Dear Reddy,

The complete block designs, such as the RCB and the lattice square (LS) designs are applicable to experiments with any number of treatments. However, these complete block designs become less efficient as the number of treatments increases, because block size increases proportionally with the number of treatments, and the homogeneity of experimental plots within a large block is difficult to maintain. That means the experimental error of a complete block design is likely to increase with the number of treatments. Thus, alternative designs for single-factor experiments with a big number of treatments are the incomplete block designs, one of which is the lattice design.

The principles followed in Augmented design are: all checks should appear in each block; new crop varieties appear only once in the whole experiment, meaning they are not replicated; yield of new varieties will be adjusted for differences in block, block size is determined by number of blocks, checks and new varieties, and number of blocks is determined by number of varieties and checks. However, modified form of augmented design (Line and Poushinsky, 1983,1985) provides row and column error control with systematic and random placing of repeating checks when large number of non-replicated entries are tested. The design can be laid out in rows and columns as a square arrangement like LS design.

Generalized lattice, or alpha designs (Peterson and Williams, 1997) provide lattice with some loss of balance and efficiency, where conventional square or rectangular lattices cannot be generated. Alpha design is flexible and exists for all combination of variety, replication and plots per block. It can have incomplete block of different size. Checks can also be used. Generally, alpha lattice designs are most effective when the block size is less than the square root of the number of treatments.

Why would you use different design for the same trial if you planned to combine the results of the trial conducted across locations? You may do, but are they balanced or not? I think if you consult a book entitled ‘Gomez and Gomez. 1984. Statistical procedures for agricultural research” you may getr more information.

In Randomized Complete Block designs (or incomplete block), blocking is done keeping in view controlling some sort of variation in the soil. Let it be fertility, slope, texture, water other gradient. This way differences among treatments is minimized inside the blocks while increased between blocks. You should definitely consult a statistician on that because here you are not referring to any gradient. Rather you are taking completely separate locations as blocks.

What I think is that you should treat both designs separately and take out the inference about the treatments (it is assumed that you have repeated checks randomly distributed in each block).

 Thank you Getachew Agegnehu and Mohammad Tahir. 

@ Getachew Agegnehu. These experiments were conducted in different years. Augmented design experiments were conducted in 2013 and Alpha lattice design experiments were conducted in 2014. They had to be analysed separately to see the actual values of each genotype. 

Different experimental designs can be combined together