brunner_munzel: Brunner-Munzel Test

Description

This is a generic function that performs a generalized asymptotic Brunner-Munzel test in a fashion similar to t.test.

Usage

brunner_munzel(
  x,
  ...,
  paired = FALSE,
  alternative = c("two.sided", "less", "greater"),
  mu = 0.5,
  alpha = 0.05,
  perm = FALSE,
  max_n_perm = 10000
)
# S3 method for default
brunner_munzel(
  x,
  y,
  paired = FALSE,
  alternative = c("two.sided", "less", "greater"),
  mu = 0.5,
  alpha = 0.05,
  perm = FALSE,
  max_n_perm = 10000,
  ...
)
# S3 method for formula
brunner_munzel(formula, data, subset, na.action, ...)

Value

A list with class "htest" containing the following components:

"statistic": the value of the test statistic.
"parameter": the degrees of freedom for the test statistic.
"p.value": the p-value for the test.
"conf.int": a confidence interval for the relative effect appropriate to the specified alternative hypothesis.
"estimate": the estimated relative effect.
"null.value": the specified hypothesized value of the relative effect.
"stderr": the standard error of the relative effect.
"alternative": a character string describing the alternative hypothesis.
"method": a character string indicating what type of test was performed.
"data.name": a character string giving the name(s) of the data.

Arguments

x: a (non-empty) numeric vector of data values.
...: further arguments to be passed to or from methods.
paired: a logical indicating whether you want a paired test.
alternative: a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
mu: a number specifying an optional parameter used to form the null hypothesis (Default = 0.5). This can be thought of as the null in terms of the relative effect, p = P (X < Y ) + 0.5 * P (X = Y); See ‘Details’.
alpha: alpha level (default = 0.05)
perm: a logical indicating whether or not to perform a permutation test over approximate t-distribution based test (default is FALSE). Highly recommend to set perm = TRUE when sample size per condition is less than 15.
max_n_perm: the maximum number of permutations (default is 10000).
y: an optional (non-empty) numeric vector of data values.
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").

Details

This function is made to provide a test of stochastic equality between two samples (paired or independent), and is referred to as the Brunner-Munzel test.

This tests the hypothesis that the relative effect, discussed below, is equal to the null value (default is mu = 0.5).

The estimate of the relative effect, which can be considered as value similar to the probability of superiority, refers to the following:

$$\hat p = p(X<Y) + \frac{1}{2} \cdot P(X=Y)$$

Note, for paired samples, this does not refer to the probability of an increase/decrease in paired sample but rather the probability that a randomly sampled value of X. This is also referred to as the "relative" effect in the literature. Therefore, the results will differ from the concordance probability provided by the ses_calc function.

The brunner_munzel function is based on the npar.t.test and npar.t.test.paired functions within the nparcomp package (Konietschke et al. 2015).

References

Brunner, E., Munzel, U. (2000). The Nonparametric Behrens-Fisher Problem: Asymptotic Theory and a Small Sample Approximation. Biometrical Journal 42, 17 -25.

Neubert, K., Brunner, E., (2006). A Studentized Permutation Test for the Nonparametric Behrens-Fisher Problem. Computational Statistics and Data Analysis.

Munzel, U., Brunner, E. (2002). An Exact Paired Rank Test. Biometrical Journal 44, 584-593.

Konietschke, F., Placzek, M., Schaarschmidt, F., & Hothorn, L. A. (2015). nparcomp: an R software package for nonparametric multiple comparisons and simultaneous confidence intervals. Journal of Statistical Software 64 (2015), Nr. 9, 64(9), 1-17. http://www.jstatsoft.org/v64/i09/

Examples

Run this code

data(mtcars)
brunner_munzel(mpg ~ am, data = mtcars)

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