Day 22: Mixed-Design ANOVA in SPSS – Combining Between- and Within-Subjects Factors

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:

  1. A between-subjects factor, where different groups are compared (e.g., males vs. females).
  2. A within-subjects factor, where the same participants are measured across multiple time points or conditions.
  3. 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:

  1. You have one between-subjects factor (e.g., group membership, gender).
  2. You have one within-subjects factor (e.g., repeated measures over time).
  3. You want to test for interaction effects between the two factors.

Key Assumptions of Mixed-Design ANOVA

  1. Normality: The dependent variable is normally distributed for each combination of factors.
  2. Sphericity: The variances of the differences between within-subject levels are equal (tested using Mauchly’s Test).
  3. 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

  1. Go to Analyze > General Linear Model > Repeated Measures.
  2. A dialog box will appear.

Step 3: Define the Within-Subjects Factor

  1. In the Within-Subject Factor Name box, enter a name for the repeated measure (e.g., Time).
  2. Set the Number of Levels (e.g., 3 for Time_1, Time_2, Time_3).
  3. Click Add, then Define.

Step 4: Assign Variables and Between-Subjects Factor

  1. Assign Time_1, Time_2, and Time_3 to their respective levels under the Within-Subjects Variables section.
  2. Move the between-subjects factor (Group) to the Between-Subjects Factor(s) box.

Step 5: Customize Options

  1. Click Plots:
    • Add Time to the Horizontal Axis and Group to the Separate Lines box.
    • Click Add, then Continue.
  2. 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.
  • Interaction Effect: Tests whether the effect of time differs by group.
    • Look at the Sig. value for Time * Group.

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.

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:

  1. Mauchly’s Test of Sphericity:

    • p = 0.01 (sphericity violated).
    • Use Greenhouse-Geisser corrected values.
  2. 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).
  3. Tests of Between-Subjects Effects:

    • Group: F(1, 5) = 4.78, p = 0.08 (not significant).
  4. 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
  1. Perform a Mixed-Design ANOVA with Session_1, Session_2, and Session_3 as the within-subjects factor and Group (Treatment vs. Control) as the between-subjects factor.
  2. Test for main effects of Session and Group, and their interaction.
  3. Interpret the profile plot and statistical significance.

Common Mistakes to Avoid

  1. Ignoring Interaction Effects: Always interpret the interaction effect before drawing conclusions about main effects.
  2. Sphericity Violations: If sphericity is violated, use the corrected values.
  3. 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!