aylmer.test {aylmer} | R Documentation |
A generalization of Fisher's exact test; much of the documentation and
R code is inspired by fisher.test()
aylmer.test(x, alternative = "two.sided", simulate.p.value = FALSE, n = 1e5, B = 2000, burnin = 100, use.brob = FALSE) aylmer.function(x, func, simulate.p.value = FALSE, n = 1e5, B = 2000, burnin=100, use.brob=FALSE, DNAME=NULL) prob(x, give.log=TRUE, use.brob = FALSE)
x |
A matrix, possibly with some NA entries, coerced
to integer (an object of class board ) |
alternative |
Indicates the alternative hypothesis. If not a
function, it must be one of “two.sided”, “greater” or
“less”. You may specify just the initial letter. Only used
in cases with one degree of freedom. If a function, then control is
passed to aylmer.function() , for which aylmer.test()
is a wrapper |
simulate.p.value |
Boolean, with default FALSE meaning to
return the results of an exact (combinatorial) test, and TRUE
meaning to compute p-values by Monte Carlo simulation |
n |
Integer specifying the maximum number of boards to list if
simulate.p.value is FALSE ; passed to allprobs()
and thence no.of.boards() . This argument has a finite
default value to prevent infinite looping |
B |
Integer specifying the number of replicates used in the Monte Carlo version of the test |
burnin |
Integer specifying the length of burn in. See details section |
use.brob |
Boolean, with default FALSE meaning to use
IEEE
arithmetic and TRUE meaning to use Brobdingnagian arithmetic |
give.log |
In function prob() , Boolean with default TRUE
meaning to return the logarithm of the answer and FALSE
meaning to return the value |
func |
In function aylmer.function() , the test function
used. The p-value returned is the probability that a random
permissible board has a test function less than that of argument
x |
DNAME |
In function aylmer.function() , the name of the
dataset to be specified; default value of NULL means to use
standard construction |
If simulate.p.value
is TRUE
, a vector of random
probabilities is used instead of the full enumeration. A total of
B+burnin
boards are generated of which the first burnin
are discarded.
An object of class “htest
”
Function prob()
gives a number that is proportional to the
probability of observing a board.
The probability of observing a board B with no NA
s,
conditional on its being permissible is, obvious notation,
ommitted; see pdf
The numerator is the same for any permissable board so is not calculated.
If simulate.p.value
is TRUE
, the default value for
B
of 2000 is likely to be low, especially for large tables, or
tables with large entries. Bear in mind that the Markov chain has high
sequential correlation.
If simulate.p.value
is FALSE
, enumerative techniques are
used. In this case, the default value for n
(10^5) is also
likely to be low: a p-value of 1 is returned because the first few
boards all have a probability much much smaller than that of the data.
Robin K. S. Hankin (R); Luke J. West (C++); an anonymous
JSS referee who suggested the approach used in
aylmer.function()
aylmer.function()
)
data(iqd) aylmer.test(iqd) aylmer.test(iqd) ## Not run: aylmer.test(iqd,simulate.p.value=TRUE) data(frogs) prob(frogs) prob(frogs,use.brob=TRUE)