Paired Samples t-test

In many situations, measurements are taken from the same subjects more than once. For example, before and after training, or pre-test and post-test scores.

The Paired Samples t-test is used to compare two related measurements to determine whether a significant change has occurred.

When to Use a Paired Samples t-test

This test is appropriate when:

• The same individuals are measured twice
• The two measurements are logically paired
• The dependent variable is numeric

Typical use cases include:

• Before vs after training scores
• Pre-treatment vs post-treatment results
• Performance before and after a system upgrade

Example Dataset

Consider employee productivity scores measured before and after a training program:

Each row represents the same employee measured at two different times.

Key Assumptions

Before applying the paired t-test:

• Data pairs must be correctly matched
• Differences should be approximately normally distributed

Normality is assessed on the difference scores, not on the raw variables.

Running Paired Samples t-test (Menu)

To run the test using SPSS menus:

• Go to Analyze → Compare Means → Paired-Samples T Test
• Select the paired variables
• Move them into Paired Variables
• Click OK

SPSS automatically computes the difference between paired values.

Using SPSS Syntax

T-TEST PAIRS=Before_Training WITH After_Training
  /CRITERIA=CI(.95).

This syntax compares the mean difference between before and after measurements.

Interpreting the Output

Focus on these values:

• Mean Difference – average change
• t-value – test statistic
• Sig. (p-value) – significance

Interpretation rule:

• p < 0.05 → significant change after intervention
• p ≥ 0.05 → no significant change

A positive mean difference indicates improvement, while a negative value indicates decline.

Paired vs Independent t-test

A common mistake is confusing paired and independent tests.

• Paired t-test → same subjects measured twice
• Independent t-test → different groups

Choosing the wrong test leads to incorrect conclusions.

Quiz 1

When is a paired samples t-test used?

Quiz 2

What variable is tested for normality?

Quiz 3

What does p < 0.05 indicate?

Quiz 4

Can this test be used for unrelated groups?

Quiz 5

What does a positive mean difference indicate?

Mini Practice

Create a dataset measuring employee performance before and after a skill workshop.

Perform a paired samples t-test and interpret the results.

What’s Next

In the next lesson, you will learn about the One Sample t-test, used to compare a sample mean against a known or hypothesized value.