\Header{t.test}{Student's t-Test}
\methalias{t.test.default}{t.test}
\methalias{t.test.formula}{t.test}
\keyword{htest}{t.test}
\begin{Description}\relax
Performs one and two sample t-tests on vectors of data.
\end{Description}
\begin{Usage}
\begin{verbatim}
t.test(x, ...)

## Default S3 method:
t.test(x, y = NULL, alternative = c("two.sided", "less", "greater"),
       mu = 0, paired = FALSE, var.equal = FALSE,
       conf.level = 0.95, ...)

## S3 method for class 'formula':
t.test(formula, data, subset, na.action, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] a numeric vector of data values.
\item[\code{y}] an optional numeric vector data values.
\item[\code{alternative}] a character string specifying the alternative
hypothesis, must be one of \code{"two.sided"} (default),
\code{"greater"} or \code{"less"}.  You can specify just the initial
letter.
\item[\code{mu}] a number indicating the true value of the mean (or
difference in means if you are performing a two sample test).
\item[\code{paired}] a logical indicating whether you want a paired
t-test.
\item[\code{var.equal}] a logical variable indicating whether to treat the
two variances as being equal. If \code{TRUE} then the pooled
variance is used to estimate the variance otherwise the Welch
(or Satterthwaite) approximation to the degrees of freedom is used.
\item[\code{conf.level}] confidence level of the interval.
\item[\code{formula}] a formula of the form \code{lhs \textasciitilde{} rhs} where \code{lhs}
is a numeric variable giving the data values and \code{rhs} a factor
with two levels giving the corresponding groups.
\item[\code{data}] an optional data frame containing the variables in the
model formula.
\item[\code{subset}] an optional vector specifying a subset of observations
to be used.
\item[\code{na.action}] a function which indicates what should happen when
the data contain \code{NA}s.  Defaults to
\code{getOption("na.action")}.
\item[\code{...}] further arguments to be passed to or from methods.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The formula interface is only applicable for the 2-sample tests.

If \code{paired} is \code{TRUE} then both \code{x} and \code{y} must
be specified and they must be the same length.  Missing values are
removed (in pairs if \code{paired} is \code{TRUE}).  If
\code{var.equal} is \code{TRUE} then the pooled estimate of the
variance is used.  By default, if \code{var.equal} is \code{FALSE}
then the variance is estimated separately for both groups and the
Welch modification to the degrees of freedom is used.
\end{Details}
\begin{Value}
A list with class \code{"htest"} containing the following components:
\begin{ldescription}
\item[\code{statistic}] the value of the t-statistic.
\item[\code{parameter}] the degrees of freedom for the t-statistic.
\item[\code{p.value}] the p-value for the test.
\item[\code{conf.int}] a confidence interval for the mean appropriate to the
specified alternative hypothesis.
\item[\code{estimate}] the estimated mean or difference in means depending on
whether it was a one-sample test or a two-sample test.
\item[\code{null.value}] the specified hypothesized value of the mean or mean
difference depending on whether it was a one-sample test or a
two-sample test.
\item[\code{alternative}] a character string describing the alternative
hypothesis.
\item[\code{method}] a character string indicating what type of t-test was
performed.
\item[\code{data.name}] a character string giving the name(s) of the data.
\end{ldescription}
\end{Value}
\begin{SeeAlso}\relax
\code{\Link{prop.test}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
t.test(1:10,y=c(7:20))      # P = .00001855
t.test(1:10,y=c(7:20, 200)) # P = .1245    -- NOT significant anymore

## Classical example: Student's sleep data
data(sleep)
plot(extra ~ group, data = sleep)
## Traditional interface
with(sleep, t.test(extra[group == 1], extra[group == 2]))
## Formula interface
t.test(extra ~ group, data = sleep)
\end{ExampleCode}
\end{Examples}

