`wilcox_TOST.Rd`

A function for TOST using the non-parametric methods of the Wilcoxon-Mann-Whitney family of tests. This function uses the normal approximation and applies a continuity correction automatically.

```
wilcox_TOST(
x,
...,
hypothesis = "EQU",
paired = FALSE,
eqb,
low_eqbound,
high_eqbound,
ses = "rb",
alpha = 0.05
)
# S3 method for default
wilcox_TOST(
x,
y = NULL,
hypothesis = "EQU",
paired = FALSE,
eqb,
low_eqbound,
high_eqbound,
ses = c("rb", "odds", "cstat"),
alpha = 0.05,
mu = 0,
...
)
# S3 method for formula
wilcox_TOST(formula, data, subset, na.action, ...)
```

- x
a (non-empty) numeric vector of data values.

- ...
further arguments to be passed to or from methods.

- hypothesis
'EQU' for equivalence (default), or 'MET' for minimal effects test, the alternative hypothesis.

- paired
a logical indicating whether you want a paired t-test.

- eqb
Equivalence bound. Can provide 1 value (negative value is taken as the lower bound) or 2 specific values that represent the upper and lower equivalence bounds.

- low_eqbound
lower equivalence bounds (deprecated).

- high_eqbound
upper equivalence bounds (deprecated).

- ses
Standardized effect size. Default is "rb" for rank-biserial correlation. Options also include "cstat" for concordance probability, or "odds" for Wilcoxon-Mann-Whitney odds (otherwise known as Agresti's generalized odds ratio).

- alpha
alpha level (default = 0.05)

- y
an optional (non-empty) numeric vector of data values.

- mu
number indicating the value around which (a-)symmetry (for one-sample or paired samples) or shift (for independent samples) is to be estimated. See stats::wilcox.test.

- formula
a formula of the form lhs ~ rhs where lhs is a numeric variable giving the data values and rhs either 1 for a one-sample or paired test or a factor with two levels giving the corresponding groups. If lhs is of class "Pair" and rhs is 1, a paired test is done.

- data
an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).

- subset
an optional vector specifying a subset of observations to be used.

- na.action
a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action").

An S3 object of class
`"TOSTnp"`

is returned containing the following slots:

"TOST": A table of class

`"data.frame"`

containing two-tailed wilcoxon signed rank test and both one-tailed results."eqb": A table of class

`"data.frame"`

containing equivalence bound settings."effsize": table of class

`"data.frame"`

containing effect size estimates."hypothesis": String stating the hypothesis being tested.

"smd": List containing information on standardized effect size.

"alpha": Alpha level set for the analysis.

"method": Type of non-parametric test.

"decision": List included text regarding the decisions for statistical inference.

For details on the calculations in this function see `vignette("robustTOST")`

.

If only x is given, or if both x and y are given and paired is TRUE, a Wilcoxon signed rank test of the null that the distribution of x (in the one sample case) or of x - y (in the paired two sample case) is symmetric about mu is performed.

Otherwise, if both x and y are given and paired is FALSE, a Wilcoxon rank sum test (equivalent to the Mann-Whitney test: see the Note) is carried out. In this case, the null hypothesis is that the distributions of x and y differ by a location shift.

David F. Bauer (1972). Constructing confidence sets using rank statistics. Journal of the American Statistical Association 67, 687–690. doi: 10.1080/01621459.1972.10481279.

Myles Hollander and Douglas A. Wolfe (1973). Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 27–33 (one-sample), 68–75 (two-sample). Or second edition (1999).

Other Robust tests:
`boot_log_TOST()`

,
`boot_t_TOST()`

,
`boot_t_test()`

,
`brunner_munzel()`

,
`log_TOST()`

Other TOST:
`boot_log_TOST()`

,
`boot_t_TOST()`

,
`simple_htest()`

,
`t_TOST()`

,
`tsum_TOST()`

```
data(mtcars)
wilcox_TOST(mpg ~ am,
data = mtcars,
eqb = 3)
#>
#> Wilcoxon rank sum test with continuity correction
#>
#> The equivalence test was non-significant W = 18.500, p = 9.75e-01
#> The null hypothesis test was significant W = 42.000, p = 1.87e-03
#> NHST: reject null significance hypothesis that the effect is equal to zero
#> TOST: don't reject null equivalence hypothesis
#>
#> TOST Results
#> Test Statistic p.value
#> NHST 42.0 0.002
#> TOST Lower 73.0 0.975
#> TOST Upper 18.5 < 0.001
#>
#> Effect Sizes
#> Estimate C.I. Conf. Level
#> Median of Differences -6.8000 [-10.9999, -3.6001] 0.9
#> Rank-Biserial Correlation -0.6599 [-0.8143, -0.4182] 0.9
#>
#>
```