wilcoxon {ASSISTant} | R Documentation |

## 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

[Package

*ASSISTant*version 1.4.3 Index]