Design and analysis of experiments
GenStat has a very general algorithm for analysis of variance of balanced experiments. There are
several directives to define the various aspects of model to be fitted:
defines the blocking structure of the design, and hence
the strata and error terms
specifies covariates for analysis of covariance
defines the treatment (or systematic) terms
For unstructured designs with a single error term, BLOCKSTRUCTURE need not be
specified, and COVARIATE is needed only for analysis of covariance. Once the model
has been defined, the y-variates can be analysed using the ANOVA directive:
performs analysis of variance
Directives are available to save information in GenStat data structures, or to produce further
output:
displays further output from analyses produced by
ANOVA
copies information from an
ANOVA analysis into
GenStat data structures
Procedure relevant to analysis of variance, in the aov module of the Library, include:
plots one- or two-way tables of means from
ANOVA
plots residuals from an
ANOVA analysis
display residuals in field layout
provides information about the settings of
ANOVA
models and variates
does random permutation tests for analysis-of-variance
tables
performs analysis of variance of a balanced or unbalanced design
with up to two treatment factors
provides further output following an analysis of variance by
A2WAY
copies information from an
A2WAY analysis into
GenStat data structures
produces graphs and statistics for bivariate analysis of
variance
finds out information about aliased model terms in analysis of
variance
analyses a multitiered design by analysis of variance specified by
up to 3 model formulae
displays further output for multitiered designs analysed by
AMTIER
forms the equation for a polynomial contrast fitted by
ANOVA
produces an analysis of variance for repeated
measurements
performs screening tests for designs with orthogonal block
structure
performs analysis of variance for unbalanced designs
produces further output for an unbalanced design (after
AUNBALANCED)
saves output from analysis of an unbalanced design (by
AUNBALANCED)
does analysis of variance for a single-channel microarray design
(parallel anova)
calculates simultaneous confidence intervals
performs a range of all pairwise multiple comparison
tests
calculates effective standard errors that give good approximate
standard errors of differences
plots effects and robust s.e. estimates from designs with two-level
factors
pre-processes censored data before analysis by
ANOVA
clusters rows and columns of a two-way interaction
table
analyses full and half diallel tables with parents
allows exploratory analysis of genotype × environment
interactions
performs Friedman's nonparametric analysis of variance
fits non-linear contrasts to quantitative factors in
ANOVA
tests homogeneity of variances
The REML algorithm is available for estimating variance components, fitting parameters of
random correlation models and for analysing unbalanced designs.
fits a variance-component model by residual (or restricted) maximum
likelihood
defines the model for
REML
controls advanced aspects of the
REML algorithm
displays further output from a
REML analysis
copies information from a
REML analysis into GenStat
data structures
defines a variance structure for random effects in a
REML model
generates an inverse relationship matrix for use when fitting
animal or plant breeding models by
REML
forms predictions from a
REML model
defines the residual term for a
REML model
prints the current model settings for
REML
Procedures relevant to REML include:
calculates functions of variance components from a
REML analysis
plots residuals from a
REML analysis
Directives are available for generating the values of factors for experimental designs, for finding
good multi-stratum and response-surface designs, for randomization and for constructing model
formulae.
uses the BLKL algorithm to construct response-surface designs
forms design keys for multi-stratum experimental designs, allowing
for confounding and aliasing of treatments
determines patterns of confounding and aliasing from
design keys, calculates resolution numbers, and extends the treatment formula to incorporate the
necessary pseudo-factors
generates values of factors in systematic order or as defined
by a design key, or forms values of pseudo-factors
puts units of vectors into random order, or randomizes units
of an experimental design
forms a model formula using structures supplied in a
pointer
Relevant procedures in the design module of the Library include:
acts as a menu-driven interface to the GenStat design system,
providing a convenient way of selecting and generating various types of factorial design, also
Latin squares, fractional factorial, lattice, alpha, balanced-incomplete-block, Box Behnken, central
composite, cyclic, neighbour-balanced, Plackett Burman, loop and reference-level designs; if you
prefer a command-based interface, the procedures that it uses (
AGDESIGN,
AKEY, AGHIERARCHICAL, AGFRACTION,
AGLATIN, AGCROSSOVERLATIN, AGSEMILATIN,
AGQLATIN, AGSQLATTICE, AGALPHA, AFALPHA,
AGCYCLIC, AFCYCLIC, AGBIB, AGBOXBEHNKEN,
AGCENTRALCOMPOSITE, AGMAINEFFECT, AGNEIGHBOUR,
AGLOOP and AGREFERENCE) can also be called directly
forms a variate of unit labels for a design
prints data forms for an experimental design
forms a factor to index the units of the final stratum of a
design
merges extra units into an experimental design
calculates the power (probability of detection) for terms in an
aov
forms a new experimental design from the product of two
designs
randomizes and prints an experimental design
finds the replication to detect a treatment effect or
contrast
plots the plan of an experimental design
represents a factor by factorial combinations of a set of
factors
forms a factor with a level for every combination of other
factors
breaks a model term down into its basic contrasts
prints or stores treatment combinations tabulated by the block
factors
calculates the replication necessary to detect a treatment
effect
calculates the sample size for binomial tests
calculates the sample size to detect specified
correlations
calculates the sample size for Lin's concordance
coefficient
calculates sample sizes for the Mann-Whitney test
calculates sample sizes for McNemar's test
calculates the sample size to obtain a specified precision
calculates the sample size for a sign test
calculates the sample size for t-tests (including equivalence
tests)
forms factors to represent carry-over effects in cross-over
trials
calculates efficiency of estimating effects in cross-over
designs
estimates the power to estimate contrasts in cross-over
designs