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  2. AFCOVARIATES procedure


Defines covariates from a model formula for ANOVA (R.W. Payne).


COVARIATES = pointer Saves the covariates
COVGROUPS = pointer Saves the pointers defined to contain the covariates formed for each term in TERMS
FACTORIAL = scalar Limit on number of factors in the model terms formed from TERMS; default 3


TERMS = formula Model terms from which to define covariates


Analysis of covariance is performed in Genstat using the ANOVA directive. The treatment model must be specified first, using the TREATMENTSTRUCTURE directive, and the underlying structure of the design (or, equivalently, the error terms for the analysis) is specified using the BLOCKSTRUCTURE directive as in ordinary analysis of variance. The extra step for analysis of covariance is to specify the covariates for the analysis using the COVARIATE directive. The covariates must be continuous variables, and so COVARIATE requires a list of variates. Alternatively, a refinement introduced in Release 12 allows you to put some of the covariates into pointers. The covariates in each pointer will then be pooled into a single line in the analysis of variance table.

However, COVARIATE does not allow for more complicated situations. For example you might want to fit a different covariate regression coefficient within each block of a randomized-block experiment, or to use the covariate to fit the effects of terms in an unbalanced design.

The AFCOVARIATES procedure has therefore been provided as an alternative to the COVARIATE directive, to allow you to specify a model formulae to define the terms to be fitted as covariates in the analysis. The model formula is specified by the TERMS parameter, using the same conventions as for example in the Genstat regression commands. The dummy variables that are generated to represent the model terms in the formula use the same parameterization as the regression commands; see Section 3.3.2 of the Guide to the Genstat Command Language, Part 2 Statistics for details.

So, for example, you can fit a different regression coefficient for the variate X within each block defined by the factor Blocks, by specifying


The COVARIATES option allows you to supply a pointer to store the covariates that are calculated (otherwise they will be unnamed, and thus usable only by later ANOVA commands). The covariates are grouped into a pointer for each model term specified by TERMS. The COVGROUPS option allows you to supply a pointer to store these pointers (otherwise they too will be unnamed, and thus usable only by later ANOVA commands). Each covariate is each defined with an extra text, using the EXTRA parameter of the VARIATE directive, to indicate the parameter that it represents. Also the IPRINT option of VARIATE is set to extra, so that this extra text will be used in output instead of the identifier of the covariate itself. Similarly, the COVGROUPS pointers are given extra texts indicating the model term that each one represents.

The FACTORIAL option sets a limit on the number of factors or variates in each of the terms formed from the TERMS formula. Any term containing more than that limit is deleted.


Parameter: TERMS.


AFCOVARIATES defines the covariates from a design matrix constructed using the TERMS directive.

Action with RESTRICT

AFCOVARIATES takes account of any restrictions on the factors or variates in the TERMS formula.

See also


Commands for: Analysis of variance.


CAPTION      'AFCOVARIATES example',!t(\
             'Completely randomized experiment with covariate',\
             'Snedecor & Cochran, p.377'); STYLE=meta,plain
FACTOR       [NVALUES=30; LABELS=!T(A,B,C)] Drug
READ         Drug,X,Y; FREPRESENTATION=labels
A 11  6    B  6  0    C 16 13
A  8  0    B  6  2    C 13 10
A  5  2    B  7  3    C 11 18
A 14  8    B  8  1    C  9  5
A 19 11    B 18 18    C 21 23
A  6  4    B  8  4    C 16 12
A 10 13    B 19 14    C 12  5
A  6  1    B  8  9    C 12 16
A 11  8    B  5  1    C  7  1
A  3  0    B 15  9    C 12 20  :
" common covariate regression coefficient over drugs "
ANOVA        [PRINT=aov,covariates; FPROBABILITY=yes] Y
" try different a different covariate regression coefficient for each drug
  (analysis will show that X.Drug B and X.Drug C are non significant, so
  only a common coefficient is needed) "
ANOVA        [PRINT=aov,covariates; FPROBABILITY=yes] Y
Updated on June 20, 2019

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