Performs Hayter's one-sided studentized range test against an ordered alternative for normal data with equal variances.
osrtTest(x, ...)# S3 method for default
osrtTest(x, g, alternative = c("greater", "less"), ...)
# S3 method for formula
osrtTest(
formula,
data,
subset,
na.action,
alternative = c("greater", "less"),
...
)
# S3 method for aov
osrtTest(x, alternative = c("greater", "less"), ...)
a numeric vector of data values, or a list of numeric data vectors.
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 greater.
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").
A list with class "osrt" that contains the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
the estimated statistic(s)
critical values for \(\alpha = 0.05\).
a character string describing the alternative hypothesis.
the parameter(s) of the test distribution.
a string that denotes the test distribution.
There are print and summary methods available.
Hayter's one-sided studentized range test (OSRT) can be used for testing several treatment levels with a zero control in a balanced one-factorial design with normally distributed variables that have a common variance. The null hypothesis, H: \(\mu_i = \mu_j ~~ (i < j)\) is tested against a simple order alternative, A: \(\mu_i < \mu_j\), with at least one inequality being strict.
The test statistic is calculated as, $$ \hat{h} = \max_{1 \le i < j \le k} \frac{ \left(\bar{x}_j - \bar{x}_i \right)} {s_{\mathrm{in}} / \sqrt{n}}, $$
with \(k\) the number of groups, \(n = n_1, n_2, \ldots, n_k\) and \(s_{\mathrm{in}}^2\) the within ANOVA variance. The null hypothesis is rejected, if \(\hat{h} > h_{k,\alpha,v}\), with \(v = N - k\) degree of freedom.
For the unbalanced case with moderate imbalance the test statistic is $$ \hat{h} = \max_{1 \le i < j \le k} \frac{ \left(\bar{x}_j - \bar{x}_i \right)} {s_{\mathrm{in}} \sqrt{1/n_j + 1/n_i}}, $$
The function does not return p-values. Instead the critical h-values
as given in the tables of Hayter (1990) for \(\alpha = 0.05\) (one-sided)
are looked up according to the number of groups (\(k\)) and
the degree of freedoms (\(v\)).
Non tabulated values are linearly interpolated with the function
approx.
Hayter, A. J.(1990) A One-Sided Studentised Range Test for Testing Against a Simple Ordered Alternative, Journal of the American Statistical Association 85, 778--785.
Hayter, A.J., Miwa, T., Liu, W. (2001) Efficient Directional Inference Methodologies for the Comparisons of Three Ordered Treatment Effects. J Japan Statist Soc 31, 153<U+2013>174.
link{hayterStoneTest} MTest
# NOT RUN {
##
md <- aov(weight ~ group, PlantGrowth)
anova(md)
osrtTest(md)
MTest(md)
# }
Run the code above in your browser using DataLab