# t test

# What is t test

**t test** is used to compare either the means of two sets of data or to compare an **observed mean m** to a **theoretical value mu**. There are different types of **t test** :

- The
**one-sample t test**used to compare an observed mean with a theoretical mean. - The
**independent t test**(or**two sample t test**) used to compare the means of two unrelated groups of samples. - The
**paired t test**used to compare two sets of paired samples.

The different **t test formula** are described in detail by following this link: t test formula.

The objective of this chapter is to show you how to **calculate t test** in **R**.

**t test calculator**is available here to calculate

**Student’s t-test**without any installation.

# t.test : R function to calculate t test

The **R** function to use for **t test statistics** is **t.test()**. It can be used to **calculate** the different types of **Student t test** mentioned above.

A simplified format of the function is:

```
# One sample t test :
# Comparison of an observed mean with a
# a theoretical mean
t.test(x, mu=0)
# Independent t test
# Comparison of the means of two independent samples (x & y)
t.test(x, y)
# Paired t test
t.test(x, y, paired=TRUE)
```

x and y are two **numeric** vectors.

The argument **“alternative =”** can be used to specify the alternative hypothesis. It must be one of **“two.side”** (**2 tailed t test**, default), **“greater”** or **“less”** (**one sided t test**) (see the **R** code below ).

`t.test(x, y, alternative=c("two.sided", "less", "greater"))`

# Results of t test R function

The result of **t.test()** function is a list of class “htest” including the following components :

**statistic**: the value of the**t test statistics****parameter**: the**degrees of freedom**for the**t test statistics****p.value**: the**p-value**for the test**conf.int**: a**confidence interval**for the mean appropriate to the specified**alternative hypothesis**.**estimate**: the means of the two groups being compared (in the case of**independent t test**) or difference in means (in the case of**paired t test**).

The format of the **R** code to use to get these values is as follow:

```
test<-t.test(x,y)
res$p.value # get the p-value
res$parameter # get the degrees of freedom
res$statistic # get the t test statistics
```

Many articles are included in this chapter. Scroll down to the bottom of this page to see some examples on how to **perform t test** in R.

# Infos

This analysis has been done with R (ver. 3.1.0).

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