Performs Welchs's t-test for multiple comparisons with one control.
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,
...
)
A list with class "PMCMR" containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
lower-triangle matrix of the estimated quantiles of the pairwise test statistics.
lower-triangle matrix of the p-values for the pairwise tests.
a character string describing the alternative hypothesis.
a character string describing the method for p-value adjustment.
a data frame of the input data.
a string that denotes the test distribution.
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.
a vector or factor object giving the group for the
corresponding elements of "x".
Ignored with a warning if "x" is a list.
the alternative hypothesis.
Defaults to two.sided.
method for adjusting p values
(see p.adjust).
a formula of the form response ~ group where
response gives the data values and group a vector or
factor of the corresponding groups.
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).
an optional vector specifying a subset of observations to be used.
a function which indicates what should happen when
the data contain NAs. Defaults to getOption("na.action").
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.
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.
pairwise.t.test, t.test,
p.adjust, tamhaneDunnettTest
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"))
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