🔍 What is ANOVA?

Analysis of Variance (ANOVA) is a statistical method used to test the hypothesis that three or more population means are equal.

• It works by comparing the variance between group means to the variance within groups.

• The result is an F-statistic and a p-value to help determine if at least one group mean is significantly different from the others.

🧪 When to Use ANOVA?

Use ANOVA when:

• You want to compare 3 or more groups

• Your dependent variable is continuous (e.g., blood pressure, weight)

• Your independent variable is categorical (e.g., treatment group)

📊 Types of ANOVA:

1. One-Way ANOVA
   – One independent variable with multiple levels (e.g., comparing blood pressure across 3 medications).

2. Two-Way ANOVA
   – Two independent variables (e.g., comparing treatment effect across gender and medication types).

3. Repeated Measures ANOVA
   – Same subjects measured across different time points or conditions.

⚠️ Assumptions of ANOVA

• Normality: The data in each group should be approximately normally distributed.

• Homogeneity of Variance: Groups should have similar variance.

• Independence: Observations should be independent of one another.

Violating these assumptions may lead to inaccurate results, and alternatives like Kruskal-Wallis or Welch’s ANOVA might be needed.

📈 Post-hoc Tests:

If ANOVA is significant, it only tells you that at least one group is different—but not which one. You’ll need post-hoc tests (e.g., Tukey’s HSD) to pinpoint the differences.

🧠 Example:

You're comparing cholesterol levels across three diet plans (A, B, and C).

• Null Hypothesis (H₀): All diets result in the same average cholesterol.

• Alternative Hypothesis (H₁): At least one diet results in a different average cholesterol.
  ANOVA tells you if there's a significant difference overall; post-hoc tests show where the differences lie.