A Latin square is a mathematical concept used in combinatorial design and statistics. It is defined as an \( n \times n \) array filled with \( n \) different symbols (often the integers \( 1 \) through \( n \)), such that each symbol appears exactly once in each row and exactly once in each column.
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A Latin square of order is a array of symbols, each occurring once in each row and column. Used as a row-column design, its symbols label treatments. Centered treatment indicators are orthogonal to both row and column indicators, because every row-treatment and column-treatment pair occurs once. This balance separates additive effects from two nuisance directions.