z P.unadj P.adj
#> 1 1 - 2 -2.13700630 0.032597479 0.032597479
#> 2 1 - 3 -2.94934889 0.003184443 0.003184443
#> 3 2 - 3 -0.88480467 0.376261991 0.376261991
#> 4 1 - 4 -2.99180882 0.002773299 0.002773299
#> 5 2 - 4 -0.85480252 0.392660483 0.392660483
#> 6 3 - 4 0.05898698 0.952962480 0.952962480
# one-sided
dunnTest(pH~pond,data=ponds2,two.sided=FALSE)
#> Dunn (1964) Kruskal-Wallis multiple comparison
#> p-values adjusted with the Holm method.
#> Comparison Z P.unadj P.adj
#> 1 1 - 2 -2.13700630 0.016298740 0.065194958
#> 2 1 - 3 -2.94934889 0.001592221 0.007961106
#> 3 2 - 3 -0.88480467 0.188130996 0.564392987
#> 4 1 - 4 -2.99180882 0.001386649 0.008319896
#> 5 2 - 4 -0.85480252 0.196330241 0.392660483
#> 6 3 - 4 0.05898698 0.476481240 0.476481240
# warning message if incomplete cases were removed
dunnTest(pH~pond,data=ponds)
#> Warning: Some rows deleted from 'x' and 'g' because missing data.
#> Dunn (1964) Kruskal-Wallis multiple comparison
#> p-values adjusted with the Holm method.
#> Comparison Z P.unadj P.adj
#> 1 1 - 2 -2.13700630 0.032597479 0.13038992
#> 2 1 - 3 -2.94934889 0.003184443 0.01592221
#> 3 2 - 3 -0.88480467 0.376261991 1.00000000
#> 4 1 - 4 -2.99180882 0.002773299 0.01663979
#> 5 2 - 4 -0.85480252 0.392660483 0.78532097
#> 6 3 - 4 0.05898698 0.952962480 0.95296248
# print dunn.test results
tmp <- dunnTest(pH~pond,data=ponds2)
print(tmp,dunn.test.results=TRUE)
#> Kruskal-Wallis rank sum test
#>
#> data: x and g
#> Kruskal-Wallis chi-squared = 11.9435, df = 3, p-value = 0.01
#>
#>
#> Comparison of x by g
#> (Holm)
#> Col Mean-|
#> Row Mean | 1 2 3
#> ---------+---------------------------------
#> 2 | -2.137006
#> | 0.1304
#> |
#> 3 | -2.949348 -0.884804
#> | 0.0159* 1.0000
#> |
#> 4 | -2.991808 -0.854802 0.058986
#> | 0.0166* 0.7853 0.9530
#>
#> alpha = 0.05
#> Reject Ho if p <= alpha