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Design of experiments

Genstat has a comprehensive set of facilities for design of experiments. Collectively, these are known as the Genstat Design System. Many different design types are covered, each with a procedure that allows you to view and choose from the available possibilities. Other procedure allow designs and data forms to be displayed. There is also a general procedure DESIGN that can be used interactively to provide a single point of access to all the design types. DESIGN and the AG… procedures that it calls provide the Select Design facilities in Genstat for Windows, while the alternative Standard Design menu uses AGHIERARCHICAL, AGLATIN and AGSQLATTICE to generate completely randomized designs, randomized blocks, Latin and Graeco-Latin squares, split-plots, strip-plots (or criss-cross designs) and lattices.

    DESIGN provides a menu-driven interface for selecting and generating experimental designs
    AGALPHA forms alpha designs for up to 100 treatments
    AGBIB generates balanced-incomplete-block designs
    AGBOXBEHNKEN generates Box-Behnken designs
    AGCENTRALCOMPOSITE generates central composite designs
    AGCROSSOVERLATIN generates Latin squares balanced for carry-over effects
    AGCYCLIC generates cyclic designs from standard generators
    AGDESIGN generates generally balanced designs – factorial designs with blocking, fractional factorial designs, Lattice squares etc.
    AGFACTORIAL generates minimum aberration complete and fractional factorial designs
    AGFRACTION generates fractional factorial designs
    AGHIERARCHICAL generates orthogonal hierarchical designs
provides a menu-driven interface for selecting and generating designs for industrial experiments
    AGLATIN generates mutually orthogonal Latin squares
    AGLOOP generates loop designs e.g. for time-course microarray experiments
    AGMAINEFFECT generates designs to estimate main effects of two-level factors
    AGNEIGHBOUR generates neighbour-balanced designs
    AGQLATIN generates complete and quasi-complete Latin squares
    AGREFERENCE generates reference-level designs e.g. for microarray experiments
    AGSEMILATIN generates semi-Latin squares
    AGSQLATTICE generates square lattice and lattice square designs
AGYOUDENSQUARE generates a Youden square
    PDESIGN prints treatment combinations tabulated by the block factors
    DDESIGN plots the plan of a design
    ADSPREADSHEET puts the data and plan of an experimental design into Genstat spreadsheets

There are also procedures that you can use to determine the sample size (i.e. replication) required for experiments that are to be analysed by analysis of variance, t-test or various non-parametric tests. You can also calculate the power (or probability of detection) for terms in analysis of variance or regression analyses.

    APOWER calculates the power (probability of detection) for terms in an analysis of variance
    RPOWER calculates the power (probability of detection) for regression models
    VPOWER uses a parametric bootstrap to estimate the power (probability of detection) for terms in a REML analysis
    ASAMPLESIZE finds the replication (sample size) to detect a treatment effect or contrast
    VSAMPLESIZE estimates the replication to detect a fixed term or contrast in a REML analysis, using parametric bootstrap
    ADETECTION calculates the minimum size of effect or contrast detectable in an analysis of variance
    SBNTEST calculates the sample size for binomial tests
    SCORRELATION calculates the sample size to detect specified correlations
    SLCONCORDANCE calculates the sample size for Lin’s concordance coefficient
    SMANNWHITNEY calculates the sample size for the Mann-Whitney test
    SMCNEMAR calculates the sample size for McNemar’s test
    SPNTEST calculates the sample size for a Poisson test
    SPRECISION calculates the sample size to obtain a specified precision
    SSIGNTEST calculates the sample size for a sign test
    STTEST calculates the sample size for t-tests, including equivalence tests and tests for non-inferiority
    DSTTEST plots power and significance for t-tests, including equivalence tests and tests for non-inferiority

The Design System is based on a range of standard generators. Some of these, such as the Galois fields used to generate Latin squares, can be formed when required – and so there is no limitation on the available designs. Repertoires of others, such as design keys, are stored in backing-store files which are scanned by the design generation procedures to form menus listing the available possibilities. Algorithms are available to form generators for new designs, and these can then be added to the design files to become an integral part of the system. Other design utilities include procedures for combining simple designs into more complicated arrangements, for forming augmented designs, and for determining how many replicates are needed. There are also directives for constructing response-surface designs and doubly resolvable row-column designs. The relevant commands include the directives

    AFMINABERRATION forms minimum aberration factorial or fractional-factorial designs
    AFRESPONSESURFACE uses the BLKL algorithm to construct designs for estimating response surfaces
    AGRCRESOLVABLE forms doubly resolvable row-column designs
    GENERATE generates values of factors in systematic order or as defined by a design key, or forms values of pseudo-factors
    RANDOMIZE puts units of vectors into random order, or randomizes units of an experimental design
    FKEY forms design keys for multi-stratum experimental designs, allowing for confounding and aliasing of treatments
    FPSEUDOFACTORS determines patterns of confounding and aliasing from design keys, and extends the treatment formula to incorporate the necessary pseudo-factors
    SET2FORMULA forms a model formula using structures supplied in a pointer

and the procedures.

    AEFFICIENCY calculates efficiency factors for experimental designs
    AFAUGMENTED forms an augmented design
    AFLABELS forms a variate of unit labels for a design
  AFRCRESOLVABLE forms doubly resolvable row-column designs, with output
    AFUNITS forms a factor to index the units of the final stratum of a design
    AKEY generates values for treatment factors using the design key method
    AMERGE merges extra units into an experimental design
    AFNONLINEAR forms D-optimal designs to estimate the parameters of a nonlinear or generalized linear model
    AFPREP searches for an efficient partially-replicated design
    APRODUCT forms a new experimental design from the product of two designs
AGNATURALBLOCK generates 1- and 2-dimensional designs with blocks of natural size
AGNONORTHOGONALDESIGN generates non-orthogonal multi-stratum designs
AGSPACEFILLINGDESIGN generates space filling designs
ARCSPLITPLOT adds extra treatments onto the replicates of a resolvable row-column design, and generates factors giving the row and column locations of the plots within the design
   ARANDOMIZE randomizes and prints an experimental design
   CDNAUGMENTEDDESIGN constructs an augmented block design, using CycDesigN if the controls are in an incomplete-block design
   CDNBLOCKDESIGN  constructs a block design using CycDesigN
   CDNPREP  constructs a multi-location partially-replicated design using CycDesigN
   CDNROWCOLUMNDESIGN  constructs a row-column design using CycDesigN
    COVDESIGN produces experimental designs efficient under analysis of covariance
    FACCOMBINATIONS forms a factor to indicate observations with identical combinations of values of a set of variates, texts or factors
    FACDIVIDE represents a factor by factorial combinations of a set of factors
    FACPRODUCT forms a factor with a level for every combination of other factors
    FBASICCONTRASTS forms the basic contrasts of a model term
    FCOMPLEMENT forms the complement of an incomplete block design
    FDESIGNFILE forms a backing-store file of information for AGDESIGN
    FHADAMARDMATRIX forms Hadamard matrices
    FOCCURRENCES forms a “concurrence” matrix recording how often each pair of treatments occurs in the same block of a design
    FPLOTNUMBER forms plot numbers for a row-by-column design
    FPROJECTIONMATRIX forms a projection matrix for a set of model terms
    XOEFFICIENCY calculates the efficiency for estimating effects in cross-over designs
    XOPOWER estimates the power of contrasts in cross-over designs


Updated on February 7, 2023

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