View source: R/hayterStoneTest.R
hayterStoneTest | R Documentation |
Performs the non-parametric Hayter-Stone procedure to test against an monotonically increasing alternative.
hayterStoneTest(x, ...)
## Default S3 method:
hayterStoneTest(
x,
g,
alternative = c("greater", "less"),
method = c("look-up", "boot", "asympt"),
nperm = 10000,
...
)
## S3 method for class 'formula'
hayterStoneTest(
formula,
data,
subset,
na.action,
alternative = c("greater", "less"),
method = c("look-up", "boot", "asympt"),
nperm = 10000,
...
)
x |
a numeric vector of data values, or a list of numeric data vectors. |
... |
further arguments to be passed to or from methods. |
g |
a vector or factor object giving the group for the
corresponding elements of |
alternative |
the alternative hypothesis. Defaults to |
method |
a character string specifying the test statistic to use.
Defaults to |
nperm |
number of permutations for the asymptotic permutation test.
Defaults to |
formula |
a formula of the form |
data |
an optional matrix or data frame (or similar: see
|
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 |
Let X
be an identically and idepentendly distributed variable
that was n
times observed at k
increasing treatment levels.
Hayter and Stone (1991) proposed a non-parametric procedure
to test the null hypothesis, H: \theta_i = \theta_j ~~ (i < j \le k)
against a simple order alternative, A: \theta_i < \theta_j
, with at least
one inequality being strict.
The statistic for a global test is calculated as,
h = \max_{1 \le i < j \le k} \frac{2 \sqrt{6} \left(U_{ij} - n_i n_j / 2 \right)}
{\sqrt{n_i n_j \left(n_i + n_j + 1 \right)}},
with the Mann-Whittney counts:
U_{ij} = \sum_{a=1}^{n_i} \sum_{b=1}^{n_j} I\left\{x_{ia} < x_{ja}\right\}.
Under the large sample approximation, the test statistic h
is distributed
as h_{k,\alpha,v}
. Thus, the null hypothesis is rejected, if h > h_{k,\alpha,v}
, with v = \infty
degree of freedom.
If method = "look-up"
the function will 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 = \infty
).
If method = "boot"
an asymptotic permutation test
is conducted and a p
-value is returned.
If method = "asympt"
is selected the asymptotic
p
-value is estimated as implemented in the
function pHayStonLSA
of the package NSM3.
Either a list of class htest
or 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.
If method = "asympt"
is selected, this function calls
an internal probability function pHS
. The GPL-2 code for
this function was taken from pHayStonLSA
of the
the package NSM3:
Grant Schneider, Eric Chicken and Rachel Becvarik (2020) NSM3: Functions and Datasets to Accompany Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods, Third Edition. R package version 1.15. https://CRAN.R-project.org/package=NSM3
Hayter, A. J.(1990) A One-Sided Studentised Range Test for Testing Against a Simple Ordered Alternative, J Amer Stat Assoc 85, 778–785.
Hayter, A.J., Stone, G. (1991) Distribution free multiple comparisons for monotonically ordered treatment effects. Austral J Statist 33, 335–346.
osrtTest
, hsAllPairsTest
,
sample
, pHayStonLSA
## Example from Shirley (1977)
## Reaction times of mice to stimuli to their tails.
x <- c(2.4, 3, 3, 2.2, 2.2, 2.2, 2.2, 2.8, 2, 3,
2.8, 2.2, 3.8, 9.4, 8.4, 3, 3.2, 4.4, 3.2, 7.4, 9.8, 3.2, 5.8,
7.8, 2.6, 2.2, 6.2, 9.4, 7.8, 3.4, 7, 9.8, 9.4, 8.8, 8.8, 3.4,
9, 8.4, 2.4, 7.8)
g <- gl(4, 10)
## Shirley's test
## one-sided test using look-up table
shirleyWilliamsTest(x ~ g, alternative = "greater")
## Chacko's global hypothesis test for 'greater'
chackoTest(x , g)
## post-hoc test, default is standard normal distribution (NPT'-test)
summary(chaAllPairsNashimotoTest(x, g, p.adjust.method = "none"))
## same but h-distribution (NPY'-test)
chaAllPairsNashimotoTest(x, g, dist = "h")
## NPM-test
NPMTest(x, g)
## Hayter-Stone test
hayterStoneTest(x, g)
## all-pairs comparisons
hsAllPairsTest(x, g)
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