ConoverTest {DescTools}  R Documentation 
Conover's Test of Multiple Comparisons
Description
Perform Conover's test of multiple comparisons using rank sums as post hoc test following a significant kruskal.test
.
Usage
ConoverTest(x, ...)
## Default S3 method:
ConoverTest(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'
ConoverTest(formula, data, subset, na.action, ...)
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 
method 
the method for adjusting pvalues for multiple comparisons. The function is calling 
alternative 
a character string specifying the alternative hypothesis, must be one of 
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 
data 
an optional matrix or data frame (or similar: see

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 
... 
further arguments to be passed to or from methods. 
Details
ConoverTest
performs the post hoc pairwise multiple comparisons procedure appropriate to follow the rejection of a KruskalWallis test.
Conover's test is more powerful than Dunn's post hoc multiple comparisons test (DunnTest
). The interpretation of stochastic dominance requires an assumption that the CDF of one group does not cross the CDF of the other.
ConoverTest makes m = k(k1)/2 multiple pairwise comparisons based on the ConoverIman tteststatistic for the ranksum differences:
\left  \bar{R}_{i}\bar{R}_{j} \right  > t_{1\alpha/2, nk} \cdot \sqrt{ s^2 \cdot \left [
\frac{n1\hat{H}^*}{nk} \right ] \cdot \left [ \frac{1}{n_i} + \frac{1}{n_j} \right ] }
with the (tie corrected) statistic of the Kruskal Wallis test
\hat{H}^* = \frac{\frac{12}{n \cdot (n+1)} \cdot \sum_{i=1}^{k}\frac{R_{i}^2}{n_i}  3\cdot(n+1) } {1\frac{\sum_{i=1}^{r} \left ( t_i^3t_i \right )}{n^3n}}
and the s^2
being
s^2 = \frac{1}{n1} \cdot \left [ \sum{R_i^2}  n \cdot \frac{(n+1)^2}{4} \right ]
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 ConoverTest(x)
to perform the test. If the samples are not yet contained in a
list, use ConoverTest(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 pvalues 
Author(s)
Andri Signorell <andri@signorell.net>, the interface is based on RCore code
References
Conover W. J., Iman R. L. (1979) On multiplecomparisons procedures, Tech. Rep. LA7677MS, Los Alamos Scientific Laboratory.
Conover, W. J. (1999) Practical Nonparametric Statistics Wiley, Hoboken, NJ. 3rd edition.
See Also
DunnTest
, NemenyiTest
, 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
ConoverTest(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
ConoverTest(x, g)
## Formula interface.
boxplot(Ozone ~ Month, data = airquality)
ConoverTest(Ozone ~ Month, data = airquality)