When to Use Repeated Measures ANOVA?

 Here’s the draft for Day 21: Repeated Measures ANOVA in SPSS, continuing the 50-day SPSS learning journey:

Day 21: Repeated Measures ANOVA in SPSS – Analyzing Within-Subjects Data

Welcome to Day 21 of your 50-day SPSS learning journey! Today, we’ll focus on Repeated Measures ANOVA, a statistical method used to analyze data where the same subjects are measured multiple times under different conditions or across time points. This technique is common in experiments, clinical trials, and longitudinal studies.

What is Repeated Measures ANOVA?

Repeated Measures ANOVA evaluates whether there are significant differences between means when the same subjects are exposed to different conditions or measured over time.

For example:

  • Comparing test scores of students after studying with three different methods.
  • Monitoring blood pressure levels of patients before, during, and after treatment.

When to Use Repeated Measures ANOVA?

Use Repeated Measures ANOVA when:

  1. You have one dependent variable (continuous).
  2. The independent variable is within-subjects (i.e., all participants are exposed to all levels of the independent variable).
  3. You want to test for differences across multiple conditions or time points.

Key Assumptions of Repeated Measures ANOVA

  1. Normality: The dependent variable is normally distributed for each condition or time point.
  2. Sphericity: The variances of the differences between conditions are equal.
    • Tested using Mauchly’s Test of Sphericity in SPSS.
    • If violated, apply corrections (e.g., Greenhouse-Geisser or Huynh-Feldt).

How to Perform Repeated Measures ANOVA in SPSS

Step 1: Open Your Dataset

For this example, use the following dataset:

ID Method_1 Method_2 Method_3
1 70 75 80
2 68 72 78
3 72 74 81
4 65 70 76
5 74 78 84
  • Method_1, Method_2, Method_3: Test scores under three different teaching methods.
  • The goal: Determine if test scores differ significantly across methods.

Step 2: Access the Repeated Measures 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 factor (e.g., Method).
  2. Set the Number of Levels (e.g., 3 for Method_1, Method_2, Method_3).
  3. Click Add, then Define.

Step 4: Assign Variables to Levels

  1. Assign the variables (Method_1, Method_2, Method_3) to their respective levels.

Step 5: Customize Options

  1. Click Plots:
    • Add the factor (e.g., Method) to the Horizontal Axis.
    • Click Add, then Continue.
  2. Click Options:
    • Check Descriptive Statistics and Estimates of Effect Size.
    • 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 the assumption of sphericity:
    • If p > 0.05, sphericity is met.
    • If p < 0.05, sphericity is violated, and you must apply corrections (e.g., Greenhouse-Geisser).

2. Tests of Within-Subjects Effects

  • Main Effect: Look at the Sig. value for the factor (e.g., Method).
    • If p < 0.05, there is a significant difference across levels of the factor.
  • Apply corrections if sphericity is violated (e.g., use Greenhouse-Geisser adjusted p-values).

3. Pairwise Comparisons

  • Compares means between each pair of conditions (e.g., Method_1 vs. Method_2).
    • If p < 0.05, the difference between the two conditions is significant.

4. Estimated Marginal Means and Profile Plot

  • Displays the means for each level of the factor and a plot visualizing the differences.

Example Interpretation

Suppose you run the Repeated Measures ANOVA and get the following results:

  1. Mauchly’s Test of Sphericity:

    • p = 0.03 (sphericity violated).
    • Use Greenhouse-Geisser adjusted values.

  2. Tests of Within-Subjects Effects:

    • Method: F(2, 8) = 12.34, p = 0.002 (significant).

    Interpretation: Test scores differ significantly across the three methods.

  3. Pairwise Comparisons:

    • Method_1 vs. Method_2: p = 0.04.
    • Method_2 vs. Method_3: p = 0.03.
    • Method_1 vs. Method_3: p = 0.001.

    Interpretation: Each method significantly differs from the others.

  4. Profile Plot:

    • Shows a clear upward trend in scores from Method_1 to Method_3.

Practice Example: Repeated Measures ANOVA

Use the following dataset:

ID Time_1 Time_2 Time_3
1 120 115 110
2 125 120 115
3 118 113 108
4 122 118 112
5 119 114 109
  1. Perform a Repeated Measures ANOVA to determine if there is a significant decrease in scores over time.
  2. Test for sphericity and apply corrections if necessary.
  3. Interpret the profile plot and pairwise comparisons.

Common Mistakes to Avoid

  1. Ignoring Sphericity: Always check Mauchly’s Test and apply corrections if necessary.
  2. Misinterpreting Profile Plots: Use statistical results alongside visualizations for robust conclusions.
  3. Overlooking Pairwise Comparisons: Significant main effects don’t reveal which levels differ—always check pairwise comparisons.

Key Takeaways

  • Repeated Measures ANOVA is used to analyze within-subjects data across multiple conditions or time points.
  • Test for sphericity and apply corrections if needed.
  • Use pairwise comparisons and profile plots to interpret differences between conditions.

What’s Next?

In Day 22 of your 50-day SPSS learning journey, we’ll explore Mixed-Design ANOVA in SPSS. This method combines both between-subjects and within-subjects factors, making it ideal for complex experimental designs. Stay tuned for more advanced techniques!


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