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Analysis of variance

Genstat has a comprehensive set of commands to do an analysis of variance. These directives define the models to be fitted:

    BLOCKSTRUCTURE defines the blocking structure of the design, and hence the strata and error terms
    COVARIATE specifies covariates for analysis of covariance
    TREATMENTSTRUCTURE 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. Balanced designs can be analysed using the ANOVA directive.

    ANOVA performs analysis of variance

Directives and procedures are available to produce plots, checks and further output from an ANOVA analysis, or to save information in Genstat data structures:

    ADISPLAY displays further output from analyses produced by ANOVA
    AGRAPH plots tables of means from ANOVA
    APLOT plots residuals from an ANOVA analysis
    AFIELDRESIDUALS display residuals in field layout
ABLUPS calculates BLUPs for block terms in an ANOVA analysis
    ACHECK checks assumptions for an ANOVA analysis
    AMCOMPARISON performs pairwise multiple comparison tests for ANOVA means
    AKEEP copies information from an ANOVA analysis into Genstat data structures
ARESULTSUMMARY provides a summary of results from an ANOVA analysis
    ASPREADSHEET saves results from an analysis of variance in a spreadsheet
A%VARIANCE calculates the percentage variance and sum of squares accounted for in the strata of an ANOVA analysis

Unbalanced designs with a single error term can be be analysed using the AUNBALANCED procedure. (Unbalanced designs with several error terms should be analysed using the commands for REML analysis of linear mixed models.)

    AUNBALANCED performs analysis of variance for unbalanced designs
    AUDISPLAY produces further output for an unbalanced design (after AUNBALANCED)
    AUGRAPH plots tables of means from AUNBALANCED
    AUPREDICT forms predictions from an unbalanced design (after AUNBALANCED)
    AUSPREADSHEET Saves results from an analysis of an unbalanced design (by AUNBALANCED) in a spreadsheet
    AUMCOMPARISON performs pairwise multiple comparison tests for means from an unbalanced analysis of variance, performed previously by AUNBALANCED
    AUKEEP saves output from analysis of an unbalanced design (by AUNBALANCED)

There are also specialized procedures for designs (balanced or unbalanced) with a single error term and one or two treatment factors.

    A2WAY performs analysis of variance of a balanced or unbalanced design with up to two treatment factors
    A2DISPLAY provides further output following an analysis of variance by A2WAY
    A2KEEP copies information from an A2WAY analysis into Genstat data structures
A2RESULTSUMMARY provides a summary of results from an analysis by A2WAY

If you are unsure what method to use, you can use the AOVANYHOW procedure to see which method is most appropriate.

    AOVANYHOW performs analysis of variance using ANOVA, AUNBALANCED, A2WAY or REML as appropriate
    AOVDISPLAY provides further output from an analysis by AOVANYHOW

Other procedures relevant to analysis of variance include:

    ABOXCOX estimates the power λ in a Box-Cox transformation, that maximizes the partial log-likelihood in ANOVA
    AFCOVARIATES defines covariates from a model formula for ANOVA
    AFMEANS forms tables of means classified by ANOVA treatment factors
    ASTATUS provides information about the settings of ANOVA models and variates
    APERMTEST does random permutation tests for analysis-of-variance tables
    ABIVARIATE produces graphs and statistics for bivariate analysis of variance
    ACONFIDENCE calculates simultaneous confidence intervals
    AMDUNNETT forms Dunnett’s simultaneous confidence interval around a control
    AMTIER analyses a multitiered design by analysis of variance specified by up to 3 model formulae
    AMTDISPLAY displays further output for multitiered designs analysed by AMTIER
    AMTKEEP saves information from the analysis of a multitiered design by AMTIER
    ACANONICAL determines the orthogonal decomposition of the sample space for a design, using an analysis of the canonical relationships between the projectors derived from two or more model formulae
    ACDISPLAY provides further output from an analysis by ACANONICAL
    ACKEEP saves information from an analysis by ACANONICAL
    VSPECTRALCHECK forms the spectral components from the canonical components of a multitiered design, and constrains any negative spectral components to zero
    AN1ADVICE aims to give useful advice if a design that is thought to be balanced fails to be analysed by ANOVA
APAPADAKIS analysis of variance with an added Papadakis covariate, formed from neighbouring residuals
    APOLYNOMIAL forms the equation for a polynomial contrast fitted by ANOVA
    ADPOLYNOMIAL plots single-factor polynomial contrasts fitted by ANOVA
    AREPMEASURES produces an analysis of variance for repeated measurements
    ARETRIEVE retrieves an ANOVA save structure from an external file
    ASTORE stores an ANOVA save structure in an external file
    ASCREEN performs screening tests for designs with orthogonal block structure
    AYPARALLEL does the same analysis of variance for several y-variates, and collates the output
    A2RDA saves results from an analysis of variance in R data frames
    AU2RDA saves results from an unbalanced analysis of variance, by AUNBALANCED, in R data frames
FALIASTERMS forms information about aliased model terms in analysis of variance
FWITHINTERMS forms factors to define terms representing the effects of one factor within another factor
    MAANOVA does analysis of variance for a single-channel microarray design (parallel anova)
    SED2ESE calculates effective standard errors that give good approximate standard errors of differences
    SEDLSI calculates least significant intervals
    LSIPLOT plots least significant intervals, saved from SEDLSI
    RTCOMPARISONS calculates comparison contrasts within a multi-way table of means
    A2PLOT plots effects and robust s.e. estimates from designs with two-level factors
    CENSOR pre-processes censored data before analysis by ANOVA
    CINTERACTION clusters rows and columns of a two-way interaction table
    DIALLEL analyses full and half diallel tables with parents
    AMMI allows exploratory analysis of genotype × environment interactions
    FMEGAENVIRONMENTS forms mega-environments based on winning genotypes from an AMMI-2 model
    FRIEDMAN performs Friedman’s nonparametric analysis of variance
    NLCONTRASTS fits non-linear contrasts to quantitative factors in ANOVA
TEQUIVALENCE performs equivalence, non-inferiority and non-superiority tests
    VHOMOGENEITY tests homogeneity of variances
    WSTATISTIC calculates the Shapiro-Wilk test for Normality


Updated on February 7, 2023

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