bwsManyOneTest {PMCMRplus}

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 NAs. 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 \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.

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.

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).

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.

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)