PMCMRplus (version 1.9.3)

kwManyOneDunnTest: Dunn's Many-to-One Rank Comparison Test

Description

Performs Dunn's non-parametric many-to-one comparison test for Kruskal-type ranked data.

Usage

kwManyOneDunnTest(x, ...)
# S3 method for default
kwManyOneDunnTest(
  x,
  g,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = c("single-step", p.adjust.methods),
  ...
)
# S3 method for formula
kwManyOneDunnTest(
  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").

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.

Details

For many-to-one comparisons (pairwise comparisons with one control) in an one-factorial layout with non-normally distributed residuals Dunn'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\(_i: \theta_0 = \theta_i\) 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.

References

Dunn, O. J. (1964) Multiple comparisons using rank sums, Technometrics 6, 241--252.

Siegel, S., Castellan Jr., N. J. (1988) Nonparametric Statistics for The Behavioral Sciences. New York: McGraw-Hill.

See Also

pmvnorm, TDist, kruskalTest, kwManyOneConoverTest, kwManyOneNdwTest

Examples

# NOT RUN {
## 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)
# }