This function performs Wilcoxon rank sum tests for one sample
or for two *paired* (dependent) samples. For *unpaired* (independent)
samples, please use the `mann_whitney_test()`

function.

A Wilcoxon rank sum test is a non-parametric test for the null hypothesis
that two samples have identical continuous distributions. The implementation
in `wilcoxon_test()`

is only used for *paired*, i.e. *dependent* samples. For
independent (unpaired) samples, use `mann_whitney_test()`

.

`wilcoxon_test()`

can be used for ordinal scales or when the continuous
variables are not normally distributed. For large samples, or approximately
normally distributed variables, the `t_test()`

function can be used (with
`paired = TRUE`

).

```
wilcoxon_test(
data,
select = NULL,
by = NULL,
weights = NULL,
mu = 0,
alternative = "two.sided",
...
)
```

- data
A data frame.

- select
Name(s) of the continuous variable(s) (as character vector) to be used as samples for the test.

`select`

can be one of the following:`select`

can be used in combination with`by`

, in which case`select`

is the name of the continous variable (and`by`

indicates a grouping factor).`select`

can also be a character vector of length two or more (more than two names only apply to`kruskal_wallis_test()`

), in which case the two continuous variables are treated as samples to be compared.`by`

must be`NULL`

in this case.If

`select`

select is of length**two**and`paired = TRUE`

, the two samples are considered as*dependent*and a paired test is carried out.If

`select`

specifies**one**variable and`by = NULL`

, a one-sample test is carried out (only applicable for`t_test()`

and`wilcoxon_test()`

)For

`chi_squared_test()`

, if`select`

specifies**one**variable and both`by`

and`probabilities`

are`NULL`

, a one-sample test against given probabilities is automatically conducted, with equal probabilities for each level of`select`

.

- by
Name of the variable indicating the groups. Required if

`select`

specifies only one variable that contains all samples to be compared in the test. If`by`

is not a factor, it will be coerced to a factor. For`chi_squared_test()`

, if`probabilities`

is provided,`by`

must be`NULL`

.- weights
Name of an (optional) weighting variable to be used for the test.

- mu
The hypothesized difference in means (for

`t_test()`

) or location shift (for`wilcoxon_test()`

and`mann_whitney_test()`

). The default is 0.- alternative
A character string specifying the alternative hypothesis, must be one of

`"two.sided"`

(default),`"greater"`

or`"less"`

. See`?t.test`

and`?wilcox.test`

.- ...
Additional arguments passed to

`wilcox.test()`

(for unweighted tests, i.e. when`weights = NULL`

).

A data frame with test results. The function returns p and Z-values as well as effect size r and group-rank-means.

The following table provides an overview of which test to use for different types of data. The choice of test depends on the scale of the outcome variable and the number of samples to compare.

Samples | Scale of Outcome | Significance Test |

1 | binary / nominal | `chi_squared_test()` |

1 | continuous, not normal | `wilcoxon_test()` |

1 | continuous, normal | `t_test()` |

2, independent | binary / nominal | `chi_squared_test()` |

2, independent | continuous, not normal | `mann_whitney_test()` |

2, independent | continuous, normal | `t_test()` |

2, dependent | binary (only 2x2) | `chi_squared_test(paired=TRUE)` |

2, dependent | continuous, not normal | `wilcoxon_test()` |

2, dependent | continuous, normal | `t_test(paired=TRUE)` |

>2, independent | continuous, not normal | `kruskal_wallis_test()` |

>2, independent | continuous, normal | `datawizard::means_by_group()` |

>2, dependent | continuous, not normal | not yet implemented (1) |

>2, dependent | continuous, normal | not yet implemented (2) |

(1) More than two dependent samples are considered as *repeated measurements*.
For ordinal or not-normally distributed outcomes, these samples are
usually tested using a `friedman.test()`

, which requires the samples
in one variable, the groups to compare in another variable, and a third
variable indicating the repeated measurements (subject IDs).

(2) More than two dependent samples are considered as *repeated measurements*.
For normally distributed outcomes, these samples are usually tested using
a ANOVA for repeated measurements. A more sophisticated approach would
be using a linear mixed model.

Bender, R., Lange, S., Ziegler, A. Wichtige Signifikanztests. Dtsch Med Wochenschr 2007; 132: e24–e25

du Prel, J.B., Röhrig, B., Hommel, G., Blettner, M. Auswahl statistischer Testverfahren. Dtsch Arztebl Int 2010; 107(19): 343–8

`t_test()`

for parametric t-tests of dependent and independent samples.`mann_whitney_test()`

for non-parametric tests of unpaired (independent) samples.`wilcoxon_test()`

for Wilcoxon rank sum tests for non-parametric tests of paired (dependent) samples.`kruskal_wallis_test()`

for non-parametric tests with more than two independent samples.`chi_squared_test()`

for chi-squared tests (two categorical variables, dependent and independent).

```
data(mtcars)
# one-sample test
wilcoxon_test(mtcars, "mpg")
#> # One Sample Wilcoxon signed rank test
#>
#> Alternative hypothesis: true location shift is not equal to 0
#>
#> V = 528, p < .001
#>
# base R equivalent, we set exact = FALSE to avoid a warning
wilcox.test(mtcars$mpg ~ 1, exact = FALSE)
#>
#> Wilcoxon signed rank test with continuity correction
#>
#> data: mtcars$mpg
#> V = 528, p-value = 8.311e-07
#> alternative hypothesis: true location is not equal to 0
#>
# paired test
wilcoxon_test(mtcars, c("mpg", "hp"))
#> # Paired Wilcoxon signed rank test
#>
#> Alternative hypothesis: true location shift is not equal to 0
#>
#> V = 0, r = 0.87, Z = -4.94, p < .001
#>
# base R equivalent, we set exact = FALSE to avoid a warning
wilcox.test(mtcars$mpg, mtcars$hp, paired = TRUE, exact = FALSE)
#>
#> Wilcoxon signed rank test with continuity correction
#>
#> data: mtcars$mpg and mtcars$hp
#> V = 0, p-value = 8.338e-07
#> alternative hypothesis: true location shift is not equal to 0
#>
# when `by` is specified, each group must be of same length
data(iris)
d <- iris[iris$Species != "setosa", ]
wilcoxon_test(d, "Sepal.Width", by = "Species")
#> # Paired Wilcoxon signed rank test
#>
#> Alternative hypothesis: true location shift is not equal to 0
#>
#> V = 247, r = 0.39, Z = -2.76, p = 0.006
#>
```