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9 Commands for analysis of varianceThis optional () chapter introduces the main commands that are used for analysis ofvariance in GenStat. The full descriptions, however, are in the GenStat Reference Manual(Part 2 for directives, or Part 3 for Procedures) or in the Guide to the GenStat CommandLanguage. These can both be accessed on line, from the Help menu on the GenStat menubar.Most of the menus described in this course use the ANOVA directive, which analysesgenerally balanced designs. These include most of the commonly occurring experimentaldesigns such as randomized blocks, Latin squares, split plots and other orthogonaldesigns, as well as designs with balanced confounding, like balanced lattices andbalanced incomplete blocks. Many partially balanced designs can also be handled, usingpseudo factors, so a very wide range of designs can be analysed.Before using ANOVA we first need to define the model that is to be fitted in the analysis.Potentially this has three parts. The BLOCKSTRUCTURE directive defines the "underlyingstructure" of the design or, equivalently, the error terms for the analysis; in the simplecases where there is only a single error term this can be omitted. TheTREATMENTSTRUCTURE directive specifies the treatment (or systematic, or fixed) termsfor the analysis. The other directive, COVARIATE, lists the covariates if an analysis ofcovariance is required. Alternatively, the AFCOVARIATES procedure can definecovariates from a model formula, for example to fit a different regression coefficient forevery level of a factor like blocks; it calculates the variates required to represent thecovariates and then specifies them as covariates for the analysis using the COVARIATEdirective.At the start of a job all these model-definition directives have null settings. However,once any one of them has been used, the defined setting remains in force for allsubsequent analyses in the same job until it is redefined.For example, the statements below were generated by the One-way ANOVA (no Blocking)menu to analyse the example in Section 1.5."One-way ANOVA (no Blocking)."BLOCK "No Blocking"TREATMENTS dietCOVARIATE "No Covariate"ANOVA [PRINT=aovtable,information,mean; FPROB=yes] weightThe BLOCK (or, in full, BLOCKSTRUCTURE) directive is given a null setting to cancel anyexisting setting; so this indicates that the design is unstructured and has a single errorterm. Similarly, the COVARIATE statement cancels any covariates that may have been setin an earlier menu. The TREATMENTS (or, in full, TREATMENTSTRUCTURE) directive isused to specify that we have a single term in the analysis, the main effect of diet.The first parameter of the ANOVA directive specifies the y-variate to be analysed. ThePRINT option is set to a list of strings to select the output to be printed. These are similarto the check boxes of the Further Output menu. The most commonly used settings are:aovtableanalysis-of-variance table,informationdetails of large residuals, non-orthogonality andany aliasing in the model,covariatesestimated coefficients and standard errors of any