# R document: Student’s t-Test

Feb 05, 2008## Student's t-Test

zz from: http://sekhon.berkeley.edu/stats/html/t.test.html

### 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).
```

```
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 data frame containing the variables in the model formula.
```

```
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.

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:

```
a character string indicating what type of t-test was performed.
```

### See Also

### Examples

t.test(1:10,y=c(7:20)) # P = .00001855t.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)