# 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.

Note that an online 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).