Density, cumulative probability, quantiles and random generation for the
distribution of the Wilcoxon rank sum statistic (also known as Mann-Whitney).
USAGE:
dwilcox(q, m, n)
pwilcox(q, m ,n)
qwilcox(p, m, n)
rwilcox(nn, m, n)
REQUIRED ARGUMENTS:
q:
vector of quantiles. Missing values (NAs) 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.
p:
vector of probabilities. Its values must be between 0 and 1.
Missing values(NAs) are allowed.
nn:
sample size. If length(nn) is greater than 1, then length(nn)
random numbers are returned.
m:
number of observations in sample x. This must be a positive integer not
greater than 50.
n:
number of observations in sample y. Also a positive integer not
greater than 50.
VALUE:
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.
SIDE EFFECTS:
The function rwilcox causes creation of the dataset .Random.seed if it does
not already exist, otherwise its value is updated.
DETAILS:
Missing values (NAs) and +-Infs
are allowed as components of q, p, or nn.
If q, m, or n are vectors
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.
BACKGROUND:
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.
REFERENCES:
Hollander, M. and Wolfe, D. (1973). Non-parametric Statistical Methods.
Wiley, New York.