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TOST with Wilcoxon-Mann-Whitney tests

wilcox_TOST.Rd

[Stable]

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.

Usage

wilcox_TOST(
  x,
  ...,
  hypothesis = "EQU",
  paired = FALSE,
  eqb,
  low_eqbound,
  high_eqbound,
  ses = "rb",
  alpha = 0.05
)

# Default S3 method
wilcox_TOST(
  x,
  y = NULL,
  hypothesis = "EQU",
  paired = FALSE,
  eqb,
  low_eqbound,
  high_eqbound,
  ses = c("rb", "odds", "logodds", "cstat"),
  alpha = 0.05,
  mu = 0,
  ...
)

# S3 method for class 'formula'
wilcox_TOST(formula, data, subset, na.action, ...)

Arguments

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.

paired

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

eqb

Equivalence bound. Can provide 1 value (symmetric bound) or 2 specific values that represent the lower and upper equivalence bounds. Like the mu argument, eqb is specified on the raw scale of the original data (e.g., the scale of the median or location shift). This parameter is independent of the ses argument, which only affects the type of standardized effect size that is reported.

low_eqbound

lower equivalence bounds (deprecated, use eqb instead).

high_eqbound

upper equivalence bounds (deprecated, use eqb instead).

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). Note that ses only determines which effect size is calculated and does not affect the equivalence bounds (eqb).

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").

Value

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.

Details

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.

References

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).

See also

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()

Examples

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
#> 
#>