One-Way ANOVA Concept and Assumptions
📌 One-Way ANOVA (Analysis of Variance) is a statistical test used to determine if there is a difference in the means of three or more independent groups.
📊 It is a parametric test requiring interval or ratio scale data.
⚙️ Post Hoc Tests are necessary to identify which specific groups differ significantly *if* the main ANOVA test yields a significant result.

Prerequisites for ANOVA Testing
✅ Normality Test: Data must be normally distributed; if not, the non-parametric alternative is the Kruskal-Wallis test.
🔬 Homogeneity of Variance Test: While not an absolute prerequisite, it dictates the choice of the Post Hoc test: use Bonferroni if variances are homogeneous, or Games-Howell if they are not.

SPSS Procedure and Interpretation Walkthrough
▶️ Data preparation in SPSS requires categorizing group membership (e.g., Value 1 = Group 1) and inputting scores.
📉 The Normality Test criteria state that if the $p$-value $> 0.05$, the data is normally distributed (in the example, all $p$-values were $> 0.05$).
🧪 The Homogeneity of Variance Test (Levene's test) in the example yielded $p = 0.739$, indicating homogeneous variances.

ANOVA and Post Hoc Analysis
🛑 The main ANOVA test result showed a significance value of $p = 0.000$, which is $< 0.05$, concluding there is a significant difference among the three groups.
👯‍♀️ Since the difference was significant and variances were homogeneous, the Bonferroni Post Hoc test was used for pairwise comparison.
↔️ Post Hoc results showed significant differences between Group 1 vs. Group 2 ($p = 0.000$) and Group 1 vs. Group 3 ($p = 0.000$), but no significant difference between Group 2 vs. Group 3 ($p = 0.212$).

Key Points & Insights
➡️ One-Way ANOVA tests for mean differences among three or more independent groups using parametric assumptions.
➡️ Normality ($p > 0.05$) and Homogeneity ($p > 0.05$ for Levene's test) must be checked before interpreting the main ANOVA result.
➡️ If ANOVA is significant ($p < 0.05$), use Bonferroni for Post Hoc tests when variances are homogeneous, or Games-Howell otherwise.
➡️ A Post Hoc $p$-value $< 0.05$ indicates a statistically significant, real difference between the two specific groups being compared.

📸 Video summarized with SummaryTube.com on Nov 25, 2025, 05:57 UTC