PMCMRplus (version 1.3.0)

scheffeTest: Scheffe's Test

Description

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

Usage

scheffeTest(x, ...)
# S3 method for default
scheffeTest(x, g, ...)
# S3 method for formula
scheffeTest(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").

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 Scheffe's test can be performed. A total of \(m = k(k-1)/2\) hypotheses can be tested. The null hypothesis H\(_{ij}: \mu_i(x) = \mu_j(x)\) is tested in the two-tailed test against the alternative A\(_{ij}: \mu_i(x) \ne \mu_j(x), ~~ i \ne j\).

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

References

Bortz, J. (1993) Statistik f<U+00FC>r Sozialwissenschaftler. 4. Aufl., Berlin: Springer.

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

Scheffe, H. (1953) A Method for Judging all Contrasts in the Analysis of Variance, Biometrika 40, 87--110.

See Also

FDist, tukeyTest

Examples

# 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(scheffeTest(x, g))
# }