gamesHowellTest {PMCMRplus} | R Documentation |
Games-Howell Test
Description
Performs Games-Howell all-pairs comparison test for normally distributed data with unequal group variances.
Usage
gamesHowellTest(x, ...)
## Default S3 method:
gamesHowellTest(x, g, ...)
## S3 method for class 'formula'
gamesHowellTest(formula, data, subset, na.action, ...)
## S3 method for class 'aov'
gamesHowellTest(x, ...)
Arguments
x |
a numeric vector of data values, a list of numeric data vectors or a fitted model object, usually an aov fit. |
... |
further arguments to be passed to or from methods. |
g |
a vector or factor object giving the group for the
corresponding elements of |
formula |
a formula of the form |
data |
an optional matrix or data frame (or similar: see
|
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 |
Details
For all-pairs comparisons in an one-factorial layout
with normally distributed residuals but unequal between-groups variances
the Games-Howell Test can be performed. Let denote a continuous random variable
with the
-the realization (
)
in the
-th group (
). Furthermore, the total
sample size is
. A total of
hypotheses can be tested: The null hypothesis is
H
is tested against the alternative
A
(two-tailed). Games-Howell Test all-pairs
test statistics are given by
with the variance of the
-th group.
The null hypothesis is rejected (two-tailed) if
with Welch's approximate solution for calculating the degree of freedom.
The -values are computed from the
Tukey
distribution.
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.
See Also
Examples
fit <- aov(weight ~ feed, chickwts)
shapiro.test(residuals(fit))
bartlett.test(weight ~ feed, chickwts) # var1 = varN
anova(fit)
## also works with fitted objects of class aov
res <- gamesHowellTest(fit)
summary(res)
summaryGroup(res)