When this occurs, as in, the crossover design is said to be balanced with respect to first-order carryover effects. How many times do you have one treatment B followed by a second treatment? This is an advantageous property for Design 8. Each treatment precedes every other treatment the same number of times once.įor example, how many times is treatment A followed by treatment B? Only once. Although with 4 periods and 4 treatments there are 4! The Latin square in has an additional property that the Latin square in does not have. Latin squares are uniform crossover designs, uniform both within periods and within sequences. Latin squares for 4-period, 4-treatment crossover designs are. As will be demonstrated later, Latin squares also serve as building blocks for other types of crossover designs. Latin squares historically have provided the foundation for r-period, r-treatment crossover designs because they yield uniform crossover designs in that each treatment occurs only once within each sequence and once within each period. If the design is uniform across sequences then you will be also be able to remove the sequence effects. If the design is uniform across periods you will be able to remove the period effects. If a design is uniform within sequences and uniform within periods, then it is said to be uniform. We focus on designs for dealing with first-order carryover effects, but the development can be generalized if higher-order carryover effects need to be considered. In actuality, the length of the washout periods between treatment administrations may be the determining factor as to whether higher-order carryover effects should be considered. Usually in period j we only consider first-order carryover effects from period j - 1 because.