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