1. **State the problem:** We are performing two one-way ANOVA tests to determine if there are significant differences among group means for two different scenarios: disordered thought levels (Question 1) and correct questions between different spacing (Question 2). 2. **ANOVA formula and rules:** - Total sum of squares (SST) = sum of squared deviations of all observations from the grand mean. - Sum of squares between groups (SSB) = sum of squared deviations of group means from the grand mean, weighted by group size. - Sum of squares within groups (SSW) = sum of squared deviations within each group. - Mean square between (MSB) = SSB / df_between. - Mean square within (MSW) = SSW / df_within. - F observed = MSB / MSW. - Reject null hypothesis if F observed ≥ F critical. 3. **Question 1 (Disordered Thought Levels):** - Groups: Waitlist (W), Oral AP (O), Injectable AP (I). - Given: n=7 per group, GM=64, total S^2=1810.33. - Calculate MS between: $$MSB = \frac{7 \times 219.43}{3-1} = \frac{1536.01}{2} = 768.005$$ - Calculate MS within: $$MSW = \frac{1810.33}{3} = 603.44$$ - Calculate F observed: $$F_{obs} = \frac{768.005}{603.44} = 1.27$$ - Compare with critical value: $$F_{crit} = 3.56$$ - Since $1.27 < 3.56$, fail to reject $H_0$. - Conclusion: No significant difference in mean disordered thought levels among groups. 4. **Question 2 (Correct Questions Between Spacing):** - Groups: Phrase (P), Normal (N), Even (E). - Given: n=7 per group, GM=61.047, total S^2=1831. - Calculate MS between: $$MSB = \frac{7 \times 11.11}{3-1} = \frac{77.77}{2} = 38.88$$ - Calculate MS within: $$MSW = \frac{1831}{3} = 610.62$$ - Calculate F observed: $$F_{obs} = \frac{38.88}{610.62} = 0.0636$$ - Compare with critical value: $$F_{crit} = 3.56$$ - Since $0.0636 < 3.56$, fail to reject $H_0$. - Conclusion: No significant difference in mean correct questions among spacing groups. 5. **Summary:** Both ANOVA tests show $F_{obs} < F_{crit}$, so we fail to reject the null hypotheses, indicating no significant differences among group means in both cases.