Hi fellow R-users,
well, say I got two groups, A and B. Nested within each group are subgroups and
in each subgroup are objects with values x and y to a certain attribute. So, I
can compute the portion of x-objects for each subgroup as #x/(#x?+?#y).
Artificial example with 12 subgroups in group A and 8 subgroups in group B:
set.seed(123)
count.x <- NULL
count.y <- NULL
j <- 1
for (i in sample(x = 10:20, size = 20, replace = TRUE)){
count.x[j] <- sample(x = 0:i, size = 1)
count.y[j] <- i - count.x[j]
j <- j + 1
}
data <- data.frame(x.portion = (count.x/(count.x + count.y)),
x.portion = (count.y/(count.x + count.y)),
group = c(rep("A", 12), rep("B", 8),
weight = (count.x + count.y)
)
I am now interested in whether or not there is a difference in the portions of
x-objects between group A and B and consider it a good idea ? as seen in the
example above ? to weight for the total number of objects in each subgroup.
Given data that is not considered a realization of some normal distribution,
thinking of a test that uses ranks still does not look like a natural solution
to this problem. But I guess it is possible. Though, Xie & Priebe (2002)*
are not exactly aiming at this, their paper might give an idea how weighting may
look like in the special case of the Mann/Whitney/Wilcoxon statistic. (Despite
the hint by John & Priebe (2007)** that this ?is not a candidate for the
practitioner?s toolbox?.)
Anyway, trying to apply the Wilcoxon rank sum test to weighted data, I was first
tempted to replicate each portion by its weight. (Bad idea: data bloat, ties and
probably a number of problems even worse.) Function wilcox_test in package coin
has got a weight argument, but
library(coin)
wilcox_test(formula = x.portion ~ group, data = data, weight = ~ weight)
leads to warning ?Rank transformation doesn?t take weights into account?.
Though, results differ from
wilcox_test(formula = x.portion ~ group, data = data)
and
wilcox.test(formula = x.portion ~ group, data = data)
The code in wilcox_test() and the functions it depends on looks a little bit
interlaced to me, but I guess it is not what I am after.
tl;dr: I am looking for a nonparametric alternative to wtd.t.test in package
weights.
Is anyone aware of an(other) implementation in R?
Cheers,
Alex
PS: For real, it is a little bit trickier as there are more than two values and
maybe even more than two groups. So Kruskal-Wallis test might be of interest,
but I thought I keep it simple for the moment.
* Jingdong Xie & Carey E. Priebe: A weighted generalization of the
Mann?Whitney?Wilcoxon statistic. In: Journal of Statistical Planning and
Inference 102 (2), 2002-04-01, pages 441?466.
(http://dx.doi.org/10.1016/S0378-3758(01)00111-2.)
** Majnu John & Carey E. Priebe: A data-adaptive methodology for finding an
optimal weighted generalized Mann-Whitney-Wilcoxon statistic. In: Computational
Statistics & Data Analysis 51 (9), 2007-05-15, pages 4337?4353.
(http://dx.doi.org/10.1016/j.csda.2006.06.003.)
--
Alexander Sommer
wissenschaftlicher Mitarbeiter
Technische Universit?t Dortmund
Fakult?t Erziehungswissenschaft, Psychologie und Soziologie
Forschungsverbund Deutsches Jugendinstitut/Technische Universit?t Dortmund
Vogelpothsweg 78
44227 Dortmund
Telefon: +49 231 755-8189
Fax: +49 231 755-6553
E-Mail: Alexander.Sommer at tu-dortmund.de
WWW: http://www.forschungsverbund.tu-dortmund.de/