The two-sample t-test is a statistical test used to compare the means of two independent groups to determine if there’s a significant difference between them. In R, you can perform a two-sample t-test using the t.test() function.

Here’s an example of how to perform a two-sample t-test in R:

 

1. First, create two vectors representing the data from the two groups

group1 <- c(12, 15, 17, 19, 22, 24, 28)
group2 <- c(18, 20, 23, 25, 29, 31, 35)

2. Next, perform the two-sample t-test using the t.test() function:

test_result <- t.test(group1, group2)

By default, the t.test() function performs a two-sided test, assuming unequal variances between the two groups. You can also specify additional arguments if necessary:

• var.equal = TRUE to assume equal variances (performing a “pooled” t-test)
• alternative = "less" or alternative = "greater" for a one-sided test

3. Finally, display the test results:

print(test_result)

This will output the t-test results, including the t-value, degrees of freedom, and p-value. You can interpret the p-value to determine if there is a significant difference between the two groups’ means. If the p-value is less than your chosen significance level (e.g., 0.05), you can conclude that there is a statistically significant difference between the two group means.

Output

> test_result <- t.test(group1, group2)
> print(test_result)

Welch Two Sample t-test

data: group1 and group2
t = -2.0203, df = 11.866, p-value = 0.06652
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-13.0731598 0.5017313
sample estimates:
mean of x mean of y 
19.57143 25.85714

Example – 2

Here’s another example:

First, let’s generate some synthetic data for two groups:

# Generate synthetic data
set.seed(42) # Set seed for reproducibility
group1 <- rnorm(n = 30, mean = 100, sd = 15) 
# 30 observations with mean=100, sd=15

group2 <- rnorm(n = 30, mean = 110, sd = 15) 
# 30 observations with mean=110, sd=15


# Perform two-sample t-test
test_result <- t.test(group1, group2)

# Print test result
print(test_result)


# Access specific values from the test result
t_statistic <- test_result$statistic
p_value <- test_result$p.value

To interpret the results, check the p-value. If the p-value is less than the chosen significance level (usually 0.05), you can reject the null hypothesis and conclude that there is a significant difference between the means of the two groups.