| % File src/library/stats/man/t.test.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2019 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{t.test} |
| \alias{t.test} |
| \alias{t.test.default} |
| \alias{t.test.formula} |
| \title{Student's t-Test} |
| \description{ |
| Performs one and two sample t-tests on vectors of data. |
| } |
| \usage{ |
| t.test(x, \dots) |
| |
| \method{t.test}{default}(x, y = NULL, |
| alternative = c("two.sided", "less", "greater"), |
| mu = 0, paired = FALSE, var.equal = FALSE, |
| conf.level = 0.95, \dots) |
| |
| \method{t.test}{formula}(formula, data, subset, na.action, \dots) |
| } |
| \arguments{ |
| \item{x}{a (non-empty) numeric vector of data values.} |
| \item{y}{an optional (non-empty) numeric vector of data values.} |
| \item{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{mu}{a number indicating the true value of the mean (or |
| difference in means if you are performing a two sample test).} |
| \item{paired}{a logical indicating whether you want a paired |
| t-test.} |
| \item{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{conf.level}{confidence level of the interval.} |
| \item{formula}{a formula of the form \code{lhs ~ 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{data}{an optional matrix or data frame (or similar: see |
| \code{\link{model.frame}}) containing the variables in the |
| formula \code{formula}. By default the variables are taken from |
| \code{environment(formula)}.} |
| \item{subset}{an optional vector specifying a subset of observations |
| to be used.} |
| \item{na.action}{a function which indicates what should happen when |
| the data contain \code{NA}s. Defaults to |
| \code{getOption("na.action")}.} |
| \item{\dots}{further arguments to be passed to or from methods.} |
| } |
| \details{ |
| The formula interface is only applicable for the 2-sample tests. |
| |
| \code{alternative = "greater"} is the alternative that \code{x} has a |
| larger mean than \code{y}. |
| |
| 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 |
| silently 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. |
| |
| If the input data are effectively constant (compared to the larger of the |
| two means) an error is generated. |
| } |
| \value{ |
| A list with class \code{"htest"} containing the following components: |
| \item{statistic}{the value of the t-statistic.} |
| \item{parameter}{the degrees of freedom for the t-statistic.} |
| \item{p.value}{the p-value for the test.} |
| \item{conf.int}{a confidence interval for the mean appropriate to the |
| specified alternative hypothesis.} |
| \item{estimate}{the estimated mean or difference in means depending on |
| whether it was a one-sample test or a two-sample test.} |
| \item{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{stderr}{the standard error of the mean (difference), used as |
| denominator in the t-statistic formula.} |
| \item{alternative}{a character string describing the alternative |
| hypothesis.} |
| \item{method}{a character string indicating what type of t-test was |
| performed.} |
| \item{data.name}{a character string giving the name(s) of the data.} |
| } |
| \seealso{ |
| \code{\link{prop.test}} |
| } |
| \examples{ |
| require(graphics) |
| |
| 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 |
| 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) |
| } |
| \keyword{htest} |