T-Test in R


As per statistics, the T-test in R is used to determine whether the mean of the two groups is equal to each other. The assumption for the test is that both groups are sampled from a normal distribution with equal fluctuation. There are two hypotheses used:

Null hypothesis:

It is assumed that the two means are the same.

Alternate hypothesis:

It is assumed that the two means are not the same.

There are two types of t-test in R

  • One sample t-test
  • Welch t-test

The t.test() function is used to provides a variety of t-test in R.

How to perform T-test in R

In the T-test, for specifying equal variances and a pooled variance estimate, we set var.equal=True. We can also use alternative=”less” or alternative=”greater” for specifying one-tailed test.

One-Sample T-test

One sample t-test is used to compares the mean of a vector against a theoretical mean. For t-test evaluation, we compute the p-value. The p-value ranges from 0 to 1. It is interpreted as:

  • If the p-value is less than 0.05, it means we reject the null hypothesis.
  • If the p-value is higher than 0.05, then it indicates that there is no evidance to reject the null hypothesis.

The syntax for performing one-sample t-test in R is as follow:

Here,

  1. x is the variable
  2. ? is described by the null hypothesis
set.seed(0)
a <- c(rnorm(75, mean = 3500, sd = 1000))
t.test(a, mu = 38000)

Output:

T-Test in R

Paired-Sample T-test

We need two vectors data to perform a paired-sample test The syntax for paired sample test is as follow:

set.seed(1500)  
a <- c(rnorm(700, mean = 450, sd = 5))  
b <- c(rnorm(700, mean = 354, sd = 4))  
t.test(a, b, paired = TRUE)

Output:

test2

Independent-Sample T-test

The independent-sample T-test can be taken in one of the three forms but it depends on the data structure and variance. These three forms are as follows:

  1. Independent-Samples T-test where v1 and v2 are numeric.
  2. Independent-Samples T-test where v1 is numeric and v2 is binary.
  3. Independent-Samples T-test with equal variances not assumed.

The syntax to perform an independent-sample t-test is as follow:

In R it is assumed that v1 and v2 are not equal, thus defaulting to Welch’s test. We set the flag var.equal=TRUE for toggling this.

Example 1: Independent-Sample T-test where y1 and y2 are numeric

set.seed(0)  
a <- c(rnorm(800, mean = 450, sd = 5))  
b <- c(rnorm(800, mean = 354, sd = 4))  
t.test(a, b, var.equal = TRUE)

Output:

test4

Example 2: Where y1 is numeric and y2 are binary

set.seed(0)  
a <- c(rnorm(800, mean = 450, sd = 5))  
b <- c(rnorm(800, mean = 354, sd = 4))  
c <- c(a, b)  
d <- c(rep("A", 800), rep("B", 800))  
t.test(c ~ d, var.equal = TRUE)

t5

Example 3: With equal variance not assumed

set.seed(0)  
a <- c(rnorm(800, mean = 450, sd = 5))  
b <- c(rnorm(800, mean = 354, sd = 4))  
t.test(a, b, var.equal = FALSE)

Output:

t6