gen-define-an-anova-and-give-one-short-worked-example-19b6

Define an ANOVA and give one short worked example.

# ANOVA (Analysis of Variance) ## Definition ANOVA is a statistical test used to determine whether there are significant differences between the means of **three or more independent groups**. It compares the variance between groups to the variance within groups. **Null hypothesis (H₀):** All group means are equal **Alternative hypothesis (H₁):** At least one group mean differs --- ## Worked Example **Question:** Does fertilizer type affect plant growth? Three fertilizers were tested on 12 plants (4 per group). Heights in cm after 1 month: - **Fertilizer A:** 20, 22, 19, 21 - **Fertilizer B:** 25, 27, 26, 26 - **Fertilizer C:** 22, 23, 21, 22 **Solution:** 1. **Calculate group means:** - Mean A = 20.5, Mean B = 26, Mean C = 22 - Grand mean = 22.83 2. **Calculate Sum of Squares:** - **Between groups (SSB):** 4[(20.5-22.83)² + (26-22.83)² + (22-22.83)²] = **62.17** - **Within groups (SSW):** Σ(each value - its group mean)² = **10.00** 3. **Calculate Mean Squares:** - MSB = 62.17/(3-1) = **31.09** - MSW = 10.00/(12-3) = **1.11** 4. **F-statistic:** F = 31.09/1.11 = **28.0** 5. **Conclusion:** With F(2,9) critical value ≈ 4.26 at α=0.05, since 28.0 > 4.26, we **reject H₀**. Fertilizer type significantly affects plant growth.