RANDOMIZATION

Randomization allows the unbiased assignment of treatments to experimental units (in this case of entries to the plots) and is a prerequisite for obtaining a valid estimate of the experimental error. One of the most common mistakes, besides replications, in the layout of breeding trials is to avoid the randomization in the first replication so that the plot order corresponds to the entry order, which is statistically incorrect. Another common mistake in Multi Environment (years and locations) Trials (MET) is to use the same randomization in all the locations within the same year.

Alphanal

Randomization can be done with various programs or manually. A free and friendly MS- DOS software is ALPHANAL produced by the Scottish Agricultural Statistics Service. Although designed for alpha-designs (incomplete block designs) it can be conveniently used also for the randomization of unreplicated trials. After opening the directory “ALPHANAL” identify the two commands, ALPHAGEN.EXE and ALPHANAL.EXE, for the generation of randomizations plans and for data analysis, respectively. The limits of ALPHAGEN are 500 entries and 20 plots per incomplete block, which represents an advantage over the corresponding command in GenStat which allows a maximum of 100 entries. Figure  20 shows the main steps in using the program in the case of a trial with 160 entries in 200 plots.

To use ALPHAGEN for the randomization of unreplicated trials with systematic checks (known also as augmented designs) or for partially replicated trials, we consider each location as a replication, and the total number of plots as the number of treatments (= entries). In deciding the number of plots per incomplete block one should have already in mind the layout of the trial. In the case of 50 columns and 4 rows, arrangements can be either 5 or 10 incomplete blocks, because 50 cannot be divided by 20 and 25 is above the limits of the programme.

Once the parameters of the trials are fixed, the programme uses an iterative process to find the most efficient design (continue to answer “yes” to the question “Do you want to search

for a better design?” until the message “There are no more efficient designs of this size” is displayed) and produces a randomization plan which can be stored with a given name. Note that the efficiency of incomplete block design is a function of the number of comparisons between genotypes within the same incomplete block and will always be less than 1 because there will always be a number of comparisons between genotypes that are in different blocks.

In the case of replicated trials, as in Stage 2, 3 and 4 and regardless of whether the trials are a physical unit as in Figure 17, or planted by different farmers as incomplete blocks or complete replications (Figure 18), the randomization follows the same process as shown in Figure 21, with minor differences as shown in Figure 22.

Assuming a Stage 3 trial with 12 entries to be grown with 2 replications and 3 farmers, we will need to enter 6 as number of replications (= number of farmers × number of replications in each farmers’ field) (Figure 22). The full randomization plan with block size = 4 is shown in Figure 23. The number of incomplete blocks in this case could have been either 2, 3 4 or 6. Small incomplete blocks are usually associated with a greater precision but with a lower efficiency as the number of comparisons between entries in different incomplete blocks increases. One has also to consider possible restrictions imposed by field shape because it is not possible to break the physical unity of an incomplete block.

The major problem with conducting the randomization with ALPHAGEN is importing the text file into Excel® _{(see pages 47–53).}

FIGURE 21

Main steps in the randomization of an unreplicated Stage 1 PPB trial with 160 entries and 200 plots using the command ALPHAGEN in ALPHANAL.

DIGGer

DiGGer is a program that finds efficient designs for non-factorial experiments with experimental units that can be specified as a rectangular array and under specified correlation structures (Coombes, 2006; Cullis, Smith and Coombes, 2006). DiGGer can find optimal or near-optimal incomplete block designs, row-column designs and spatial designs. The program, together with manuals and examples, can be freely downloaded from http://www.austatgen.org/files/software/downloads/

DiGGer was developed for cereal variety trials with plots in rectangular arrays, but can be used for any design that can be described in row and column layouts. Designs may have treatments with unequal replication and may have missing plots. Designs may be optimized for comparisons between groups of treatments.

DiGGer is available as a standalone executable and as an R package. The standalone version runs from an input file or interactively in a command window. The

FIGURE 22

Main steps in the randomization of a replicated Stage 2, 3 or 4 trial with 2 replications, 12 entries and incomplete blocks of size 4, using the command ALPHAGEN in ALPHANAL. The trial is grown by 3 farmers.

FIGURE 23

Randomization of a Stage 3 trial using an incomplete block design with 12 entries, 2 replications, incomplete blocks of size 4 planted by 3 farmers

R package generates search specifications that can be modified before the search is run.

Figure  24 shows the case of a simple variety trial with 24 entries in three replications: after clicking on DIGGer.exe the window shown in Figure 24 appears, which is self-explanatory. After receiving an answer to the last question, DiGGer runs a search, during which the search output is produced in the command window showing the progress of the search. The programme produces 5 files:

• digdisgn.in is the input file that controls the search;

• digdisgn.trt is the treatment information file, with treatment name, number, replication and group details; • digdisgn.out is the output file recording the details of the

search and its progress;

• digdisgn.log is created and updated after each 10% of a search phase and holds a matrix representation of the design and • digdisgn.list is also created and updated after each 10%

of each search phase, and holds a field-book listing of the design, unit by unit, as rows nested within columns.

The .lst file, an example of which is given in Figure  25, gives the field-book listing of the design as rows nested within

columns, and can be directly imported into an Excel® _{or database file. The treatment names}

are given in the ID column, treatment numbers in the ENTRY column and ROW, RANGE

FIGURE 24

Interactive DiGGer: simple case

FIGURE 25

(column) and REP (replicate) details. The TRT column holds design numbers used by DiGGer and these are the numbers that appear in the .log file.

The software can handle a maximum of 1500 experimental units (treatment × replications). In the case of partially replicated designs the PRDiGGer function uses blocking specifications to even out the placement of unreplicated treatments and control treatments throughout a design. The function is aimed at designs with some unreplicated treatments. The function requires the minimum input of treatment information (typically a .csv file) with “Name”, “Entry No.”, “No.Reps”, “Group”, the dimensions of the design and the blocking sequences, and produces a colour-coded plot of the design and a .csv file with the field-book listing of the design.

At the time of writing this manual, the PRDiGGer function has not been yet included in the DiGGer package and for its use we suggest contacting Neil Coombes ([email protected]. au).