Q26: If two Latin squares each of the same order are... - Design of Experiments - Agricultural Statistics- ICAR JRF/SRF 2024 | Agrigyan

• Orthogonal Latin Squares (Graeco-Latin Squares):
• Latin square of order $n$ is an $n \times n$ square array containing $n$ distinct symbols such that each symbol appears exactly once in each row and once in each column.
• Orthogonality: Two Latin squares of the same order $n$ are said to be orthogonal if, when one square is superimposed over the other, every ordered pair of symbols $(A_i, B_j)$ occurs exactly once across all $n^2$ cells.
• pair of orthogonal Latin squares forms a Graeco-Latin square, which allows simultaneous elimination of two extraneous sources of variation in experimental design.
• Other Terms:
• Conjugate Latin square: Formed by transposing rows, columns, or symbols.
• Reduced (Standardized) Latin square: One where both the first row and first column are arranged in natural order.
• Conclusion: The two squares are Orthogonal (Option 3).

Correct option: (3) Orthogonal