t.test {stats} R Documentation

## Student's t-Test

### Description

Performs one and two sample t-tests on vectors of data.

### Usage

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 = na.pass, ...)


### Arguments

 x a (non-empty) numeric vector of data values. y an optional (non-empty) numeric vector of data values. alternative a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter. mu a number indicating the true value of the mean (or difference in means if you are performing a two sample test). paired a logical indicating whether you want a paired t-test. var.equal a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used. conf.level confidence level of the interval. formula a formula of the form lhs ~ rhs where lhs is a numeric variable giving the data values and rhs either 1 for a one-sample or paired test or a factor with two levels giving the corresponding groups. If lhs is of class "Pair" and rhs is 1, a paired test is done, see Examples. data an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula). subset an optional vector specifying a subset of observations to be used. na.action a function which indicates what should happen when the data contain NAs. ... further arguments to be passed to or from methods. For the formula method, this includes arguments of the default method, but not paired.

### Details

alternative = "greater" is the alternative that x has a larger mean than y. For the one-sample case: that the mean is positive.

If paired is TRUE then both x and y must be specified and they must be the same length. Missing values are silently removed (in pairs if paired is TRUE). If var.equal is TRUE then the pooled estimate of the variance is used. By default, if var.equal is 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 "htest" containing the following components:

 statistic the value of the t-statistic. parameter the degrees of freedom for the t-statistic. p.value the p-value for the test. conf.int a confidence interval for the mean appropriate to the specified alternative hypothesis. estimate the estimated mean or difference in means depending on whether it was a one-sample test or a two-sample test. 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. stderr the standard error of the mean (difference), used as denominator in the t-statistic formula. alternative a character string describing the alternative hypothesis. method a character string indicating what type of t-test was performed. data.name a character string giving the name(s) of the data.

prop.test

### Examples

## Two-sample t-test
t.test(1:10, y = c(7:20))      # P = .00001855
t.test(1:10, y = c(7:20, 200)) # P = .1245    -- NOT significant anymore

with(mtcars, t.test(mpg[am == 0], mpg[am == 1]))

## Formula interface
t.test(mpg ~ am, data = mtcars)

## One-sample t-test
t.test(sleep$extra) ## Formula interface t.test(extra ~ 1, data = sleep) ## Paired t-test ## The sleep data is actually paired, so could have been in wide format: sleep2 <- reshape(sleep, direction = "wide", idvar = "ID", timevar = "group") ## Traditional interface t.test(sleep2$extra.1, sleep2\$extra.2, paired = TRUE)