Student's t-Test

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

t.test(x, ...)

## S3 method for class 'default': 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, \dots)

a (non-empty) numeric vector of data values.
an optional (non-empty) numeric vector of data values.
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
a number indicating the true value of the mean (or difference in means if you are performing a two sample test).
a logical indicating whether you want a paired t-test.
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.
confidence level of the interval.
a formula of the form lhs ~ rhs where lhs is a numeric variable giving the data values and rhs a factor with two levels giving the corresponding groups.
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).
an optional vector specifying a subset of observations to be used.
a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action").
further arguments to be passed to or from methods.

The formula interface is only applicable for the 2-sample tests.

alternative = "greater" is the alternative that x has a larger mean than y.

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.


  • A list with class "htest" containing the following components:
  • statisticthe value of the t-statistic.
  • parameterthe degrees of freedom for the t-statistic.
  • p.valuethe p-value for the test.
  • conf.inta confidence interval for the mean appropriate to the specified alternative hypothesis.
  • estimatethe estimated mean or difference in means depending on whether it was a one-sample test or a two-sample test.
  • null.valuethe specified hypothesized value of the mean or mean difference depending on whether it was a one-sample test or a two-sample test.
  • alternativea character string describing the alternative hypothesis.
  • methoda character string indicating what type of t-test was performed.
  • data.namea character string giving the name(s) of the data.

See Also


  • t.test
  • t.test.default
  • t.test.formula
library(stats) 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)
Documentation reproduced from package stats, version 3.3, License: Part of R 3.3

Community examples

richie@datacamp.com at Jan 17, 2017 stats v3.3.1

If you have prior reason to suspect that group 1 should have less effect than group 2, you can use a one-sided T-test, which has more power. **Warning**: you can't decide you want a one-sided T-test just because it has more power. You have to have a convincing reason why the difference should only be in one direction. ```{r} t.test(extra ~ group, data = sleep, alternative = "less") ``` The data in the sleep dataset are actually pairs of measurements: the same people were tested with each drug. This means that you should really use a paired test. ```{r} t.test(extra ~ group, data = sleep, paired = TRUE) ```