snkTest() R function from [PMCMRplus]

Student-Newman-Keuls Test

Performs Student-Newman-Keuls all-pairs comparisons test for normally distributed data with equal group variances.


snkTest(x, ...)

## Default S3 method:
snkTest(x, g, ...)

## S3 method for class 'formula'
snkTest(formula, data, subset, na.action, ...)

## S3 method for class 'aov'
snkTest(x, ...)

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.
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 all-pairs comparisons in an one-factorial layout with normally distributed residuals and equal variances Student-Newman-Keuls 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 Tukey-distribution.

Examples


fit <- aov(weight ~ feed, chickwts)
shapiro.test(residuals(fit))
bartlett.test(weight ~ feed, chickwts)
anova(fit)

## also works with fitted objects of class aov
res <- snkTest(fit)
summary(res)
summaryGroup(res)

References

Keuls, M. (1952) The use of the "studentized range" in connection with an analysis of variance, Euphytica 1 , 112--122.

Newman, D. (1939) The distribution of range in samples from a normal population, expressed in terms of an independent estimate of standard deviation, Biometrika 31 , 20--30.

Student (1927) Errors of routine analysis, Biometrika 19 , 151--164.

snkTest function