\name{g.test}
\alias{g.test}
\title{Log-Likelihood Ratio Test for Count Data}
\usage{
g.test(x, y = NULL, correct = NONE, p = rep(1/length(x), length(x)),
           simulate.p.value = FALSE, B = 2000)
}
\arguments{
    \item{x}{a vector or matrix.}
    \item{y}{a vector; ignored if \code{x} is a matrix.}
    \item{correct}{a logical indicating whether to apply continuity
    	correction when computing the test statistic.}
    \item{p}{a vector of probabilities of the same length of \code{x}.}
    \item{simulate.p.value}{a logical indicating whether to compute
	p-values by Monte Carlo simulation.}
    \item{B}{an integer specifying the number of replicates used in the
	Monte Carlo simulation.}
}
\description{
    \code{g.test} performs log-likelihood ratio tests on contingency tables.
}
\details{
    If \code{x} is a matrix with one row or column, or if \code{x} is a
    vector and \code{y} is not given, \code{x} is treated as a
    one-dimensional contingency table.  In this case, the hypothesis
    tested is whether the population probabilities equal those in
    \code{p}, or are all equal if \code{p} is not given. 

    If \code{x} is a matrix with at least two rows and columns, it is
    taken as a two-dimensional contingency table, and hence its entries
    should be nonnegative integers.  Otherwise, \code{x} and \code{y}
    must be vectors or factors of the same length; incomplete cases are
    removed, the objects are coerced into factor objects, and the
    contingency table is computed from these.  Then, log-likelihood
    ratio test of the null that the joint distribution of the cell
    counts in a 2-dimensional contingency table is the product of the row
    and column marginals is performed.

    Continuity correction is only used in the df=1 case if
    \code{correct} is \code{yates}.  Williams' approximation to
    chi-squared distribution is calculated is \code{correct} is
    \code{williams}
}
\value{
    A list with class \code{"htest"} containing the following
    components:
    \item{statistic}{the value the G test statistic.}
    \item{parameter}{the degrees of freedom of the approximate
	chi-squared distribution of the test statistic.
    \item{p.value}{the p-value for the test.}
    \item{method}{a character string indicating the type of test
	performed, and continuity correction, or Williams' chi-squared
	approximation was used.}
    \item{data.name}{a character string giving the name(s) of the data.}
    \item{observed}{the observed counts.}
    \item{expected}{the expected counts under the null hypothesis.}
}
\references{
  Robert R. Sokal & F. James Rohlf (1995),
  \emph{Biometry}, 3rd ed.
  New York: W. H. Freeman & Company.
  Pages 690--760.

  Jerrold H. Zar (1999),
  \emph{Biostatistical Analysis}, 4th ed.
  New Jersey: Prentice-Hall Inc.
  Pages 473--514.
}
\examples{
## Goodness of fit example (Sokal & Rohlf Box 17.1 Part 1 pp 699)
pheno <- c(63,31,28,12,39,16,40,12)
mendel <- c(18,6,6,2,12,4,12,4)
g.test(pheno,p=(mendel/sum(mendel)),correct="williams")$p.value
                                     ## p = 0.2696 
## 2x2 Test of independence example (Sokal & Rohlf Box 17.6 pp 731)
x <- matrix(c(12, 16, 22, 50), nc = 2)
g.test(x)$statistic                  ## G = 1.332489 
g.test(x,correct="williams")$p.value ## p = 0.2537082 

## Effect of simulating p-values
x <- matrix(c(12, 5, 7, 7), nc = 2)
g.test(x)$p.value                    ## p = 0.2408640 
g.test(x,simulate.p.value=TRUE, B = 10000)$p.value
                                     ## around 0.13!
}
\keyword{htest}