R: BWS Many-To-One Comparison Test

bwsManyOneTest {PMCMRplus} | R Documentation

## BWS Many-To-One Comparison Test

### Description

Performs Baumgartner-Weiß-Schindler many-to-one comparison test.

### Usage

    bwsManyOneTest(x, ...)

    ## Default S3 method:
    bwsManyOneTest(
      x,
      g,
      alternative = c("two.sided", "greater", "less"),
      method = c("BWS", "Murakami", "Neuhauser"),
      p.adjust.method = p.adjust.methods,
      ...
    )

    ## S3 method for class 'formula'
    bwsManyOneTest(
      formula,
      data,
      subset,
      na.action,
      alternative = c("two.sided", "greater", "less"),
      method = c("BWS", "Murakami", "Neuhauser"),
      p.adjust.method = p.adjust.methods,
      ...
    )

### Arguments

`x` | a numeric vector of data values, or a list of numeric data vectors.
`...` | further arguments to be passed to or from methods.
`g` | a vector or factor object giving the group for the corresponding elements of `"x"`. Ignored with a warning if `"x"` is a list.
`alternative` | the alternative hypothesis. Defaults to `two.sided`.
`method` | a character string specifying the test statistic to use. Defaults to `BWS`.
`p.adjust.method` | method for adjusting p values (see `p.adjust`).
`formula` | a formula of the form `response ~ group` where `response` gives the data values and `group` a vector or factor of the corresponding groups.
`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 `NA`s. Defaults to `getOption("na.action")`.

### Details

For many-to-one comparisons (pairwise comparisons with one control) in an one-factorial layout with non-normally distributed residuals Baumgartner-Weiß-Schindler's non-parametric test can be performed. Let there be k groups including the control, then the number of treatment levels is m = k - 1. Then m pairwise comparisons can be performed between the i-th treatment level and the control. H_i: F_0 = F_i is tested in the two-tailed case against A_i: F_0 \ne F_i, ~~ (1 ≤ i ≤ m).

This function is a wrapper function that sequentially calls `bws_stat` and `bws_cdf` for each pair. For the default test method (`"BWS"`) the original Baumgartner-Weiß-Schindler test statistic B and its corresponding Pr(>|B|) is calculated. For `method == "BWS"` only a two-sided test is possible.

For `method == "Murakami"` the modified BWS statistic denoted B* and its corresponding Pr(>|B*|) is computed by sequentially calling `murakami_stat` and `murakami_cdf`. For `method == "Murakami"` only a two-sided test is possible.

If `alternative == "greater"` then the alternative, if one population is stochastically larger than the other is tested: H_i: F_0 = F_i against A_i: F_0 ≥ F_i, ~~ (1 ≤ i ≤ m). The modified test-statistic B* according to Neuhäuser (2001) and its corresponding Pr(>B*) or Pr(<B*) is computed by sequentally calling `murakami_stat` and `murakami_cdf` with `flavor = 2`.

The p-values can be adjusted to account for Type I error inflation using any method as implemented in `p.adjust`.

### Value

A list with class `"PMCMR"` containing the following components:

method

  a character string indicating what type of test was performed.

data.name

  a character string giving the name(s) of the data.

statistic

  lower-triangle matrix of the estimated quantiles of the pairwise test statistics.

p.value

  lower-triangle matrix of the p-values for the pairwise tests.

alternative

  a character string describing the alternative hypothesis.

p.adjust.method

  a character string describing the method for p-value adjustment.

model

  a data frame of the input data.

dist

  a string that denotes the test distribution.

### References

Baumgartner, W., Weiss, P., Schindler, H. (1998) A nonparametric test for the general two-sample problem, Biometrics 54, 1129–1135.

Murakami, H. (2006) K-sample rank test based on modified Baumgartner statistic and its power comparison, J. Jpn. Comp. Statist. 19, 1–13.

Neuhäuser, M. (2001) One-side two-sample and trend tests based on a modified Baumgartner-Weiss-Schindler statistic. Journal of Nonparametric Statistics 13, 729–739.

### See Also

`murakami_stat`, `murakami_cdf`, `bws_stat`, `bws_cdf`.

### Examples

    out <- bwsManyOneTest(weight ~ group, PlantGrowth, p.adjust="holm")
    summary(out)

    ## A two-sample test
    set.seed(1245)
    x <- c(rnorm(20), rnorm(20,0.3))
    g <- gl(2, 20)
    summary(bwsManyOneTest(x ~ g, alternative = "less", p.adjust="none"))
    summary(bwsManyOneTest(x ~ g, alternative = "greater", p.adjust="none"))

    ## Not run:
    ## Check with the implementation in package BWStest
    BWStest::bws_test(x=x[g==1], y=x[g==2], alternative = "less")
    BWStest::bws_test(x=x[g==1], y=x[g==2], alternative = "greater")

    ## End(Not run)

[Package PMCMRplus version 1.6.0 Index]