# Two Sample t-test in R (2 Examples)

This tutorial shows how you can two sample t-test in R. Note that, Two sample t-test is also called independent sample t-test or unpaired sample t-test.

Method 1: Vector format

t.test(vector_1, vector_2, var.equal = TRUE)

Method 2: Data frame format

t.test(Y ~ group, data = df_name , var.equal = TRUE)

## Data and Hypothesis

Suppose you want to test whether women and men differ in their attitudes toward a brand, and the attitude is measured on a 7-point scale (1= Not like at all, 7 = Like it a lot).

The following is the hypothetical data, one column for men’s attitudes and another one for women’s attitudes toward the brand.

The following are the null and alternative hypotheses for two sample t-test.

• H0 (Null Hypothesis): Men and women have the same attitudes.
• Ha (Null Hypothesis): Men and women do not have the same attitudes.

## Example for Method 1

``````# vectors of men and women
men_data<-c(4,6,7,7,6,7)
women_data<-c(4,3,4,5,2,1)

# equal variance
res1 <- t.test(men_data, women_data, var.equal = TRUE)
res1

# unequal variance
res2 <- t.test(men_data, women_data, var.equal = FALSE)
res2``````

The following is the output. The first part “Two Sample t-test” is for the equal variance. As we can see, the p-value is smaller than 0.05 and thus we reject the null hypothesis and conclude that men and women differ in attitudes.

The second part “Welch Two Sample t-test” is for unequal variance. We can see that t statistic is the same as the first part. (Note that, as long as the sample numbers are the same for two groups, t statistics are always the same. See the discussion here. )

```	Two Sample t-test

data:  men_data and women_data
t = 3.9094, df = 10, p-value = 0.002916
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
1.290146 4.709854
sample estimates:
mean of x mean of y
6.166667  3.166667

Welch Two Sample t-test

data:  men_data and women_data
t = 3.9094, df = 9.5124, p-value = 0.003208
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
1.27819 4.72181
sample estimates:
mean of x mean of y
6.166667  3.166667 ```

## Example for Method 2

This example of two sample t-test is for situation where data is a data frame. In the following, we can create a data frame first. Then, use the same t.test() function to do the two sample t-test in R.

``````# vectors of men and women
men_data<-c(4,6,7,7,6,7)
women_data<-c(4,3,4,5,2,1)

# Create a data frame
df_combined <- data.frame(
group = rep(c("Woman", "Man"), each = 6),
attitudes = c(women_data,  men_data))

# Compute two sample t-test in R
results_2 <- t.test(attitudes ~ group, data = df_combined , var.equal = TRUE)
results_2``````

The following is the output of two sample t-test in R. We can see that the result is the same as in the last example.

```	Two Sample t-test

data:  attitudes by group
t = 3.9094, df = 10, p-value = 0.002916
alternative hypothesis: true difference in means between group Man and group Woman is not equal to 0
95 percent confidence interval:
1.290146 4.709854
sample estimates:
mean in group Man mean in group Woman
6.166667            3.166667 ```