Forms alpha designs by standard generators for up to 100 treatments (M.F. Franklin & R.W. Payne).
Option
PRINT = string token |
Controls whether or not to print a plan or the generator of of the design (design, generator); if unset in an interactive run AGALPHA will ask whether the design and generator are to be printed, in a batch run the default is not to print anything |
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Parameters
LEVELS = scalars |
Number of treatments |
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NREPLICATES = scalars |
Number of replicates |
NBLOCKS = scalars |
Number of blocks per replicate |
SEED = scalars |
Seed for randomization; a negative value implies no randomization |
TREATMENTS = factors |
Identifier for the treatment factor |
REPLICATES = factors |
Identifier for the replicate factor |
BLOCKS = factors |
Identifier for the factor to index the blocks within replicates |
UNITS = factors |
Identifier for the factor to index the units (or plots) within each block |
STATEMENT = texts |
Saves a command to recreate each design (useful if the design information has been specified in response to questions from AGALPHA) |
Description
Alpha designs are a very flexible class of resolvable incomplete block designs. A resolvable design is one in which each block contains only a selection of the treatments, but the blocks can be grouped together into subsets in which each treatment is replicated once. The groupings of blocks thus form replicates, and the block structure of the design is
Replicates / Blocks / Units
Such designs are particularly useful when there are many treatments to examine and the variability of the units is such that the block size needs to be kept small. Alpha designs were thus devised originally for the analysis of plant breeding trials (Patterson & Williams 1976), where many varieties may need to be evaluated in a single trial, and have the advantage that they can provide effective designs for any number of treatments.
The formation of an alpha design requires a generating array, as explained in the description of procedure AFALPHA, and the effectiveness of the design that is produced will be very dependent on the choice of array. Procedure AGALPHA selects an appropriate array from those presented by Patterson, Williams & Hunter (1978) and Williams (1975), and then calls AFALPHA to generate the design.
AGALPHA is easiest to use interactively. It then asks questions to determine the necessary information to select the generating array: for example, the number of treatments, the number of blocks per replicate and so on. The parameters allow you to anticipate questions, or to define all the necessary information if you want to use AGALPHA in batch. If, however, you wish to recreate the same design later, the STATEMENT parameter allows you to save a Genstat text structure containing a command specifying the same information.
The number of treatments can be defined using the LEVELS parameter. Similarly, the NREPLICATES and NBLOCKS parameters define the number of replicates and the number of blocks per replicate. If the number of blocks per replicate is greater than or equal to the number of units (or plots) per block, generators are available for either two, three or four replicates; otherwise there can only be two. The SEED parameter allows you to specify a seed to be used to randomize the design. In batch the default seed is -1, to suppress randomization. If you do not set SEED when running interactively AGALPHA will ask for a seed, and again a negative value suppresses any randomization. The remaining parameters, TREATMENTS, REPLICATES, BLOCKS and UNITS, allow you to specify identifiers for the treatment, replicate, block-within-replicate and unit-within-block factors. If these are not specified in a batch run, AGALPHA will use identifiers that are local within the procedure and thus lost at the end of the procedure. If you are running interactively, AGALPHA will ask you to provide identifiers, and these will remain available after AGALPHA has finished running.
AGALPHA has a PRINT option which can be set to design to print the plan of the design, and generator to print the generator of the design. By default, if you are running Genstat in batch, neither are printed. If you do not set PRINT when running interactively, AGALPHA will ask whether or not you wish to print the design or generator.
Option: PRINT.
Parameters: LEVELS, NREPLICATES, NBLOCKS, SEED, TREATMENTS, REPLICATES, BLOCKS, UNITS, STATEMENT.
Method
The QUESTION procedure is used to obtain the necessary details of the design. Procedure AFALPHA is then called to generate the design.
References
Patterson, H.D. & Williams E.R. (1976). A new class of resolvable incomplete block designs. Biometrika, 63, 83-92.
Patterson, H.D., Williams E.R. & Hunter, E.A. (1978). Block designs for variety trials. Journal of Agricultural Science, Cambridge, 90, 395-400.
Williams, E.R. (1975). A new class of resolvable block designs. Ph.D. Thesis, University of Edinburgh.
See also
Procedure: AFALPHA.
Commands for: Design of experiments, REML analysis of linear mixed models.
Example
CAPTION 'AGALPHA example',\
!t('This prints the (unrandomized) plan of a design for 24',\
'treatments with 3 replicates and 6 blocks per replicate.');\
STYLE=meta,plain
AGALPHA [PRINT=design] LEVELS=24; NREPLICATES=3; NBLOCKS=6; SEED=-1;\
TREATMENTS=variety; REPLICATES=rep; BLOCKS=block; UNITS=plot