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AFAUGMENTED procedure

Forms an augmented design (R.W. Payne).

Options

PRINT = string tokens Controls printed output (design); default * i.e. none
TREATMENTSTRUCTURE = formula Treatment terms, other than GENOTYPES, to be included in the analysis
BLOCKSTRUCTURE = formula Defines the block structure of the basic design
COVARIATE = variates Specifies any covariates to be included in the analysis
LEVTEST = variate Levels to represent the test genotypes in the augmented GENOTYPES factor
LEVCONTROL = scalar or variate Levels to represent the control genotype(s) if these are not already in the GENOTYPES factor
GENOTYPES = factor Genotype factor
CONTROLS = factor Factor identifying the controls
TESTVSCONTROL = factor Factor representing the comparison between test and control genotypes
SUBPLOTS = factor Factor to represent the subplots to be created for the test genotypes in the basic design
NSUBPLOTS = scalar Number of subplots to create within each plot of the basic design
SUBCONTROLS = scalar or variate Subplots to be used for control genotypes, if not already pre-allocated in the GENOTYPES and SUBPLOTS factors; default selects subplots for the controls at random within each whole-plot
NREPTEST = scalar or variate Number of times to replicate the test genotypes; default 1
SEED = scalar Seed for the random numbers used to randomize the allocation of the genotypes (a negative value implies no randomization); default 0

No parameters

Description

An augmented design is a design for assessing large numbers of treatments, usually test genotypes in a variety trial. The trial also contains controls; these are replicated while the tests are usually unreplicated.

The design is constructed from a basic design, which can be any standard design, for example, a randomized complete block design or a Latin square. In the simplest situation, a control genotype is allocated to each plot of the basic design. The design is then expanded, or augmented, so that each plot of the basic design is split into subplots. (So the plots of the basic design become the whole-plots of the augmented design.) The control genotype is allocated to one of the subplots in each plot, and test genotypes are allocated to the other subplots.

So you first need to generate the basic design, using a procedure like AGHIERARCHICAL or AGLATIN. You can then use AFAUGMENTED to augment it.

In the simplest situation, the basic design has blocking factors identifying its plots, and a treatment factor defined to indicate the control genotype allocated to each plot. For example, Lin & Poushinsky (1983) used a 4 × 4 Latin square as their basic design, with 4 different control genotypes. In Genstat this can be constructed using AGLATIN

POINTER [VALUES=Genotypes] tfact

AGLATIN [PRINT=*; ANALYSE=no] NROWS=4; NSQUARES=1; SEED=584578;\

            TREATMENTFACTORS=tfact; ROWS=Rows; COLUMNS=Columns

They then split each plot into 9 subplots, allocating the control to subplot 5 in each plot, and randomly allocated 128 test genotypes to the other subplots across the design. The Genstat command to do this is

VARIATE [VALUES=5...132] Tests

AFAUGMENTED [PRINT=design; BLOCKSTRUCTURE=Rows*Columns;\

            LEVTEST=Tests; GENOTYPES=Genotypes;\

            NSUBPLOTS=9; SUBCONTROLS=5]

The BLOCKSTRUCTURE option specifies the blocking structure of the basic design (here rows crossed with columns), and thus the blocking factors that need to be expanded. The GENOTYPES option specifies the genotypes factor which, on input, indicates the control genotype on each plot. The NSUBPLOTS option specifies the number of subplots to define within each plot, and the SUBCONTROL option specifies the subplot(s) to contain the control(s). The LEVTEST option specifies which levels of the augmented GENOTYPES factor are to represent the test genotypes. Setting option PRINT=design prints the design, using procedure PDESIGN; by default it is not printed.

Note that, if there are insufficient test genotypes, some plots may contain NSUBPLOTS minus one subplots. An error is given if there are too few genotypes for any of the plots to contain NSUBPLOTS subplots.

The SEED option specifies a seed for the random numbers that are used to make the allocations. The default value of zero continues an existing sequence of random numbers if any have already been used in the current Genstat job, or obtains a random seed using the system clock if none have been used already. You can also set SEED=-1 if you want to suppress any randomization.

If the design has other treatments (as well as GENOTYPES), these can be specified using the TREATMENTSTRUCTURE option. This takes a model formula as its setting (so you would define the treatment terms that are to be included in the analysis). However, but it is sufficient just to list the factors if you prefer. These will then be expanded similarly to the blocking factors. Likewise, if you have covariates whose values are defined on the plots of the basic design, these can be specified using the COVARIATE option.

You can use the CONTROLS option to save a factor with a level for each control, and another level for all the test genotypes. You can also use the TESTVSCONTROL option to save a factor with one level for the control genotypes, and another level for the test genotypes. (These will be identical if there is only one control genotype.)

