Day 22: Mixed-Design ANOVA in SPSS – Combining Between- and Within-Subjects Factors
Welcome to Day 22 of your 50-day SPSS learning journey! Today, we’ll explore Mixed-Design ANOVA, a statistical technique that combines both between-subjects factors (e.g., gender) and within-subjects factors (e.g., time or condition). This method is ideal for analyzing complex experimental designs that involve repeated measures across different groups.
What is Mixed-Design ANOVA?
A Mixed-Design ANOVA evaluates the effects of:
- A between-subjects factor, where different groups are compared (e.g., males vs. females).
- A within-subjects factor, where the same participants are measured across multiple time points or conditions.
- The interaction effect between the two factors.
For example, you might use Mixed-Design ANOVA to investigate whether males and females respond differently to a treatment over three time points.
When to Use Mixed-Design ANOVA?
Use Mixed-Design ANOVA when:
- You have one between-subjects factor (e.g., group membership, gender).
- You have one within-subjects factor (e.g., repeated measures over time).
- You want to test for interaction effects between the two factors.
Key Assumptions of Mixed-Design ANOVA
- Normality: The dependent variable is normally distributed for each combination of factors.
- Sphericity: The variances of the differences between within-subject levels are equal (tested using Mauchly’s Test).
- Homogeneity of Variance: The variance of the dependent variable is equal across groups (tested with Levene’s Test).
How to Perform Mixed-Design ANOVA in SPSS
Step 1: Open Your Dataset
For this example, use the following dataset:
ID | Group | Time_1 | Time_2 | Time_3 |
---|---|---|---|---|
1 | Male | 70 | 75 | 80 |
2 | Female | 72 | 78 | 85 |
3 | Male | 68 | 73 | 77 |
4 | Female | 75 | 80 | 88 |
5 | Male | 65 | 70 | 74 |
6 | Female | 77 | 83 | 90 |
- Group: Between-subjects factor (Male vs. Female).
- Time_1, Time_2, Time_3: Within-subjects factor (repeated measures).
- Dependent Variable: Scores across time points.
Step 2: Access the Mixed-Design ANOVA Tool
- Go to Analyze > General Linear Model > Repeated Measures.
- A dialog box will appear.
Step 3: Define the Within-Subjects Factor
- In the Within-Subject Factor Name box, enter a name for the repeated measure (e.g.,
Time
). - Set the Number of Levels (e.g., 3 for Time_1, Time_2, Time_3).
- Click Add, then Define.
Step 4: Assign Variables and Between-Subjects Factor
- Assign
Time_1
,Time_2
, andTime_3
to their respective levels under the Within-Subjects Variables section. - Move the between-subjects factor (
Group
) to the Between-Subjects Factor(s) box.
Step 5: Customize Options
- Click Plots:
- Add
Time
to the Horizontal Axis andGroup
to the Separate Lines box. - Click Add, then Continue.
- Add
- Click Options:
- Check Descriptive Statistics, Estimates of Effect Size, and Homogeneity Tests.
- Check Compare Main Effects for pairwise comparisons.
- Click Continue.
Step 6: Run the Analysis
Click OK to generate the output.
Interpreting the Output
The SPSS output includes several key sections:
1. Mauchly’s Test of Sphericity
- Tests whether the sphericity assumption is met for the within-subjects factor (
Time
):- If p > 0.05, sphericity is met.
- If p < 0.05, apply corrections (e.g., Greenhouse-Geisser).
2. Tests of Within-Subjects Effects
- Main Effect of Time: Tests whether there is a significant difference across the time points.
- Look at the Sig. value for
Time
.
- Look at the Sig. value for
- Interaction Effect: Tests whether the effect of time differs by group.
- Look at the Sig. value for
Time * Group
.
- Look at the Sig. value for
3. Tests of Between-Subjects Effects
- Tests whether there is a significant difference between groups (e.g., Male vs. Female).
- Look at the Sig. value for
Group
.
- Look at the Sig. value for
4. Profile Plot
- Visualizes the interaction between the within- and between-subjects factors.
- If the lines cross or diverge, there may be a significant interaction effect.
Example Interpretation
Suppose you run the Mixed-Design ANOVA and get the following results:
-
Mauchly’s Test of Sphericity:
- p = 0.01 (sphericity violated).
- Use Greenhouse-Geisser corrected values.
-
Tests of Within-Subjects Effects:
- Time: F(2, 10) = 18.34, p < 0.001 (significant).
- Time * Group: F(2, 10) = 5.12, p = 0.03 (significant interaction).
-
Tests of Between-Subjects Effects:
- Group: F(1, 5) = 4.78, p = 0.08 (not significant).
-
Profile Plot:
- The plot shows that females improve more over time compared to males.
Interpretation:
- Test scores significantly improve over time (main effect of
Time
). - The effect of time differs by gender (interaction effect), with females showing greater improvement.
Practice Example: Mixed-Design ANOVA
Use the following dataset:
ID | Group | Session_1 | Session_2 | Session_3 |
---|---|---|---|---|
1 | Treatment | 50 | 60 | 70 |
2 | Control | 55 | 58 | 60 |
3 | Treatment | 52 | 62 | 75 |
4 | Control | 54 | 57 | 61 |
5 | Treatment | 51 | 63 | 72 |
6 | Control | 53 | 56 | 59 |
- Perform a Mixed-Design ANOVA with
Session_1
,Session_2
, andSession_3
as the within-subjects factor andGroup
(Treatment vs. Control) as the between-subjects factor. - Test for main effects of
Session
andGroup
, and their interaction. - Interpret the profile plot and statistical significance.
Common Mistakes to Avoid
- Ignoring Interaction Effects: Always interpret the interaction effect before drawing conclusions about main effects.
- Sphericity Violations: If sphericity is violated, use the corrected values.
- Unbalanced Groups: Ensure your groups have similar sample sizes for valid results.
Key Takeaways
- Mixed-Design ANOVA combines between- and within-subjects factors to analyze complex experimental designs.
- Always check for interaction effects and adjust for sphericity violations.
- Use profile plots for visualizing the interaction between factors.
What’s Next?
In Day 23 of your 50-day SPSS learning journey, we’ll explore Survival Analysis in SPSS. You’ll learn how to analyze time-to-event data and estimate survival probabilities. Stay tuned for another advanced statistical technique!