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AFMEANS procedure

Forms tables of means classified by ANOVA treatment factors (R.W. Payne).


PRINT = string tokens What to print (means, sed, sedsummary, ese, lsd, lsdsummary); default mean, sed
MEANS = table Saves means; default *
SED = symmetric matrix Saves matrices of standard errors of differences between means; default *
ESE = table Saves effective standard errors; default *
LSD = symmetric matrix Saves least significant differences between means; default *
LSDLEVEL = scalar Significance level (%) for least significant differences; default 5
DFMEANS = symmetric matrices Saves degrees of freedom for comparisons between every pair of entries in the table of means
EQFACTORS = factors Factors whose levels are to be assumed to be equal within the comparisons between means, when calculating effective standard errors
SAVE = ANOVA save structure Save structure to provide the table of means; default uses the save structure from the most recent ANOVA


CLASSIFY = vectors Factors to classify table of means (from those in the TREATMENTSTRUCTURE in the ANOVA analysis)


AFMEANS calculates and prints tables of predicted means classified by treatment factors from an ANOVA analysis. It uses the same method as ANOVA itself, but with the extension that the term defined by the full list of factors need not have been included in the analysis. So, for example, you can obtain an A × B table of means, even if the model contained only the A and B main effects. Alternatively, in a more realistic scenario, you may have significant A.B and B.C interactions, but no A.B.C interaction. You might then still want to present an A × B × C table means, even though you might not want to include an A.B.C interaction.

The factors classifying the table of means are specified by the CLASSIFY parameter. By default the means are formed for the most recent ANOVA, but you can use the SAVE option to supply the save structure from an earlier analysis.

Printed output is controlled by settings of the PRINT option:

    means means,
    ese effective standard errors of the means,
    sed standard errors for differences between the means,
    sedsummary summary of the standard errors for differences between the means,
    dfmeans degrees of freedom for the standard errors of differences between means,
    lsd least significant differences between the means, and
    lsdsummary summary of the least significant differences between the means.

The default is to print means and a summary of the standard errors of differences. Note: if all the differences between means have the same standard error of difference, a summary is printed for the settings sed and lsd, instead of the full symmetric matrix of values. The LSDLEVEL option specifies the significance level (%) to use in the calculation of least significant differences (default 5%). The EQFACTORS option allows you to specify factors within the tables of means whose levels are assumed to be equal for the two means, when calculating effective standard errors.

The MEANS, SED, ESE, LSD and DFMEANS options allow the results to be saved in appropriate Genstat data structures.


Parameter: CLASSIFY.

See also

Directive: ANOVA.

Procedure: AUPREDICT.

Commands for: Analysis of variance.


CAPTION    'AFMEANS example',!t('Split plot design, see the',\
           'Guide to Genstat, Part 2, Section 4.2.1.'); STYLE=meta,plain
SPLOAD     [PRINT=*] '%GENDIR%/Data/Oats.gsh'
" Convert yields to cwt per acre."
CALCULATE  yield=(yield*80)/(112*4)
" Subplots nested within whole-plots nested within blocks."
BLOCK      blocks/wplots/subplots
" Define the treatment model with only main effects of variety & nitrogen."
TREATMENTS variety+nitrogen
ANOVA      [PRINT=aov,means; PSE=means,differences] yield
" Calculate variety-by-nitrogen predicted means."
AFMEANS    [PRINT=means,sed,ese,dfmeans; SED=sed; DFMEANS=dfm]\
Updated on June 20, 2019

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