aylmer.test: A Generalization of Fisher's exact test

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

A generalization of Fisher's exact test; much of the documentation and R code is inspired by fisher.test()

Usage

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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)

Arguments

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

Details

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.

Value

An object of class “htest

Note

Function prob() gives a number that is proportional to the probability of observing a board.

The probability of observing a board B with no NAs, 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.

Author(s)

Robin K. S. Hankin (R); Luke J. West (C++); an anonymous JSS referee who suggested the approach used in aylmer.function()

References

See Also

fisher.test, randomprobs

Examples

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data(iqd)

aylmer.test(iqd)

## Not run: aylmer.test(iqd,simulate.p.value=TRUE)

data(frogs)
prob(frogs)
prob(frogs,use.brob=TRUE)

aylmer documentation built on May 29, 2017, 1:12 p.m.