Video 2. Latin Square and Graeco-Latin Square Design of Experiments DOE Explained with Examples

Latin square designs shown in Figure 6 are orthogonal arrangements of the levels of the treatment factor in a square created by the equal number of rows and columns as the levels of the treatment factors. In the randomized complete block design, only one known nuisance factor was blocked to reduce the experimental errors. In the Latin Square design, two blocking factors are arranged across the row and the column of the square. Therefore, two nuisance factors could be blocked to reduce even more experimental error. Often, the nuisance factors controlled in a Latin-Square are known as row and column factor for obvious reason. The levels of the treatment factor are represented by Latin letters and arranged orthogonally in the cells of the square. Therefore, each letter is appeared exactly once in a row or a column but takes different position in the next row or column. It can be noted that one additional nuisance factor can be blocked without increasing the number of experimental units. Latin Square design was observed to be used dated back to Euler (1782), Fisher (1925, 1926), and Bose (1938) (Bose, 1938; Hinkelmann & Kempthorne, 2008).

Figure 6. Example Latin Square Designs

Latin Square Design of Experiments Analysis Model

The analysis model for Latin square design is an effects model provided in Equation 2.

Equation 2