Definition:Latin Square/Experimental Design
Definition
In the context of design theory, a Latin square allows classification by three mutually orthogonal factors which can be denoted by rows, columns and conventional "Latin" letters.
Treatments are designated by letters, and allocated to units under restricted randomization, each treatment occurring exactly once in each row and column.
Hence the Latin square provides a useful double-blocking system to increase precision, by reducing two potential sources of variation not relating to treatments.
In the analysis of variance, the degrees of freedom for the error mean square are low for Latin squares smaller than order $6$, but this problem can be overcome by using more than one Latin square.
The fact that the number of treatments must equal the number of rows or columns can lead to difficulties in practice.
Also see
- Results about Latin squares can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Latin square
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Latin square