\name{phi2tetra}
\alias{phi2tetra}
\alias{phi2poly}
\title{ Convert a phi coefficient to a tetrachoric correlation }
\description{Given a phi coefficient (a Pearson r calculated on two dichotomous variables), and the marginal frequencies (in percentages), what is the corresponding estimate of the tetrachoric correlation?

Given a two x two table of counts \cr
\tabular{lll}{
\tab a \tab b \cr
\tab c \tab d  \cr
}
The phi coefficient is (a - (a+b)*(a+c))/sqrt((a+b)(a+c)(b+d)(c+c)).

This function reproduces the cell entries for specified marginals and then calls the tetrachoric function. (Which was originally based upon John Fox's polychor function.)
The phi2poly name will become deprecated in the future. 
}

\usage{
phi2tetra(ph,m,n=NULL,correct=TRUE)
phi2poly(ph,cp,cc,n=NULL,correct=TRUE) #deprecated
}
%- maybe also 'usage' for other objects documented here.
\arguments{
  \item{ph}{phi }
  \item{m}{a vector of the selection ratio and probability of criterion.  In the case where ph is a matrix, m is a vector of the frequencies of the selected cases}
  \item{correct}{When finding tetrachoric correlations, should we correct for continuity for small marginals.  See \code{\link{tetrachoric}} for a discussion.}
  \item{n}{If the marginals are given as frequencies, what was the total number of cases?}
  \item{cp}{ probability of the predictor -- the so called selection ratio }
  \item{cc}{probability of the criterion -- the so called success rate. }
}
\details{used to require the mvtnorm package but this has been replaced with mnormt
}
\value{a tetrachoric correlation
}
\author{ William Revelle}
\seealso{ \code{\link{tetrachoric}}, \code{\link{Yule2phi.matrix}}, \code{\link{phi2poly.matrix}} }
\examples{
 phi2tetra(.3,c(.5,.5))
#phi2poly(.3,.3,.7)
}
\keyword{ models }% at least one, from doc/KEYWORDS
\keyword{ models }% __ONLY ONE__ keyword per line