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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