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

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 designs

COVDESIGN
produces experimental designs efficient under analysis of covariance

PDESIGN
prints treatment combinations tabulated by the block factors

DDESIGN
plots the plan of a design

AFORMS
prints data forms for a design



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

ASAMPLESIZE
finds the replication (sample size) to detect a treatment effect or contrast

RPOWER
calculates the power (probability of detection) for regression models

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

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


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, and for determining how many replicates are needed. There is also a directive for constructing response-surface designs. The relevant commands include the directives


AFRESPONSESURFACE
uses the BLKL algorithm to construct designs for estimating response surfaces

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

 

AFLABELS
forms a variate of unit labels for a design

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

APRODUCT
forms a new experimental design from the product of two designs

ARANDOMIZE
randomizes and prints an experimental design

COVDESIGN
produces experimental designs efficient under analysis of covariance

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

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