# Paired t-test in R (2 Examples)

Method 1 for paired t-test is for a situation group 1 and group 2 are two separate vectors, whereas Method 2 is for two groups of data in the same column.

Method 1:

t.test(group_1, group_2, paired = TRUE)

Method 2:

t.test(y~group, data=my_data, paired = TRUE)

## Data and Hypothesis

Suppose we would like to test whether students perform differently in Exam 1 and Exam 2. Since a student is measured at time 1 (Exam 1) and time 2 (Exam 2), that is why it is paired data. The following is the hypothetical data.

The following is the null and alternative hypotheses for the paired t-test.

• Null Hypothesis: Exam 1 and Exam 2 are not significantly different.
• Alternative Hypothesis: Exam 1 and Exam 2 are significantly different.

### R code Example for Method 1

``````# Exam 1 and Exam 2 data
Exam1<-c(65,70,75,80,68,95)
Exam2 <-c(75,71,90,98,65,99)

# The following writes Exam1 and Exam2 separately within t.test():
t.test(Exam1, Exam2, paired = TRUE)``````

Output:

```	Paired t-test

data:  Exam1 and Exam2
t = -2.2361, df = 5, p-value = 0.07559
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-16.121994   1.121994
sample estimates:
mean of the differences
-7.5 ```

P-value of 0.756 is greater than 0.05. That means that we failed to reject the null hypothesis. Therefore, we conclude that Exam 1 and Exam 2 scores are not significantly different.

### R code Example for Method 2

We are going to use the same data in example 1, but to use a different data format. It will also again use `t.test()` but using the column name of `group` in the dataframe of Exam_data.

Note, Exam_data is a dataframe that is created in the following code.

``````# Exam 1 and Exam 2 data
Exam1<-c(65,70,75,80,68,95)
Exam2 <-c(75,71,90,98,65,99)

# Create a data frame for paired t-test in R
Exam_data <- data.frame(
group = rep(c("Exam1", "Exam2"), each = 6),
score = c(Exam1, Exam2))

# print out the dataframe:
print(Exam_data)

# The following uses data frame format:
t.test(score~group, data=Exam_data, paired = TRUE)``````

Output of the data frame:

```   group score
1  Exam1    65
2  Exam1    70
3  Exam1    75
4  Exam1    80
5  Exam1    68
6  Exam1    95
7  Exam2    75
8  Exam2    71
9  Exam2    90
10 Exam2    98
11 Exam2    65
12 Exam2    99```

The following is output of paired t-test. Since we use the same data and get the same result, the interpretation and conclusion are exactly the same as in Example 2.

```	Paired t-test

data:  score by group
t = -2.2361, df = 5, p-value = 0.07559
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-16.121994   1.121994
sample estimates:
mean of the differences
-7.5 ```
Categories R