imbalance in Latin Square [Design Issues]

posted by mittyri – Russia, 2023-03-28 01:01 (389 d 12:19 ago) – Posting: # 23515
Views: 2,358

Dear Relaxation!

let me cite the classical book written by Byron Jones and Michael G. Kenward:

❝ Although this design has maximum efficiency in the absence of carry-over effects, it is not as efficient at estimating the direct treatment effects as it could be. To achieve the highest possible efficiency the design must be balanced. The term balance refers to the combinatorial properties that the design must possess. In a balanced design, not only does each treatment occur once with each subject, but, over the whole design each treatment occurs the same number of times in each period and the number of subjects who receive treatment i in some period followed by treatment j in the next period is the same for all i != j. The design in Table 4.1[Latin square] is not balanced because treatment A is followed three times by treatment B and treatment B is never followed by treatment A.

Kind regards,

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