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, ...)

## 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, ...)
```

### 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 (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` 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.

`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)