Calculates r effect size for Mann-Whitney two-sample rank-sum test, or a table with an ordinal variable and a nominal variable with two levels; confidence intervals by bootstrap.

```
wilcoxonR(
x,
g = NULL,
group = "row",
coin = FALSE,
ci = FALSE,
conf = 0.95,
type = "perc",
R = 1000,
histogram = FALSE,
digits = 3,
reportIncomplete = FALSE,
...
)
```

A single statistic, r. Or a small data frame consisting of r, and the lower and upper confidence limits.

- x
Either a two-way table or a two-way matrix. Can also be a vector of observations.

- g
If

`x`

is a vector,`g`

is the vector of observations for the grouping, nominal variable. Only the first two levels of the nominal variable are used.- group
If

`x`

is a table or matrix,`group`

indicates whether the`"row"`

or the`"column"`

variable is the nominal, grouping variable.- coin
If

`FALSE`

, the default, the Z value is extracted from a function similar to the`wilcox.test`

function in the stats package. If`TRUE`

, the Z value is extracted from the`wilcox_test`

function in the coin package. This method may be much slower, especially if a confidence interval is produced.- ci
If

`TRUE`

, returns confidence intervals by bootstrap. May be slow.- conf
The level for the confidence interval.

- type
The type of confidence interval to use. Can be any of "

`norm`

", "`basic`

", "`perc`

", or "`bca`

". Passed to`boot.ci`

.- R
The number of replications to use for bootstrap.

- histogram
If

`TRUE`

, produces a histogram of bootstrapped values.- digits
The number of significant digits in the output.

- reportIncomplete
If

`FALSE`

(the default),`NA`

will be reported in cases where there are instances of the calculation of the statistic failing during the bootstrap procedure.- ...
Additional arguments passed to the

`wilcox_test`

function.

Salvatore Mangiafico, mangiafico@njaes.rutgers.edu

r is calculated as Z divided by square root of the total observations.

This statistic reports a smaller effect size than does
Glass rank biserial correlation coefficient
(`wilcoxonRG`

), and cannot reach
-1 or 1. This effect is exaserbated when sample sizes
are not equal.

Currently, the function makes no provisions for `NA`

values in the data. It is recommended that `NA`

s be removed
beforehand.

When the data in the first group are greater than
in the second group, r is positive.
When the data in the second group are greater than
in the first group, r is negative.
Be cautious with this interpretation, as R will alphabetize
groups if `g`

is not already a factor.

When r is close to extremes, or with small counts in some cells, the confidence intervals determined by this method may not be reliable, or the procedure may fail.

`freemanTheta`

,
`wilcoxonRG`

```
data(Breakfast)
Table = Breakfast[1:2,]
library(coin)
chisq_test(Table, scores = list("Breakfast" = c(-2, -1, 0, 1, 2)))
wilcoxonR(Table)
data(Catbus)
wilcox.test(Steps ~ Gender, data = Catbus)
wilcoxonR(x = Catbus$Steps, g = Catbus$Gender)
```

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