Repeated Measures ANOVA Assignment Help — Sphericity and SPSS Steps

What Is Repeated Measures ANOVA and When Do You Use It?

Repeated measures ANOVA compares three or more related measurements taken from the same subjects: for example, scores measured at baseline, one month, and three months into an intervention. Use it when you have one continuous dependent variable measured at three or more time points (or conditions) on the same people.

If you only have two related measurements, use the paired samples t-test instead. If you have three or more independent groups instead of repeated measures on the same people, use one-way ANOVA instead.

Assumptions You Must Check Before Running It in SPSS

• Sphericity. The variances of the differences between all pairs of related measurements should be roughly equal. SPSS tests this automatically with Mauchly’s Test of Sphericity, produced alongside your main output.
• If Mauchly’s test is significant (p < .05), sphericity is violated: don’t read the standard “Sphericity Assumed” row. Instead use a corrected row: Greenhouse-Geisser (more conservative, generally preferred) or Huynh-Feldt (used when Greenhouse-Geisser’s epsilon estimate is above .75).
• Normality of the dependent variable at each time point.

How to Run It in SPSS (Step by Step)

1. Go to Analyze > General Linear Model > Repeated Measures.
2. In the Repeated Measures Define Factor(s) dialog, name your Within-Subject Factor (e.g. “Time”) and enter the Number of Levels (e.g. 3 for baseline/1-month/3-month).
3. Click Add, then Define.
4. Move your three (or more) related variables into the Within-Subjects Variables box, in order.
5. Click Options, request Descriptive statistics and Estimates of effect size, then Continue > OK.

How to Interpret the Output

1. Check Mauchly’s Test of Sphericity first. If p > .05, sphericity holds: read the “Sphericity Assumed” row in the Tests of Within-Subjects Effects table. If p ≤ .05, read the Greenhouse-Geisser row instead.
2. From the correct row, read the F-value, df (note these are often non-integer after a Greenhouse-Geisser correction), and Sig.
3. Report partial eta-squared as the effect size.
4. If the overall test is significant, run post-hoc pairwise comparisons with Bonferroni correction (available directly in the Options dialog) to identify which specific time points differ.

How to Report the Results in APA Format

Mauchly’s test indicated that the assumption of sphericity had been violated, χ²(2) = 8.91, p = .012, so degrees of freedom were corrected using Greenhouse-Geisser estimates (ε = .85). There was a significant effect of time on anxiety scores, F(1.70, 49.30) = 14.62, p < .001, partial η² = .34.

Repeated Measures ANOVA vs One-Way ANOVA: Understanding the Difference

Repeated measures ANOVA compares the same subjects across three or more time points or conditions. One-way ANOVA compares three or more different, independent groups. Treating repeated measurements as if they were independent groups (running a one-way ANOVA on repeated data) ignores the correlation between measurements from the same person and gives an incorrect result.

Not sure which one your design needs? See the full SPSS statistical test guide, or get help with this specific assignment.