Split-Plot, Strip-Plot, Crossover Designs & Analysis of Covariance (ANCOVA) - Agricultural Statistics | Agrigyan

• Analysis of Hierarchical (Nested) Designs:
• Statement (A): Nested Classification: Since each instructor teaches exclusively within one specific course and does not teach across all courses, Instructor is strictly nested within Course. (True)
• Statement (B): Absence of Interaction: In nested models, factors cannot cross; consequently, interaction terms between Course and Instructor do not exist (the variation is captured as Instructor within Course). (True)
• Statement (C): Error Degrees of Freedom Calculation:
• Total observations: $N = 3 \text{ courses} \times 2 \text{ instructors} \times 3 \text{ scores} = 18$.
• Course $df = 3 - 1 = 2$.
• Instructor (within Course) $df = 3 \times (2 - 1) = 3$.
• Error $df = 3 \times 2 \times (3 - 1) = 6 \times 2 = 12$.
• The statement claims error $df = 10$, which is False (it is 12).
• Statement (D): Decomposition: The pooled 'Instructor within Course' SS ($df = 3$) can be partitioned into 3 orthogonal single-degree-of-freedom components corresponding to each course. (True)
• Conclusion: Statements (A), (B) and (D) only are correct (Option 2).

Correct option: (2) (A), (B) and (D) only.