If you want to specify several controls in each whole-plot of the augmented design, you can define the basic design to have subplots already, namely those with the controls. For example, the program below has a balanced-incomplete-block design for three treatments as the basic design. The first block has controls 1 and 3, the second has 2 and 3, and the third has 1 and 2. So we start with two subplots. The AFAUGMENTED command expands the design to have eight subplots, adding 18 test genotypes. . The SUBCONTROLS option is now set to a variate to put the controls onto subplots 3 and 6, randomizing the allocation within each plot.

FACTOR [LEVELS=3; VALUES=1,1,2,2,3,3] Blocks

FACTOR [LEVELS=3; VALUES=1,3,2,3,1,2] Genotypes

VARIATE [VALUES=101...118] Tests

VARIATE [VALUES=3,6] Csubs

AFAUGMENTED [PRINT=design; BLOCKSTRUCTURE=Blocks;\

            LEVTEST=Tests; GENOTYPES=Genotypes;\

            NSUBPLOTS=8; SUBCONTROL=Csubs]

You can predefine the SUBPLOTS factor if you want to allocate the controls to the subplots explicitly, yourself. For example,

FACTOR [LEVELS=32; VALUES=2,6...30] plots

FACTOR [LEVELS=2; VALUES=(1,2)4] genotypes

AFAUGMENTED [SUBPLOTS=plots; LEVTEST=!(3...26);\

            GENOTYPES=genotypes; CONTROLS=controls]

puts control 1 in block 1 explicitly onto subplot 2, and control 2 in block 1 explicitly onto subplot 6, etc. The NSUBPLOTS option of AFAUGMENTED then need not be set, but will default to the number of levels defined for SUBPLOTS. Of course, if you do predefine the SUBPLOTS factor, you no longer need to have the same number of controls in each plot.

You can even define a null basic design. The “augmented” design will then simply consist of some control and test genotypes allocated to the (sub)plots within the field (with the SUBPLOTS and SUBCONTROL options determining the allocation of the controls as before). For example:

FACTOR [LEVELS=32; VALUES=2,6...30] plots

FACTOR [LEVELS=2; VALUES=(1,2)4] genotypes

VARIATE [VALUES=3...26] tests

AFAUGMENTED [SUBPLOTS=plots; LEVTEST=tests;\

            GENOTYPES=genotypes; CONTROLS=controls]

By default, the test genotypes are unreplicated. You can set the NREPTEST option to a scalar to replicate every test genotype the same number of times, or to a variate to have different numbers of replicates (as, for example. in a partially-replicated design).

Options: PRINT, TREATMENTSTRUCTURE, BLOCKSTRUCTURE, COVARIATE, LEVTEST, LEVCONTROL, GENOTYPES, CONTROLS, TESTVSCONTROL, SUBPLOTS, NSUBPLOTS, SUBCONTROL, NREPTEST, SEED.

Parameters: none.

Action with RESTRICT

The procedure does not allow for restrictions, and will cancel any that have been applied.

Reference

Lin, C.S. & Poushinsky, G. (1983). A modified augmented design for an early stage of plant selection involving a large number of test lines without replication. Biometrics, 39, 553-561.

See also

Commands for: Design of experiments.

Example

CAPTION     'AFAUGMENTED example',\
            !t('This generates an augmented design based on a 4x4 Latin',\
            'square, as in Lin & Poushinsky (1983, Biometrics).');\
            STYLE=meta,plain
AGLATIN     [PRINT=*; ANALYSE=no] NROWS=4; NSQUARES=1; SEED=584578;\
            TREATMENTFACTORS=!p(Genotype); ROWS=Row; COLUMNS=Column
AFAUGMENTED [PRINT=design; BLOCKSTRUCTURE=Row*Column;\
            LEVTEST=!(5...132); LEVCONTROL=5; GENOTYPES=Genotype;\
            NSUBPLOTS=9; SUBCONTROL=5; TESTVSCONTROL=TvsC; CONTROLS=Control]
PRINT       TvsC,Genotype,Control,Row,Column

CAPTION     !t('This has a balanced-incomplete-block design',\
            'as its basic design, showing how to form a design',\
            'with more than one control per whole-plot.')
FACTOR      [LEVELS=3; VALUES=1,1,2,2,3,3] Blocks
FACTOR      [LEVELS=3; VALUES=1,3,2,3,1,2] Genotypes
AFAUGMENTED [PRINT=design; BLOCKSTRUCTURE=Blocks; LEVTEST=!(101...118);\
            GENOTYPES=Genotypes; NSUBPLOTS=8; SUBCONTROL=!(3,6)]

CAPTION     !t('This has a null basic design, showing how to form a design',\
            'with systematic repeating controls.')
" design with systematic repeating controls "
FACTOR      [LEVELS=32; VALUES=2,6...30] plots
FACTOR      [LEVELS=2; VALUES=(1,2)4] genotypes
AFAUGMENTED [SUBPLOTS=plots; LEVTEST=!(3...26);\
            GENOTYPES=genotypes; CONTROLS=controls]
PRINT       plots,genotypes,controls
Updated on March 11, 2019

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