Generates fractional factorial designs (M.F. Franklin & 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 AGFRACTION will ask whether the design is to be printed, in a batch run the default is not to print the design |
|---|---|
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 |
FACTORIAL = scalar |
Limit on number of factors in treatments terms in the analysis of variance; default 2 |
FILENAME = text |
Name of the backing store file containing the design information; default uses the standard fractional design file |
Parameters
LEVELS = scalars |
Number of levels of the treatment factors in each design |
|---|---|
FRACTION = scalars |
Denominator of required fraction |
NTREATMENTFACTORS = scalars |
Number of treatment factors |
NUNITS = scalars |
Number of units per block |
SEED = scalars |
Seed to be used to randomize each design; a negative value implies no randomization |
TREATMENTFACTORS = pointers |
Specifies identifiers for the treatment factors |
BLOCKS = factors |
Identifier for the block factor |
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 AGFRACTION) |
Description
AGFRACTION generates fractional factorial designs from stored keys & other information. It also sets the block and treatment formulae (using the BLOCKSTRUCTURE and TREATMENTSTRUCTURE directives) to allow the design to be analysed by ANOVA.
The procedure relies upon a backing-store file that contains a repertoire of available designs, together with the information required to form them. There is a standard file, used by default, but the FILENAME option allows you to specify another if you wish to form your own alternative file.
AGFRACTION has two other options. The PRINT option 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, AGFRACTION will ask whether or not you wish to print the design. Similarly the ANALYSE option governs whether or not AGFRACTION produces a skeleton analysis-of-variance table (containing just source of variation, degrees of freedom and efficiency factors). Again AGFRACTION 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. The FACTORIAL option sets a limit on the number of factors in the treatment terms in the analysis of variance; by default, this is two.
The information required to select the design and give identifiers to its factors can be defined using the parameters of AGFRACTION. In an interactive run, AGFRACTION will ask questions to obtain any necessary information that is not supplied in this way; when running in batch, if any of the required information has not been specified, AGFRACTION will terminate with a warning message.
It is thus easiest to use AGFRACTION interactively. Then all the information necessary to select and define the required design will be obtained by (clearly explained) questions. You need set the parameters only if you wish to anticipate some of the questions, or if you wish to use AGFRACTION 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 levels of the treatment factors can be defined using the LEVELS parameter. The FRACTION parameter defines the denominator of the required fraction, and the NTREATMENTFACTOR parameter specifies how many treatment factors the design is to contain. Thus, for example,
AGFRACTION [PRINT=design] LEVELS=2; FRACTION=4; NTREATMENTF=6
would print the plan of a quarter replicate of a 26 design.
For some of the designs it is possible also to allow a blocking factor (and you will be given details of what is feasible if you are running AGFRACTION interactively). The NUNITS parameter can then be used to define the number of units per block.
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 AGFRACTION will ask for a seed, and again a negative value suppresses any randomization.
The TREATMENTFACTORS parameter can specify a pointer to supply identifiers for the treatment factors in the design. For example, if there are two factors you could define their identifiers to be A and B by forming the pointer Tf (say) with the statement
POINTER [VALUES=A,B] Tf
and then setting TREATMENTFACTORS=Tf. Alternatively, and more succinctly, you could put TREATMENTFACTORS=!p(A,B), where !p(A,B) is an unnamed pointer containing the required two identifiers. The remaining parameters, BLOCKS and UNITS, allow you to specify identifiers for the block and unit-within-block factors. If the treatment, block or unit factors are not specified in a batch run, AGFRACTION will use identifiers that are local within the procedure and thus lost at the end of the procedure. If you are running interactively, AGFRACTION will ask you to provide identifiers, and these will remain available after AGFRACTION has finished running.
Options: PRINT, ANALYSE, FACTORIAL, FILENAME.
Parameters: LEVELS, FRACTION, NTREATMENTFACTORS, NUNITS, SEED, TREATMENTFACTORS, BLOCKS, UNITS, STATEMENT.
Method
The QUESTION procedure is used to obtain the details of the required design. The design is then generated using GENERATE and the other standard Genstat directives for calculation and manipulation.
See also
Procedures: AGDESIGN, AGFACTORIAL, AGHIERARCHICAL.
Commands for: Design of experiments, Analysis of variance.
Example
CAPTION 'AGFRACTION example',!t(\
'This example prints the (unrandomized) plan',\
'of a quarter replicate of a 2x2x2x2x2x2.'); STYLE=meta,plain
AGFRACTION [PRINT=design; ANALYSE=no] LEVELS=2; FRACTION=4;\
NTREATMENTFACTORS=6; NUNITS=16; TREATMENTFACTORS=!p(A,B,C,D,E,F);\
SEED=-1
" To see the full repertoire of designs, you should run
AGFRACTION interactively, without setting the parameters."