tukeyTest: Tukey's Test

Description

Performs Tukey's all-pairs comparisons test for normally distributed data with equal group variances.

Usage

tukeyTest(x, ...)
# S3 method for default
tukeyTest(x, g, ...)
# S3 method for formula
tukeyTest(formula, data, subset, na.action, ...)

Arguments

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

…

further arguments to be passed to or from methods.

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").

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 all-pairs comparisons in an one-factorial layout with normally distributed residuals and equal variances Tukey's test can be performed. A total of $m = k (k - 1) / 2$ hypotheses can be tested. The null hypothesis H $_{i j} : μ_{i} (x) = μ_{j} (x)$ is tested in the two-tailed test against the alternative A $_{i j} : μ_{i} (x) \neq μ_{j} (x), i \neq j$ .

The p-values are computed from the Tukey-distribution.

References

L. Sachs (1997) Angewandte Statistik, New York: Springer.

J. Tukey (1949) Comparing Individual Means in the Analysis of Variance, Biometrics 5, 99--114.

Examples

Run this code

# NOT RUN {
set.seed(245)
mn <- rep(c(1, 2^(1:4)), each=5)
sd <- rep(1, 25)
x <- mn + rnorm(25, sd = sd)
g <- factor(rep(1:5, each=5))

fit <- aov(x ~ g)
shapiro.test(residuals(fit))
bartlett.test(x ~ g) # var1 = varN
anova(fit)
summary(tukeyTest(x, g))
# }

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