Key differences between the two-sample t-test and paired t-test

Two-Sample T-Test

The two-sample t-test, also known as an independent t-test, is used to determine whether there is a significant difference between the means of two independent (unrelated) groups. It is typically used when you have two separate groups and want to assess whether their means are statistically different from each other....

Paired T-Test

The paired t-test, also known as a dependent t-test or matched-pairs t-test, is used when you want to compare the means of two related groups or when each data point in one group is naturally paired with a data point in the other group. The formula for the paired t-test is given by:...

Key differences between the two-sample t-test and paired t-test

Function Two-Sample T-Test Paired T-Test Data Relationship Compares means of two independent groups with no natural pairing between the observations. Compares means of two related groups where each data point in one group is paired with a data point in the other. Assumptions Assumes independence of samples and may assume equal variances. Assumes that the paired differences follow a normal distribution and are independent. Use Cases Used when you want to compare two distinct groups or populations. Used when you have before-and-after measurements or paired data points....

Code for Two-Sample t-Test: Comparing School Scores

R # Generate example dataset.seed(123)school1_scores <- rnorm(30, mean = 75, sd = 10)  school2_scores <- rnorm(30, mean = 80, sd = 12)  # Perform a two-sample t-testt_test_result <- t.test(school1_scores, school2_scores) # Print the resultprint(t_test_result)...

Code for Paired t-Test: Before and After Treatment Comparison

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Comparing Product Sales with Two-Sample T-Test

R # Generate example dataset.seed(456)before_treatment <- rnorm(20, mean = 140, sd = 10)  after_treatment <- before_treatment - rnorm(20, mean = 5, sd = 4)  # Perform a paired t-testpaired_t_test_result <- t.test(before_treatment, after_treatment, paired = TRUE) # Print the resultprint(paired_t_test_result)...

Paired T-Test for Exam Scores Before and After a Training Course

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Conclusion

R # Generate example dataset.seed(456)product_A_sales <- rnorm(40, mean = 500, sd = 50)  product_B_sales <- rnorm(45, mean = 480, sd = 60)  # Perform a two-sample t-testt_test_result <- t.test(product_A_sales, product_B_sales) # Print the resultprint(t_test_result)...