DescTools (version 0.99.37)

NemenyiTest: Nemenyi Test

Description

Performs Nemenyi's test of multiple comparisons.

Usage

NemenyiTest(x, ...)
# S3 method for default
NemenyiTest(x, g, dist = c("tukey", "chisq"), out.list = TRUE, ...)
# S3 method for formula
NemenyiTest(formula, data, subset, na.action, ...)

Arguments

x

a numeric vector of data values, or a list of numeric data vectors.

g

a vector or factor object giving the group for the corresponding elements of x. Ignored if x is a list.

dist

the distribution used for the test. Can be tukey (default) or chisq.

out.list

logical, defining if the output should be organized in listform.

formula

a formula of the form lhs ~ rhs where lhs gives the data values and rhs 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").

…

further arguments to be passed to or from methods.

Value

A list of class htest, containing the following components:

statistic

Nemenyi test

p.value

the p-value for the test

null.value

is the value of the median specified by the null hypothesis. This equals the input argument mu.

alternative

a character string describing the alternative hypothesis.

method

the type of test applied

data.name

a character string giving the names of the data.

Details

Nemenyi proposed a test based on rank sums and the application of the family-wise error method to control Type I error inflation, if multiple comparisons are done. The Tukey and Kramer approach uses mean rank sums and can be employed for equally as well as unequally sized samples without ties.

References

Nemenyi, P. B. (1963) Distribution-Free Multiple Comparisons New York, State University of New York, Downstate Medical Center

Hollander, M., Wolfe, D.A. (1999) Nonparametric Statistical Methods New York, Wiley, pp. 787

Friedman, M. (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance Journal of the American Statistical Association, 32:675-701

Friedman, M. (1940) A comparison of alternative tests of significance for the problem of m rankings Annals of Mathematical Statistics, 11:86-92

See Also

DunnTest, ConoverTest

Examples

# NOT RUN {
## Hollander & Wolfe (1973), 116.
## Mucociliary efficiency from the rate of removal of dust in normal
##  subjects, subjects with obstructive airway disease, and subjects
##  with asbestosis.
x <- c(2.9, 3.0, 2.5, 2.6, 3.2) # normal subjects
y <- c(3.8, 2.7, 4.0, 2.4)      # with obstructive airway disease
z <- c(2.8, 3.4, 3.7, 2.2, 2.0) # with asbestosis

NemenyiTest(list(x, y, z))

## Equivalently,
x <- c(x, y, z)
g <- factor(rep(1:3, c(5, 4, 5)),
            labels = c("Normal subjects",
                       "Subjects with obstructive airway disease",
                       "Subjects with asbestosis"))

NemenyiTest(x, g)

## Formula interface.
boxplot(Ozone ~ Month, data = airquality)
NemenyiTest(Ozone ~ Month, data = airquality)

# Hedderich & Sachs, 2012, p. 555
d.frm <- data.frame(x=c(28,30,33,35,38,41, 36,39,40,43,45,50, 44,45,47,49,53,54),
                    g=c(rep(LETTERS[1:3], each=6)), stringsAsFactors=TRUE)

NemenyiTest(x~g, d.frm)
# }