adKSampleTest: Anderson-Darling k-Sample Test

In PMCMRplus: Calculate Pairwise Multiple Comparisons of Mean Rank Sums Extended

Anderson-Darling k-Sample Test

Description

Performs Anderson-Darling k-sample test.

Usage

adKSampleTest(x, ...)

## Default S3 method:
adKSampleTest(x, g, ...)

## S3 method for class 'formula'
adKSampleTest(formula, data, subset, na.action, ...)

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.
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

The null hypothesis, H_0: F_1 = F_2 = \ldots = F_k is tested against the alternative, H_\mathrm{A}: F_i \ne F_j ~~(i \ne j), with at least one unequality beeing strict.

This function only evaluates version 1 of the k-sample Anderson-Darling test (i.e. Eq. 6) of Scholz and Stephens (1987). The p-values are estimated with the extended empirical function as implemented in ad.pval of the package kSamples.

Value

A list with class "htest" 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

the estimated quantile of the test statistic.

p.value

the p-value for the test.

parameter

the parameters of the test statistic, if any.

alternative

a character string describing the alternative hypothesis.

estimates

the estimates, if any.

null.value

the estimate under the null hypothesis, if any.

References

Scholz, F.W., Stephens, M.A. (1987) K-Sample Anderson-Darling Tests. Journal of the American Statistical Association 82, 918–924.

See Also

adAllPairsTest, adManyOneTest, ad.pval.

Examples

## 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
g <- factor(x = c(rep(1, length(x)),
                   rep(2, length(y)),
                   rep(3, length(z))),
             labels = c("ns", "oad", "a"))
dat <- data.frame(
   g = g,
   x = c(x, y, z))

## AD-Test
adKSampleTest(x ~ g, data = dat)

## BWS-Test
bwsKSampleTest(x ~ g, data = dat)

## Kruskal-Test
## Using incomplete beta approximation
kruskalTest(x ~ g, dat, dist="KruskalWallis")
## Using chisquare distribution
kruskalTest(x ~ g, dat, dist="Chisquare")

## Not run: 
## Check with kruskal.test from R stats
kruskal.test(x ~ g, dat)

## End(Not run)
## Using Conover's F
kruskalTest(x ~ g, dat, dist="FDist")

## Not run: 
## Check with aov on ranks
anova(aov(rank(x) ~ g, dat))
## Check with oneway.test
oneway.test(rank(x) ~ g, dat, var.equal = TRUE)

## End(Not run)

PMCMRplus documentation built on Nov. 27, 2023, 1:08 a.m.