Day 28: MANOVA in SPSS – Analyzing Multiple Dependent Variables Simultaneously

Day 28: MANOVA in SPSS – Analyzing Multiple Dependent Variables Simultaneously

Welcome to Day 28 of your 50-day SPSS learning journey! Today, we’ll focus on Multivariate Analysis of Variance (MANOVA), a powerful statistical technique for analyzing the differences between groups when there are multiple dependent variables. MANOVA extends ANOVA by allowing you to examine interrelated outcomes.

What is MANOVA?

MANOVA tests whether groups differ across a combination of two or more dependent variables. By accounting for the correlations between dependent variables, MANOVA provides a more holistic analysis than running multiple ANOVAs separately.

For example:

  • Examining whether students from different schools differ in both math scores and science scores.
  • Analyzing how exercise programs affect both weight loss and muscle gain.

When to Use MANOVA?

Use MANOVA when:

  1. You have two or more dependent variables (continuous).
  2. You have one or more independent variables (categorical).
  3. The dependent variables are correlated.

Key Assumptions of MANOVA

  1. Normality: Dependent variables should be normally distributed for each group.
  2. Homogeneity of Covariance Matrices: Variance-covariance matrices of dependent variables should be equal across groups (tested using Box’s M test).
  3. Independence: Observations should be independent of one another.
  4. Linearity: Relationships between dependent variables should be linear.

How to Perform MANOVA in SPSS

Step 1: Open Your Dataset

For this example, use the following dataset of students’ test scores by teaching method:

ID Method Math_Score Science_Score
1 Traditional 75 80
2 Online 70 78
3 Blended 85 88
4 Traditional 80 83
5 Online 68 75
6 Blended 90 92
  • Method: Independent variable (categorical: Traditional, Online, Blended).
  • Math_Score, Science_Score: Dependent variables (continuous).

Step 2: Access the MANOVA Tool

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

Step 3: Define Variables

  1. Move the dependent variables (Math_Score and Science_Score) to the Dependent Variables box.
  2. Move the independent variable (Method) to the Fixed Factor(s) box.

Step 4: Customize Options

  1. Click Model:
    • Select Full factorial to include all main effects and interactions.
  2. Click Statistics:
    • Check Descriptive statistics, Estimates of effect size, and Homogeneity tests.
  3. Click Plots:
    • Add Method to the Horizontal Axis to create a plot of group means.
  4. Click Options:
    • Check Display means for and select Method.
    • Click Continue.

Step 5: Run the Analysis

Click OK to generate the output.

Interpreting the Output

1. Box’s M Test

  • Tests the assumption of homogeneity of covariance matrices:
    • If p > 0.001, the assumption is met.
    • If violated, proceed with caution or use more robust techniques like Pillai’s Trace.

2. Multivariate Tests

  • Shows overall significance for group differences using statistics like Pillai’s Trace, Wilks’ Lambda, Hotelling’s Trace, and Roy’s Largest Root.
    • Example: If Wilks’ Lambda p < 0.05, there are significant differences between groups across the dependent variables.

3. Tests of Between-Subjects Effects

  • Provides separate ANOVA results for each dependent variable.
    • Example: If p < 0.05 for Math_Score, teaching methods have a significant effect on math scores.

4. Descriptive Statistics

  • Displays group means for each dependent variable.
    • Example: The mean math score for the Blended group might be higher than for other groups.

5. Estimated Marginal Means Plot

  • Visualizes the mean differences across groups for each dependent variable.

Example Interpretation

Suppose you run the MANOVA and get the following results:

  1. Box’s M Test: p = 0.02 (assumption met).

  2. Multivariate Tests:

    • Wilks’ Lambda: F(4, 20) = 4.56, p = 0.01.
    • Interpretation: There are significant differences between teaching methods across math and science scores.

  3. Tests of Between-Subjects Effects:

    • Math_Score: F(2, 12) = 8.12, p = 0.005.
    • Science_Score: F(2, 12) = 6.45, p = 0.01.
    • Interpretation: Teaching method significantly affects both math and science scores.

  4. Descriptive Statistics:

    • Blended: Math = 87.5, Science = 90.
    • Traditional: Math = 77.5, Science = 81.5.
    • Online: Math = 69, Science = 76.5.

Conclusion: The Blended method results in the highest scores for both math and science, making it the most effective teaching method.

Practice Example: Perform MANOVA

Use the following dataset:

ID Diet_Type Weight_Loss Muscle_Gain
1 Low-Carb 8 5
2 Low-Fat 6 4
3 High-Protein 10 7
4 Low-Carb 7 6
5 Low-Fat 5 3
6 High-Protein 12 8
  1. Perform a MANOVA with Weight_Loss and Muscle_Gain as dependent variables and Diet_Type as the independent variable.
  2. Test for significant group differences and interpret the results.

Common Mistakes to Avoid

  1. Ignoring Assumptions: Always test for normality and homogeneity of covariance matrices before interpreting results.
  2. Running Multiple ANOVAs Instead of MANOVA: MANOVA accounts for correlations between dependent variables, providing more robust results.
  3. Misinterpreting Multivariate Tests: Focus on the overall significance (e.g., Wilks’ Lambda) before analyzing individual effects.

Key Takeaways

  • MANOVA analyzes group differences across multiple dependent variables simultaneously.
  • Use multivariate tests (e.g., Wilks’ Lambda) to evaluate overall significance.
  • Examine descriptive statistics and estimated marginal means for detailed insights.

What’s Next?

In Day 29 of your 50-day SPSS learning journey, we’ll explore Canonical Correlation Analysis in SPSS. You’ll learn how to examine relationships between two sets of variables simultaneously. Stay tuned for this advanced multivariate technique!


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