wilcoxon {ASSISTant}

Compute the standardized Wilcoxon test statistic for two samples

Description

We compute the standardized Wilcoxon test statistic with mean 0 and and standard deviation 1 for samples x and y. The R function stats::wilcox.test() returns the statistic

Usage

wilcoxon(x, y, theta = 0)

Arguments

x

a sample numeric vector

y

a sample numeric vector

theta

a value > 0 but < 1/2.

Details

U = \sum_i R_i - \frac{m(m + 1)}{2}

where R_i are the ranks of the first sample x of size m. We compute

\frac{(U - mn(1/2 + \theta))}{\sqrt{mn(m + n + 1) / 12}}

where \theta is the alternative hypothesis shift on the probability scale, i.e. P(X > Y) = 1/2 + \theta.

Value

the standardized Wilcoxon statistic