kwManyOneNdwTest {PMCMRplus}

Nemenyi-Damico-Wolfe Many-to-One Rank Comparison Test

Description

Performs Nemenyi-Damico-Wolfe non-parametric many-to-one comparison test for Kruskal-type ranked data.

Usage

kwManyOneNdwTest(x, ...)

## Default S3 method:
kwManyOneNdwTest(
  x,
  g,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = c("single-step", p.adjust.methods),
  ...
)

## S3 method for class 'formula'
kwManyOneNdwTest(
  formula,
  data,
  subset,
  na.action,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = c("single-step", 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.

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 the Nemenyi-Damico-Wolfe 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: \theta_0 = \theta_i is tested in the two-tailed case against A_i: \theta_0 \ne \theta_i, ~~ (1 \le i \le m).

If p.adjust.method == "single-step" is selected, the p-values will be computed from the multivariate normal distribution. Otherwise, the p-values are computed from the standard normal distribution using any of the p-adjustment methods as included 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

This function is essentially the same as kwManyOneDunnTest, but there is no tie correction included. Therefore, the implementation of Dunn's test is superior, when ties are present.

References

Damico, J. A., Wolfe, D. A. (1989) Extended tables of the exact distribution of a rank statistic for treatments versus control multiple comparisons in one-way layout designs, Communications in Statistics - Theory and Methods 18, 3327–3353.

Nemenyi, P. (1963) Distribution-free Multiple Comparisons, Ph.D. thesis, Princeton University.

See Also

pmvt, TDist, kruskalTest, kwManyOneDunnTest, kwManyOneConoverTest

Examples

## Data set PlantGrowth
## Global test
kruskalTest(weight ~ group, data = PlantGrowth)

## Conover's many-one comparison test
## single-step means p-value from multivariate t distribution
ans <- kwManyOneConoverTest(weight ~ group, data = PlantGrowth,
                             p.adjust.method = "single-step")
summary(ans)

## Conover's many-one comparison test
ans <- kwManyOneConoverTest(weight ~ group, data = PlantGrowth,
                             p.adjust.method = "holm")
summary(ans)

## Dunn's many-one comparison test
ans <- kwManyOneDunnTest(weight ~ group, data = PlantGrowth,
                             p.adjust.method = "holm")
summary(ans)

## Nemenyi's many-one comparison test
ans <- kwManyOneNdwTest(weight ~ group, data = PlantGrowth,
                        p.adjust.method = "holm")
summary(ans)

## Many one U test
ans <- manyOneUTest(weight ~ group, data = PlantGrowth,
                        p.adjust.method = "holm")
summary(ans)

## Chen Test
ans <- chenTest(weight ~ group, data = PlantGrowth,
                    p.adjust.method = "holm")
summary(ans)