tests | R Documentation |
Tests different nulls against a free alternative
equalp.test(H, ...) knownp.test(H, p, ...) samep.test(H, i, give=FALSE, ...) specificp.test(H, i, specificp=1/size(H), alternative = c("two.sided","less","greater"), ...) specificp.ne.test(H, i, specificp=1/size(H), ...) specificp.gt.test(H, i, specificp=1/size(H), delta=1e-5, ...) specificp.lt.test(H, i, specificp=1/size(H), ...) ## S3 method for class 'hyper2test' print(x, ...)
H |
A likelihood function, an object of class |
p |
In |
... |
Further arguments passed by |
i |
A character vector of names |
specificp |
Strength, real number between 0 and 1 |
alternative |
a character string specifying the alternative
hypothesis, must be one of |
give |
Boolean, with |
x |
Object of class |
delta |
Small value for numerical stability |
Given a hyper2
likelihood function, there are a number of
natural questions to ask about the strengths of the players; see
Hankin 2010 (JSS) for examples. An extended discussion is presented
in vignette “hyper2
” and the functions documented here
cover most of the tests used in the vignette.
The tests return an object with class hyper2test
, which has its
own print method.
Function equalp.test(H,p)
tests the null that all
strengths are equal to vector p
. If p
is missing, it
tests \mjeqnH_0\colon p_1=p_2=\cdots=p_n=\frac1nH0:
p1=p2=...=pn=1/n, for example equalp.test(icons)
Function knownp.test()
tests the null that the strengths
are equal to the elements of named vector p
; it is a
generalization of equalp.test()
. Example:
knownp.test(icons,zipf(6))
.
Function specificp.test(H,i,p)
tests
\mjeqnH_0\colon p_i=pH0: p_i=p, for example
specificp.test(icons,"NB",0.1)
Function samep.test()
tests \mjeqnH_0\colon
p_i_1=p_i_2=\cdots=p_i_komitted, for example
samep.test(icons,c("NB","L"))
tests that NB
has the same
strength as L
.
Functions specificp.ne.test(H,i,p)
,
specificp.gt.test(H,i,p)
, and specificp.lt.test(H,i,p)
are low-level helper functions that implement one- or two-sided versions
of specificp.test()
via the alternative
argument,
following t.test()
The test functions return a list with class "hyper2test"
containing the following components:
statistic |
the difference in support between the null and alternative |
p.value |
the (asymptotic) p-value for the test, based on Wilks's theorem |
estimate |
the maximum likelihood estimate for p |
method |
a character string indicating what type of test was performed |
data.name |
a character string giving the name(s) of the data. |
Function specificp.gt.test()
includes quite a bit of messing
about to ensure that frequently-used idiom like
specificp.gt.test(icons,"NB",0)
works as expected, testing a null
of p_NB=0
. In the case of testing a strength's being zero, the
support function is often quite badly-behaved near the constraint [think
tossing a coin with probability p twice, observing one head and
one tail, and testing p=0; at the constraint, the likelihood is
zero, the support negative infinity, and the gradient of the support is
infinite]. Numerically, the code tests p_NB=delta
. Note that
similar machinations are not required in specificp.lt.test()
because a null of p_NB=1
is unrealistic.
Function samep.test()
does not have access to gradient
information so it is slow, inaccurate, and may fail completely for
high-dimensional datasets. If any(i==n)
, this constrains the
fillup value; this makes no difference mathematically but the function
idiom is involved.
maxp
equalp.test(chess) # samep.test(icons,c("NB","L")) # knownp.test(icons,zipf(icons))
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