Latin square
A design layout that balances treatment order so practice and fatigue can't bias results.
What it means
A Latin square is an experimental design in which treatments are arranged in a grid so that each treatment appears exactly once in every row and exactly once in every column, allowing two nuisance variables to be controlled simultaneously while testing the treatments. In behavioral research it is used especially to counterbalance the order of conditions in within-subject experiments: by assigning different participants different sequences according to the square, the design ensures each condition occurs equally often in each ordinal position, so order effects such as practice, fatigue, and carryover are spread evenly across conditions rather than confounded with any one of them. This yields the efficiency of repeated measures—every participant experiences every condition—without letting the sequence systematically favor a particular treatment. The two 'blocking' dimensions, the rows and columns, are removed from the comparison much as in blocking generally. Its assumptions include no interaction between the row, column, and treatment factors. It matters because it is a compact, economical way to obtain unbiased comparisons when both order and individual differences threaten validity.
Examples
In a study where each taster samples four recipes, a Latin square assigns tasting orders so that each recipe is tried first, second, third, and fourth equally often across tasters.
A team testing four checkout designs runs each design first, second, third and fourth across equal numbers of testers, so no design wins simply by being seen while people were fresh.
In a trial of three painkillers, patients take all three across separate weeks in sequences drawn from a Latin square, so lingering drowsiness never lands on the same drug twice.