Latin square
a type of within-subjects design in which treatments, denoted by Latin letters, are administered in sequences that are systematically varied such that each treatment occurs equally often in each position of the sequence (first, second, third, etc.). The number of treatments administered must be the same as the number of groups or individual participants receiving them. For example, for an experimental design involving four treatments (A, B, C, and D) and four people, one person might receive Treatment A, then B, then C, and then D; a second person might receive them in sequence B, C, D, and A; a third person in sequence C, D, A, and B; and a fourth person in sequence D, A, B, and C. It is important to note that although Latin squares control for order effects they do not control for carryover effects or practice effects. See also balanced Latin square; Graeco-Latin square.