% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/ttestBF.R
\name{ttestBF}
\alias{ttestBF}
\title{Function for Bayesian analysis of one- and two-sample designs}
\usage{
ttestBF(
  x = NULL,
  y = NULL,
  formula = NULL,
  mu = 0,
  nullInterval = NULL,
  paired = FALSE,
  data = NULL,
  rscale = "medium",
  posterior = FALSE,
  callback = function(...) as.integer(0),
  ...
)
}
\arguments{
\item{x}{a vector of observations for the first (or only) group}

\item{y}{a vector of observations for the second group (or condition, for
paired)}

\item{formula}{for independent-group designs, a (optional) formula
describing the model}

\item{mu}{for one-sample and paired designs, the null value of the mean (or
mean difference)}

\item{nullInterval}{optional vector of length 2 containing lower and upper bounds of an interval hypothesis to test, in standardized units}

\item{paired}{if \code{TRUE}, observations are paired}

\item{data}{for use with \code{formula}, a data frame containing all the
data}

\item{rscale}{prior scale.  A number of preset values can be given as
strings; see Details.}

\item{posterior}{if \code{TRUE}, return samples from the posterior instead
of Bayes factor}

\item{callback}{callback function for third-party interfaces}

\item{...}{further arguments to be passed to or from methods.}
}
\value{
If \code{posterior} is \code{FALSE}, an object of class
  \code{BFBayesFactor} containing the computed model comparisons is
  returned. If \code{nullInterval} is defined, then two Bayes factors will
  be computed: The Bayes factor for the interval against the null hypothesis
  that the standardized effect is 0, and the corresponding Bayes factor for
  the compliment of the interval.

  If \code{posterior} is \code{TRUE}, an object of class \code{BFmcmc},
  containing MCMC samples from the posterior is returned.
}
\description{
This function computes Bayes factors, or samples from the posterior, for
one- and two-sample designs.
}
\details{
The Bayes factor provided by \code{ttestBF} tests the null hypothesis that
the mean (or mean difference) of a normal population is \eqn{\mu_0}{mu0}
(argument \code{mu}). Specifically, the Bayes factor compares two
hypotheses: that the standardized effect size is 0, or that the standardized
effect size is not 0. For one-sample tests, the standardized effect size is
\eqn{(\mu-\mu_0)/\sigma}{(mu-mu0)/sigma}; for two sample tests, the
standardized effect size is \eqn{(\mu_2-\mu_1)/\sigma}{(mu2-mu1)/sigma}.

A noninformative Jeffreys prior is placed on the variance of the normal
population, while a Cauchy prior is placed on the standardized effect size.
The \code{rscale} argument controls the scale of the prior distribution,
with \code{rscale=1} yielding a standard Cauchy prior. See the references
below for more details.

For the \code{rscale} argument, several named values are recognized:
"medium", "wide", and "ultrawide". These correspond
to \eqn{r} scale values of \eqn{\sqrt{2}/2}{sqrt(2)/2}, 1, and \eqn{\sqrt{2}}{sqrt(2)}
respectively.

The Bayes factor is computed via Gaussian quadrature.
}
\note{
The default priors have changed from 1 to \eqn{\sqrt{2}/2}. The
  factor of \eqn{\sqrt{2}}  is to be consistent
  with Morey et al. (2011) and
  Rouder et al. (2012), and the factor of \eqn{1/2} in both is to better scale the
  expected effect sizes; the previous scaling put more weight on larger
  effect sizes. To obtain the same Bayes factors as Rouder et al. (2009),
  change the prior scale to 1.
}
\examples{
## Sleep data from t test example
data(sleep)
plot(extra ~ group, data = sleep)

## paired t test
ttestBF(x = sleep$extra[sleep$group==1], y = sleep$extra[sleep$group==2], paired=TRUE)

## Sample from the corresponding posterior distribution
samples = ttestBF(x = sleep$extra[sleep$group==1],
           y = sleep$extra[sleep$group==2], paired=TRUE,
           posterior = TRUE, iterations = 1000)
plot(samples[,"mu"])
}
\references{
Morey, R. D., Rouder, J. N., Pratte, M. S., & Speckman, P. L.
  (2011). Using MCMC chain outputs to efficiently estimate Bayes factors.
  Journal of Mathematical Psychology, 55, 368-378

  Morey, R. D. & Rouder, J. N. (2011). Bayes Factor Approaches for Testing
  Interval Null Hypotheses. Psychological Methods, 16, 406-419

  Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G.
  (2009). Bayesian t-tests for accepting and rejecting the null hypothesis.
  Psychonomic Bulletin & Review, 16, 225-237
}
\seealso{
\code{\link{integrate}}, \code{\link{t.test}}
}
\author{
Richard D. Morey (\email{richarddmorey@gmail.com})
}
\keyword{htest}
