Generates square lattice and lattice square designs (R.W. Payne).
Options
PRINT = string token |
Controls whether or not to print a plan of the design (design); if unset in an interactive run AGSQLATTICE will ask whether the design is to be printed, in a batch run the default is not to print the design |
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ANALYSE = string token |
Controls whether or not to analyse the design, and produce a skeleton analysis-of-variance table using ANOVA (no, yes); default is to ask if this is unset in an interactive run, and not to analyse if it is unset in a batch run |
DESIGNTYPE = string token |
What type of design to form (squarelattice, latticesquare); default squa |
Parameters
LEVELS = scalars |
Number of treatments in each design |
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NREPLICATES = scalars |
Number of replicates in each design, taken by default to be the maximum number available in a batch run |
SEED = scalars |
Seed for randomization; a negative value implies no randomization |
TREATMENTS = factors |
Identifier for the treatment factor for each design |
PSEUDOFACTORS = pointers |
Identifier for the pseudo-factors required if the design is not a balanced lattice |
REPLICATES = factors |
Identifier for the replicate factor for each design |
BLOCKS = factors |
Identifier for the factor to index the blocks within replicates of a square lattice |
ROWS = factors |
Identifier for the factor to index the rows within replicates of a lattice square |
COLUMNS = factors |
Identifier for the factor to index the columns within replicates of a lattice square |
UNITS = factors |
Identifier for the factor to index the units (or plots) within the blocks of a square lattice |
STATEMENT = texts |
Saves a command to recreate the design (useful if the design information has been specified in response to questions from AGSQLATTICE) |
EXCLUDEREPLICATES = scalars or variates |
Replicates to exclude during randomization |
Description
AGSQLATTICE can form either square lattice or lattice square designs. These are designs for a single treatment factor with a number of levels that is the square of some integer k. The square lattice has replicates, each containing k blocks of k units (or plots), and different treatment contrasts are confounded with blocks in each replicate. The block structure of the design is thus
Replicates / Blocks / Units
Alternatively, the lattice square has a row-by-column structure, with k rows and k columns within each replicate. So the block structure is now
Replicates / (Rows * Columns)
Lattices are used, for example, in variety trials where there are many treatments to examine and the variability of the units is such that the block size needs to be kept reasonably small. For some numbers of treatments, it is possible to generate enough different replicates so that every treatment contrast is confounded with blocks in one of the replicates of a square lattice, or with rows and with columns in one of the replicates in a lattice square. The design is then balanced. If insufficient replicates are available, or if you choose to use less than the full set available, the design is unbalanced and needs pseudo-factors for its analysis by the ANOVA directive. However, AGSQLATTICE can generate these for you automatically.
AGSQLATTICE is easiest to use interactively. It then asks questions to determine the information required to generate the design. Its options and parameters allow you to anticipate questions, or to define all the necessary information if you want to use AGSQLATTICE in batch. However, if 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 DESIGNTYPE option controls whether a square lattice or a lattice square is generated. By default, if you are running Genstat in batch, a square lattice is generated. If you do not set DESIGNTYPE when running interactively, AGSQLATTICE will ask what sort of design you want.
The number of treatments can be defined using the LEVELS parameter. Similarly, the NREPLICATES parameter can define the number of replicates; by default, in a batch run, the maximum available number of replicates is formed. 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 AGSQLATTICE will ask for a seed, and again a negative value suppresses any randomization. You can use the EXCLUDEREPLICATES parameter to specify a scalar or variate giving numbers of replicates that you do not wish to randomize. (This can be useful in “demonstration experiments”, when the treatments may need to be kept in a systematic order in some parts of the trial, but it is not a good idea in more normal situations.)
The TREATMENTS and REPLICATES parameters allow you to specify identifiers for the treatment and replicate factors, and the PSEUDOFACTORS parameter allows you to specify a pointer to represent the pseudo-factors if these are required. The BLOCKS and UNITS parameters specify identifiers for the block-within-replicate and unit-within-block factors of a square lattice, while the ROWS and COLUMNS parameters specify identifiers for the row- and column-within-replicate factors of a lattice square. If any of these parameters is not specified in a batch run, AGSQLATTICE will use an identifier that is local within the procedure and thus lost at the end of the procedure. If you are running interactively, AGSQLATTICE will ask you to provide identifiers, and these will remain available after it has finished running.
AGSQLATTICE has a PRINT option which can be set to design to print the plan of the design. By default, if you are running Genstat in batch, the plan is not printed. If you do not set PRINT when running interactively, AGSQLATTICE will ask whether or not you wish to print the design. Similarly the ANALYSE option governs whether or not AGSQLATTICE produces a skeleton analysis-of-variance table (containing just source of variation, degrees of freedom and efficiency factors). Again AGSQLATTICE assumes that this is not required if ANALYSE is unset in a batch run, and asks whether it is required if ANALYSE is unset in an interactive run.
Options: PRINT, ANALYSE, DESIGNTYPE.
Parameters: LEVELS, NREPLICATES, SEED, TREATMENTS, PSEUDOFACTORS, REPLICATES, BLOCKS, ROWS, COLUMNS, UNITS, STATEMENT, EXCLUDEREPLICATES.
Method
The design is formed by arranging the k×k treatments in a square array. For a square lattice, the blocks of the first replicate are formed from the rows of the array and those of the second replicate from the columns. The blocks for other replicates, if required, are formed using the treatment factors of a set of (NREPLICATES-1) mutually orthogonal k by k Latin squares constructed using procedure AGLATIN. The rows and columns of the k×k array and the treatment factors of the mutually orthogonal Latin squares are used similarly, in pairs, to form the rows and the columns within each of the replicate of the lattice square.
See also
Procedures: AGALPHA, AGCYCLIC.
Commands for: Design of experiments, Analysis of variance.
Example
CAPTION 'AGSQLATTICE example',\
'5 x 5 Lattice with 3 replicates.'; STYLE=meta,plain
AGSQLATTICE [PRINT=design; ANALYSE=yes] LEVELS=25; NREPLICATES=3; SEED=-1;\
TREATMENTS=variety; PSEUDOFACTORS=pf;\
REPLICATES=rep; BLOCKS=block; UNITS=plot
ASTATUS