One-Way ANOVA F-Statistic Calculation | UPSC ISS 2022 Paper-2 | Problem-23 | RitwikMath

### ⏱️ 0:00 – Problem Setup
- Number of methods (treatments): \( k = 3 \)
- Observations per method: 7
- Total observations:
\[
n = 3 \times 7 = 21
\]

Given:
- \( SS_{Treatment} = 147.3456 \)
- \( SS_{Total} = 202.3126 \)

---

### ⏱️ 0:45 – Degrees of Freedom
\[
df_T = k - 1 = 2
\]
\[
df_E = n - k = 21 - 3 = 18
\]

---

### ⏱️ 1:07 – Sum of Squares for Error
\[
SS_E = SS_{Total} - SS_{Treatment}
= 202.3126 - 147.3456 = 54.967
\]

---

### ⏱️ 1:22 – Mean Squares

#### Mean Square for Treatment:
\[
MS_T = \frac{147.3456}{2} = 73.6728
\]

#### Mean Square for Error:
\[
MS_E = \frac{54.967}{18} \approx 3.0537
\]

---

### ⏱️ 1:39 – F-Statistic
\[
F = \frac{MS_T}{MS_E}
= \frac{73.6728}{3.0537} \approx 24.13
\]

---

### ⏱️ 1:52 – Final Answer
\[
F \approx 24.13
\]

👉 **Option A is correct**

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## 🔍 Key Concepts Covered:
- One-way ANOVA
- Partitioning of total variation
- Degrees of freedom
- Mean squares
- F-statistic calculation

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## 🎯 Exam Relevance:
Highly important for:
- **UPSC Statistics Optional**
- **ISS Exam**
- **CSIR-NET, GATE, IIT JAM**
- ANOVA & Hypothesis Testing

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