Question

Please explain why.

Note that Latin square designs are equivalent to specific fractional factorial designs (e.g., the 4x4 Latin square design is equivalent to a 4^3-1fractional factorial design).

Please explain why.

Answer 1

In Latin Square design a single factor of primary interest, typically called the treatment factor and several nuisance factors. For Latin square designs there are 2 nuisance factors.

"A factorial experiment in which only an adequately chosen fraction of the treatment combinations required for the complete factorial experiment is selected to be run."

For an M × M Latin square if M = 2^k then the three factors (rows, columns, and treatments) can also be studied using the same number of runs and a 2^3k-k fractional factorial design. The advantage to this is that the results can be easily analyzed using Yates' algorithm and the confounding pattern is readily available. While every Latin square corresponds to a subset of the points in a complete 2^3k design, only one standard square corresponds to a 2^3k-k fractional factorial design, and all the others correspond to designs where the contrasts are not all orthogonal.

Latin square design is a fractional factorial experiment which requires less experimentation to determine the main treatment results.Both can reduce the no. of experiments simulation runs .