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:
Where,
- Σd is the sum of the differences
- degree of freedom = n – 1
Here are some key characteristics of the paired t-test:
Assumptions:
- The differences between the pairs should follow a normal distribution.
- The paired differences should be independent.
Use Cases:
- Comparing the performance of students before and after a tutoring program (where each student’s score is measured both before and after).
- Evaluating whether a new drug has a significant effect on blood pressure (with measurements taken before and after administering the drug).
Hypotheses:
Null Hypothesis (H0): There is no significant difference between the means of the paired groups (the mean of the differences is zero).
H0: u1 = u2 or H0: u1 –u2 = 0
Alternative Hypothesis (Ha): There is a significant difference between the means of the paired groups.
H1: u1 is not equal to u2 or H1: u1 – u2 is not equal to zero.
Differences Between two-sample, t-test and paired t-test
Statistical tests are essential tools in data analysis, helping researchers make inferences about populations based on sample data. Two common tests used to compare the means of different groups are the two-sample t-test and the paired t-test. Both tests are based on the t-distribution, but they have distinct use cases and assumptions. In this article, we’ll explore the differences between these two tests in R, when to use each one, and how to conduct them in practice.
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