Day 20: Two-Way ANOVA in SPSS – Analyzing Interaction Effects

Day 20: Two-Way ANOVA in SPSS – Analyzing Interaction Effects

Welcome to Day 20 of your 50-day SPSS learning journey! Today, we’ll explore Two-Way ANOVA, a statistical method used to determine the effect of two independent variables (factors) on a dependent variable. Two-Way ANOVA also allows you to examine interaction effects, which occur when the effect of one factor depends on the level of another factor.

What is Two-Way ANOVA?

Two-Way ANOVA tests three main effects:

  1. The main effect of Factor A.
  2. The main effect of Factor B.
  3. The interaction effect between Factor A and Factor B.

For example, you might want to analyze how gender (male/female) and teaching method (online/in-person) affect test scores, and whether the effect of teaching method differs by gender.

When to Use Two-Way ANOVA?

Use Two-Way ANOVA when:

  1. You have one dependent variable (continuous).
  2. You have two independent variables (categorical).
  3. You want to test for interaction effects between the independent variables.

How to Perform Two-Way ANOVA in SPSS

Step 1: Open Your Dataset

For this example, use the following dataset:

ID Gender Method Test_Score
1 Male Online 75
2 Female Online 80
3 Male In-Person 85
4 Female In-Person 90
5 Male Online 70
6 Female Online 78
7 Male In-Person 88
8 Female In-Person 92
  • Gender: Independent variable 1 (categorical).
  • Method: Independent variable 2 (categorical).
  • Test_Score: Dependent variable (continuous).

Step 2: Access the Two-Way ANOVA Tool

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

Step 3: Select Variables

  1. Move the dependent variable (Test_Score) to the Dependent Variable box.
  2. Move the two independent variables (Gender and Method) to the Fixed Factors box.

Step 4: Customize Options

  1. Click Model and ensure Full factorial is selected to include interaction effects.
  2. Click Plots:
    • Add one independent variable (e.g., Gender) to the Horizontal Axis and the other (e.g., Method) to the Separate Lines box.
    • Click Add, then Continue.
  3. Click Options:
    • Check Descriptive statistics and Estimates of effect size to display additional information.
    • Click Continue.

Step 5: Run the Analysis

Click OK to generate the output.

Interpreting the Output

The SPSS output includes several key sections:

1. Descriptive Statistics Table

  • Displays the mean and standard deviation for each group combination (e.g., males using online vs. in-person methods).

2. Tests of Between-Subjects Effects

  • Main Effects: Look at the Sig. value for each independent variable (e.g., Gender, Method).
    • If p < 0.05, the variable has a significant effect on the dependent variable.
  • Interaction Effect: Look at the Sig. value for Gender * Method.
    • If p < 0.05, there is a significant interaction effect.

3. Estimated Marginal Means

  • Provides the adjusted means for each group combination.

4. Profile Plot

  • Visualizes the interaction effect.
    • If the lines intersect, it indicates an interaction between the two factors.

Example Interpretation

Suppose you run the Two-Way ANOVA and get the following results:

  1. Main Effects:

    • Gender: p = 0.04 (significant).
    • Method: p = 0.02 (significant).

    Interpretation: Both gender and teaching method have a significant impact on test scores.

  2. Interaction Effect:

    • Gender * Method: p = 0.03 (significant).

    Interpretation: The effect of teaching method depends on gender.

  3. Profile Plot:

    • The plot shows that females perform better with in-person teaching, while males perform similarly across both methods.

Practice Example: Perform Two-Way ANOVA

Use the following dataset:

ID Age_Group Diet_Type Weight_Loss
1 Young Low-Carb 10
2 Middle Low-Carb 12
3 Young Low-Fat 8
4 Middle Low-Fat 9
5 Young Low-Carb 11
6 Middle Low-Carb 13
7 Young Low-Fat 7
8 Middle Low-Fat 8
  1. Perform a Two-Way ANOVA with Weight_Loss as the dependent variable, Age_Group and Diet_Type as the independent variables.
  2. Check for main effects and interaction effects.
  3. Interpret the profile plot and statistical significance.

Common Mistakes to Avoid

  1. Ignoring Interaction Effects: Always interpret interaction effects before main effects, as they can change the story.
  2. Unbalanced Groups: Unequal sample sizes in groups can affect results.
  3. Assumption Violations: Ensure normality and homogeneity of variances (use Levene’s test) before interpreting results.

Key Takeaways

  • Two-Way ANOVA analyzes the effects of two independent variables and their interaction on a dependent variable.
  • Use profile plots to visually interpret interaction effects.
  • Always verify assumptions and check for significant main and interaction effects before drawing conclusions.

What’s Next?

In Day 21 of your 50-day SPSS learning journey, we’ll explore Repeated Measures ANOVA in SPSS. You’ll learn how to analyze within-subjects data, such as measurements taken over time or under different conditions. Stay tuned for another exciting analysis method!


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