Repeated Measures ANOVA
In many studies, the same subjects are measured multiple times under different conditions or time points.
When measurements are related in this way, a regular One-Way ANOVA is not appropriate.
The Repeated Measures ANOVA is used to analyze mean differences when the same subjects are observed repeatedly.
Why Repeated Measures ANOVA Is Needed
Consider a scenario where employee performance is measured:
- Before training
- During training
- After training
All measurements come from the same employees. Because the observations are related, we must account for this dependency.
Repeated Measures ANOVA does exactly that.
When to Use Repeated Measures ANOVA
This test is appropriate when:
- The same subjects are measured 3 or more times
- The dependent variable is numerical
- The independent variable represents time or condition
Common applications include:
- Pre-test, mid-test, post-test studies
- Clinical trials over multiple visits
- Productivity measured across phases
Example Dataset
Assume productivity scores measured at three time points:
| Employee_ID | Before | During | After |
|---|---|---|---|
| 1701 | 60 | 68 | 75 |
| 1702 | 65 | 70 | 78 |
| 1703 | 62 | 69 | 74 |
The research question is: Does productivity change significantly over time?
Understanding the Logic
Repeated Measures ANOVA compares:
- Variation within subjects
- Variation across conditions or time points
Because each subject acts as their own control, this method reduces variability and increases statistical power.
Key Assumptions
Important assumptions include:
- Dependent variable is approximately normal
- Observations are related (same subjects)
- Sphericity assumption holds
SPSS tests sphericity automatically using Mauchly’s Test.
If sphericity is violated, SPSS provides corrected results (Greenhouse-Geisser, Huynh-Feldt).
Running Repeated Measures ANOVA (Menu)
To run the test using SPSS menus:
- Go to Analyze → General Linear Model → Repeated Measures
- Define the within-subject factor (e.g., Time with 3 levels)
- Assign variables to each level
- Click OK
SPSS generates ANOVA tables, sphericity tests, and effect sizes.
Using SPSS Syntax
GLM Before During After
/WSFACTOR=Time 3 Polynomial
/METHOD=SSTYPE(3)
/PRINT=DESCRIPTIVE
/CRITERIA=ALPHA(.05).
This syntax analyzes productivity changes across three time points.
Interpreting the Output
Key values to interpret:
- F-value for the within-subject factor
- Sig. (p-value)
- Sphericity test results
Interpretation rule:
- p < 0.05 → significant difference across time points
- p ≥ 0.05 → no significant change
If sphericity is violated, use corrected p-values.
Common Mistakes
Frequent errors include:
- Using One-Way ANOVA for repeated data
- Ignoring sphericity violations
- Misinterpreting corrected results
Understanding assumptions is essential for valid conclusions.
Quiz 1
When is repeated measures ANOVA used?
When the same subjects are measured multiple times.
Quiz 2
What does sphericity refer to?
Equality of variances of differences.
Quiz 3
Which SPSS test checks sphericity?
Mauchly’s Test.
Quiz 4
What if sphericity is violated?
Use corrected p-values.
Quiz 5
What is the main advantage of repeated measures design?
Reduced variability and higher statistical power.
Mini Practice
A fitness program measures participants’ endurance at three time points.
Perform a repeated measures ANOVA to determine whether endurance changes significantly over time.
Use Repeated Measures ANOVA and interpret the corrected p-value if needed.
What’s Next
In the next lesson, you will learn about Nonparametric Tests, used when assumptions of parametric tests are not met.