dwilcox(q, m, n, log = FALSE) pwilcox(q, m ,n) qwilcox(p, m, n) rwilcox(nn, m, n, bigdata=F)
bdVector
of quantiles. Missing values (
NA
s) are allowed.
q
represents the sum of the ranks of the sample
x
in
c(x,y)
where
y
represents the elements of another sample.
bdVector
of probabilities. Its values must be between 0 and 1.
Missing values(
NA
s) are allowed.
length(nn)
is greater than 1, then
length(nn)
random numbers are returned.
x
. This must be a positive integer not
greater than 50.
y
. Also a positive integer not
greater than 50.
TRUE
, an object of type
bdVector
is returned.
Otherwise, a
vector
object is returned. This argument can be used only if the bigdata library section has been loaded.
TRUE
, dwilcox will return the log of the
density, not the density itself.
dwilcox
returns values for the exact probability at discrete values of
q
.
Other functions return cumulative probability (
pwilcox
),
quantiles (
qwilcox
), or a random sample (
rwilcox
) for the rank sum
probability distribution.
rwilcox
causes creation of the dataset
.Random.seed
if it does
not already exist, otherwise its value is updated.
Missing values (
NA
s) and
+-Inf
s
are allowed as components of
q
,
p
, or
nn
.
If
q
,
m
, or
n
are vectors or
bdVector
s
of different lengths,
m
, and
n
will be made to conform to the length of
q
by replicating their values cyclically. The values of both
m
and
n
are rounded to the nearest integer value before any calculations are made.
If data consist of two random samples, a sample
x
of size
m
,
and a sample
y
(independent of sample
x
) of size
n
, then
the Wilcoxon rank sum statistic is the sum of the ranks of
x
in the combined sample
c(x,y)
.
This statistic can then be used for a non-parametric test of
location shift between the parent populations.
The Wilcoxon rank sum statistic takes on values between
m*(m+1)/2
and
m*(m+2*n+1)/2
.
For details on the uniform random number generator implemented in S-PLUS,
see the
set.seed
help file.
For
wilcox.test
, S-PLUS uses the Wilcoxon rank sum test
W
(see the BACKGROUND section above), while R computes the Mann and Whitney
U
statistic:
For samples
x
and
y
, for each value of
x
, count the number of values of
y
that are less than
x
. The sum of these counts is
U
.
The
W
and
U
statistics differ by a function of the sample sizes, and thus the Wilcoxon distribution is defined differently between R and S-PLUS.
Hollander, M. and Wolfe, D. (1973). Non-parametric Statistical Methods. Wiley, New York.
pwilcox(24, 4, 6) # the probability of q<=24 dwilcox(11:20,9,3) # probabilities for q <- 11:20