R: Student's t-Test

t.test {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)

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