WILL HELP YOU IN YOUR RESEARCH SUBJECT

1. Paired t-Test
A Statistical Method for Comparing
Two Related Samples

2. Introduction
• The paired t-test is a statistical method used to
compare the means of two related groups.
• It is useful when the same subjects are
measured before and after a treatment.

3. When to Use a Paired t-Test
• • When data is collected from the same
subjects at two different time points.
• • When measuring a characteristic before and
after an intervention.
• • When using matched pairs, such as twins or
related individuals.

4. Assumptions
• • The data is continuous.
• • The samples are dependent (paired).
• • The differences between paired
observations are normally distributed.

5. Formula for the Paired t-Test
• t = (Mean Difference) / (Standard Error of
Difference)
• t = (d̄) / (s_d / √n)
• where:
• d̄ = mean of the differences,
• s_d = standard deviation of differences,
• n = number of pairs.

6. Example Calculation
• Example: A group of students takes a test
before and after a training session.
• Their scores are compared using a paired t-
test.
• Steps:
• 1. Compute the differences.
• 2. Find the mean and standard deviation of
differences.

7. Interpreting the Results
• • If p-value < 0.05, reject the null hypothesis
(significant difference).
• • If p-value ≥ 0.05, fail to reject the null
hypothesis (no significant difference).
• • Consider confidence intervals to interpret
results further.