% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/UM.eqtest.R
\name{UM.eqtest}
\alias{UM.eqtest}
\title{Equality tests for two multinomial samples}
\usage{
UM.eqtest(N1, N2, p0, nreps, verbose = TRUE)
}
\arguments{
\item{N1}{Size of sample 1.}

\item{N2}{Size of sample 2.}

\item{p0}{Common probability vector from which to draw the multinomial samples.  Can also be a matrix, in which case each simulation randomly draws with replacement from the rows of p0.}

\item{nreps}{Number of replications of the simulation.}

\item{verbose}{Logical.  If \code{TRUE} prints message every \code{5000} replications.}
}
\value{
An \code{nreps x 2} matrix with the simulated chi-squared and LR values.
}
\description{
Generate multinomial samples from a common probability vector and calculate the Chi-square and Likelihood Ratio test statistics.
}
\details{
The chi-squared and likelihood ratio test statistics are calculated from multinomial samples \eqn{(Y_1^1, Y_2^1), \ldots, (Y_1^M, Y_2^M)}{(Y_11, Y_21),\ldots,(Y_1M, Y_2M)}, where
\deqn{
  Y_k^m \stackrel{\textrm{ind}}{\sim} \textrm{Multinomial}(N_k, p_0^m),
}{
  Y_km ~ind Multinomial(N_k, p_m),
}
where \eqn{p_0^m}{p_m} is the \eqn{m}th row of \code{p0}.
}
\examples{
# bootstrapped p-value calculation against equal genotype proportions
# in lakes Michipicoten and Simcoe

# contingency table
popId <- c("Michipicoten", "Simcoe")
ctab <- UM.suff(fish215[fish215$Lake \%in\% popId,])$tab
ctab

# MLE of probability vector
p.MLE <- colSums(ctab)/sum(ctab)
# sample sizes
N1 <- sum(ctab[1,]) # Michipicoten
N2 <- sum(ctab[2,]) # Simcoe

# bootstrapped test statistics (chi^2 and LRT)
T.boot <- UM.eqtest(N1 = N1, N2 = N2, p0 = p.MLE, nreps = 1e3)

# observed test statistics
T.obs <- c(chi2 = chi2.stat(ctab), LRT = LRT.stat(ctab))
# p-values
rowMeans(t(T.boot) > T.obs)
}