PMCMRplus (version 1.9.3)

welchManyOneTTest: Welchs's Many-To-One Comparison Test

Description

Performs Welchs's t-test for multiple comparisons with one control.

Usage

welchManyOneTTest(x, ...)
# S3 method for default
welchManyOneTTest(
  x,
  g,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = p.adjust.methods,
  ...
)
# S3 method for formula
welchManyOneTTest(
  formula,
  data,
  subset,
  na.action,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = p.adjust.methods,
  ...
)
# S3 method for aov
welchManyOneTTest(
  x,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = p.adjust.methods,
  ...
)

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 "x". Ignored with a warning if "x" is a list.

alternative

the alternative hypothesis. Defaults to two.sided.

p.adjust.method

method for adjusting p values (see p.adjust).

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 many-to-one comparisons in an one-factorial layout with normally distributed residuals and unequal variances Welch's t-test can be used. A total of \(m = k-1\) hypotheses can be tested. The null hypothesis H\(_{i}: \mu_0(x) = \mu_i(x)\) is tested in the two-tailed test against the alternative A\(_{i}: \mu_0(x) \ne \mu_i(x), ~~ 1 \le i \le k-1\).

This function is basically a wrapper function for t.test(..., var.equal = FALSE). The p-values for the test are calculated from the t distribution and can be adusted with any method that is implemented in p.adjust.methods.

References

Welch, B. L. (1947) The generalization of "Student's" problem when several different population variances are involved, Biometrika 34, 28--35.

Welch, B. L. (1951) On the comparison of several mean values: An alternative approach, Biometrika 38, 330--336.

See Also

pairwise.t.test, t.test, p.adjust, tamhaneDunnettTest

Examples

# NOT RUN {
set.seed(245)
mn <- rep(c(1, 2^(1:4)), each=5)
sd <- rep(1:5, each=5)
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)
anova(fit)
summary(welchManyOneTTest(fit, alternative = "greater", p.adjust="holm"))

# }