welchManyOneTTest() R function from [PMCMRplus]

Welchs's Many-To-One Comparison Test

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


welchManyOneTTest(x, ...)

## Default S3 method:
welchManyOneTTest(
  x,
  g,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = p.adjust.methods,
  ...
)

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

## S3 method for class '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").

Returns

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.

Examples


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"))

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.

welchManyOneTTest function