t.test                 package:ctest                 R Documentation

Student's t-Test

Description:

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

Usage:

     t.test(x, y = NULL, alternative = c("two.sided", "less", "greater"),
            mu = 0, paired = FALSE, var.equal = FALSE,
            conf.level = 0.95, ...)
     t.test(formula, data, subset, na.action, ...)

Arguments:

       x: a numeric vector of data values.

       y: an optional numeric vector 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
          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' a factor with two
          levels giving the corresponding groups.

    data: an optional data frame containing the variables in the model
          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 `NA's.  Defaults to `getOption("na.action")'.

     ...: further arguments to be passed to or from methods.

Details:

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

     If `paired' is `TRUE' then both `x' and `y' must be specified and
     they must be the same length.  Missing values are 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.

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.

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.

See Also:

     `prop.test'

Examples:

     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
     attach(sleep)
     t.test(extra[group == 1], extra[group == 2])
     detach()
     ## Formula interface
     t.test(extra ~ group, data = sleep)

