bwsManyOneTest() R function from [PMCMRplus]

BWS Many-To-One Comparison Test

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


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 NAs. Defaults to getOption("na.action").

Returns

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.

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 $_i: F_0 \ne F_i, ~~ (1 \le i \le m)$ .

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 $_i: F_0 \ge F_i, ~~ (1 \le i \le m)$ . 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.

Note

Factor labels for g must be assigned in such a way, that they can be increasingly ordered from zero-dose control to the highest dose level, e.g. integers {0, 1, 2, ..., k} or letters {a, b, c, ...}. Otherwise the function may not select the correct values for intended zero-dose control.

It is safer, to i) label the factor levels as given above, and to ii) sort the data according to increasing dose-levels prior to call the function (see order, factor).

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)

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. J Nonparametric Stat 13 , 729--739.

bwsManyOneTest function