One-Way ANOVA: Therapy Types and Depression Scores

Interpretation

Test Type: One-Way Between-Subjects ANOVA with Tukey’s HSD
Purpose: Comparing depression scores across four therapy types (CBT, Psychodynamic, Humanistic, and Control)

Descriptive Statistics

CBT showed the lowest depression scores on average, while the Control group showed the highest (5.35 point difference).

Omnibus ANOVA

• F(3, 110) = 2.89, p = .036
• Significant: at least one therapy type differs from others

Effect Size

eta_sq = 487.623 / 6229.811
# η² = .078

Result: η² = .08 (medium effect)

Post-Hoc Comparisons (Tukey HSD)

• CBT vs Psychodynamic: Mean difference = -4.22, p = .042 → Significant (CBT lower by 4.22 points)
• CBT vs Humanistic: Mean difference = -2.56, p = .287 → Not significant
• CBT vs Control: Mean difference = -5.35, p = .018 → Significant (CBT lower by 5.35 points)
• Psychodynamic vs Humanistic: Mean difference = 1.66, p = .685 → Not significant
• Psychodynamic vs Control: Mean difference = -1.13, p = .891 → Not significant

Summary: CBT produced significantly lower depression scores than both Psychodynamic therapy and the Control group. The three non-CBT conditions (Psychodynamic, Humanistic, and Control) did not differ significantly from each other.

APA-Formatted Results

“A one-way ANOVA revealed a significant effect of therapy type on depression scores, F(3, 110) = 2.89, p = .036, η² = .08. Post-hoc comparisons using Tukey’s HSD indicated that CBT (M = 18.32, SD = 6.75) resulted in significantly lower depression scores than Psychodynamic therapy (M = 22.54, SD = 8.12, p = .042) and the Control group (M = 23.67, SD = 9.21, p = .018). CBT did not differ significantly from Humanistic therapy (M = 20.88, SD = 7.46, p = .287). Psychodynamic, Humanistic, and Control groups did not differ significantly from each other (all ps > .05).”

What NOT to Report

• Sum of Squares, Mean Square (calculation artifacts)
• Within Groups row from ANOVA table
• Redundant comparisons (e.g., Humanistic vs CBT, which mirrors CBT vs Humanistic)
• Missing comparisons from the post-hoc table (Humanistic vs Control)

Common Mistakes to Avoid

1. Stopping at the omnibus F without examining post-hoc tests
2. Concluding “all groups differ” when only CBT differs from some groups
3. Forgetting to note the incomplete post-hoc table (missing Humanistic-Control comparison)
4. Omitting η² effect size
5. Not specifying the direction of effects (which group had lower depression)