Generates designs to estimate main effects of two-level factors (R.W. Payne).
Options
PRINT = string token |
Controls printed output (design, catalogue); if unset in an interactive run AGMAINEFFECT will ask whether the design or catalogue are to be printed, in a batch run the default is not to print anything |
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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 |
FOLDED = string token |
Whether to include an extra “folded” replicate with the levels of each factor interchanged (no, yes); default no |
SEED = scalar |
Seed to be used to randomize each design; a negative value implies no randomization |
STATEMENT = texts |
Saves a command to recreate the design (useful if the design information has been specified in response to questions from AGMAINEFFECT) |
Parameter
TREATMENTFACTOR = factors |
Treatment factors |
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Description
AGMAINEFFECT generates designs for estimating main effects of factors with two levels, using a minimum number of experimental units; see Plackett & Burman (1946). The numbers of treatment factors for which designs are available can be printed by setting option PRINT=catalogue. They are, however, all expressible as 4n-1 for some integer n. The treatment factors are listed using the TREATMENTFACTOR parameter. If this is omitted in an interactive run, you will be asked how many factors you want and their names.
The basic design allows the main effects to be estimated, but has no residual degrees of freedom. This is fine if you merely want to screen the main effects to identify the largest. Otherwise you can generate a design for more factors than are needed, and then use the degrees of freedom of the unnecessary factors to provide the residual. Alternatively, if you set option FOLDED=yes, AGMAINEFFECT will include a “folded” replicate of the design: this is identical to the initial replicate except that the levels of the factors are swapped (level one instead of level two and vice versa). This particular arrangement has the advantage that no main effect is aliased with any first-order interaction.
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 AGMAINEFFECT will ask for a seed, and again a negative value suppresses any randomization. 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, AGMAINEFFECT will ask whether or not you wish to print the design. Similarly the ANALYSE option governs whether or not AGMAINEFFECT produces a skeleton analysis-of-variance table (containing just source of variation, degrees of freedom and efficiency factors). Again AGMAINEFFECT 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 ANOVA option ORTHOGONAL is set to yes for the analysis. (If this is not done, the larger designs can take a very long time to analyse.)
The STATEMENT option allows you to save a Genstat text structure containing a command to recreate the design. This is particularly useful if AGMAINEFFECT is being used interactively, and the information to define the design has been provided in response to questions from the procedure.
Options: PRINT, ANALYSE, FOLDED, SEED, STATEMENT.
Parameter: TREATMENTFACTOR.
Method
The designs are based on Hadamard matrices, which can be generated by procedure FHADAMARDMATRIX. The QUESTION procedure is used to obtain the necessary details of the design and this is then generated by the standard Genstat manipulation directives.
Reference
Plackett, R.L. & Burman, J.P. (1946). The design of optimum factorial experiments. Biometrika, 33, 305-325 & 328-332.
See also
Directive: AFRESPONSESURFACE.
Procedures: AGBOXBEHNKEN, AGCENTRALCOMPOSITE, AGFACTORIAL, FHADAMARDMATRIX.
Commands for: Design of experiments.
Example
CAPTION 'AGMAINEFFECT example'; STYLE=meta AGMAINEFFECT [PRINT=design; ANALYSE=yes] A,B,C,D,E,F,G