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AOVDISPLAY procedure

Provides further output from an analysis by AOVANYHOW (R.W. Payne).


PRINT = string tokens Controls printed output from the analysis (aovtable, information, means, residuals); default aovt, info, mean
FPROBABILITY = string token Printing of probabilities for variance ratios in the analysis-of-variance table (yes, no); default no
PLOT = string tokens Which residual plots to provide (fittedvalues, normal, halfnormal, histogram); default * i.e. none
COMBINATIONS = string token Factor combinations for which to form predicted means (present, estimable); default esti
ADJUSTMENT = string token Type of adjustment to be made when predicting means (marginal, equal, observed); default marg
PSE = string tokens Types of standard errors to be printed with the predicted means (differences, alldifferences, lsd, alllsd, means; default diff
LSDLEVEL = scalar Significance level (%) for least significant differences; default 5
EFLOSS = scalar Maximum loss of efficiency occurring on any treatment contrast if the analysis is done by regression
EXIT = scalar Code indicating the method of analysis


SAVE = identifiers Save structure from AOVANYHOW; default uses the save structure from the most recent AOVANYHOW analysis


The AOVANYHOW procedure assesses a data set to select the most appropriate method for analysis of variance. If the design is orthogonal or balanced it uses the ANOVA directive. Otherwise, if there is no blocking in the design (i.e. there is only one random term) it uses the Genstat regression facilities through procedure A2WAY or AUNBALANCED. Finally, if there are additional random terms, it looks to see if these contain any useful information about the treatments in order to choose between regression and REML.

This procedure, AOVDISPLAY, allows further output to be produced from an analysis by AOVANYHOW. By default, the output is from the most recent analysis done by AOVANYHOW. However, you can print the output from an earlier analysis by setting the SAVE parameter to a pointer containing the analysis information, saved earlier using the SAVE parameter of AOVANYHOW.

The printed output is controlled by the PRINT option. The settings are limited to those that can produce analogous output from any of the analysis methods:

    aovtable analysis-of-variance table from ANOVA or regression, or Wald and F tests for fixed effects from REML,
    information design type, efficiency factors and name of the command used for the analysis,
    means tables of (predicted) means, and
    residuals residuals (fitted values are printed too for analyses by regression or REML).

Probabilities can be printed for variance ratios by setting option FPROBABILITY=yes.

Tables of means from regression and REML are calculated using the PREDICT and VPREDICT directives, respectively. The first step (A) of their calculations forms the full table of predictions, classified by every factor in the model. The second step (B) averages the full table over the factors that do not occur in the table of means. The COMBINATIONS option specifies which cells of the full table are to be formed in Step A. The default setting, estimable, fills in all the cells other than those that involve parameters that cannot be estimated, for example because of aliasing. Alternatively, setting COMBINATIONS=present excludes the cells for factor combinations that do not occur in the data. The ADJUSTMENT option then defines how the averaging is done in Step B. The default setting, marginal, forms a table of marginal weights for each factor, containing the proportion of observations with each of its levels; the full table of weights is then formed from the product of the marginal tables. The setting equal weights all the combinations equally. Finally, for regression analyses, the setting observed uses the WEIGHTS option of PREDICT to weight each factor combination according to its own individual replication in the data.

The PSE option controls the types of standard errors that are produced to accompany the tables of means, with settings:

    differences summary of standard errors for differences between pairs of means,
    alldifferences standard errors for differences between all pairs of means,
    lsd summary of least significant differences between pairs of means,
    alllsd least significant differences between all pairs of means,
    means effective standard errors for analyses by ANOVA, or approximate effective standard errors for analyses by regression or REML – these are formed by procedure SED2ESE with the aim of allowing good approximations to the standard errors for differences to be calculated by the usual formula of sedi,j = √( esei2 + esej2 ).

The default is differences. The LSDLEVEL option sets the significance level (as a percentage) for the least significant differences.

The PLOT option allows various residual plots to be requested: fittedvalues for a plot of residuals against fitted values, normal for a Normal plot, halfnormal for a half Normal plot, and histogram for a histogram of residuals.

You can save a scalar indicating the recommended method of analysis by using the EXIT option. The scalar can take values with the following meanings.

0.   The design is orthogonal. Analyse by ANOVA.

1.   The design is balanced. Analyse by ANOVA.

2.   The design unbalanced. It has 1 or 2 treatment factors and no blocking. Analyse by A2WAY.

3.   The design unbalanced and has 1 or 2 treatment factors. No more than a proportion defined by the EFLIMIT option of the information on any treatment contrast is estimated between block terms. Analyse by A2WAY.

4.   The design unbalanced, and there are either weights or more than 2 treatment factors. There is no blocking. Analyse by AUNBALANCED.

5.   The design is unbalanced, and there either are weights or more than 2 treatment factors. No more than a proportion defined by the EFLIMIT option of the information on any treatment contrast is estimated between block terms. Analyse by AUNBALANCED.

6.   The design unbalanced with several block (i.e. random) terms. Analyse by REML.

The EFLOSS option can save the maximum loss of efficiency that would occur on any treatment contrast if the analysis is done by regression.


Parameter: SAVE.

Action with RESTRICT

If the Y variate or any of the factors or covariates was restricted, only the units not excluded by the restriction will have been analysed.

See also

Procedure: AOVANYHOW.

Commands for: Analysis of variance.


CAPTION  'AOVANYHOW example 1',\
         'Split plot design, see Guide to Genstat, Part 2, Section 4.2.1.';\
&        [LEVELS=3] Wplots
&        [LEVELS=4] Subplots
GENERATE Blocks,Wplots,Subplots
FACTOR   [LABELS=!T('0 cwt','0.2 cwt','0.4 cwt','0.6 cwt')] Nitrogen
&        [LABELS=!T(Victory,'Golden rain',Marvellous)]      Variety
VARIATE  Yield; DECIMALS=2; EXTRA=' of oats in cwt. per acre'
READ     [SERIAL=yes] Nitrogen,Variety,Yield
 4 3 2 1 1 2 4 3 1 2 3 4 3 1 2 4 4 1 2 3 2 1 3 4
 2 3 4 1 4 2 3 1 1 4 2 3 3 4 1 2 1 3 4 2 2 3 4 1
 4 1 3 2 3 4 1 2 3 4 2 1 3 1 4 2 4 3 1 2 1 2 3 4 :
 3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 2 2 2 2
 2 2 2 2 3 3 3 3 1 1 1 1 3 3 3 3 2 2 2 2 1 1 1 1
 2 2 2 2 1 1 1 1 3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 :
156 118 140 105 111 130 174 157 117 114 161 141
104  70  89 117 122  74  89  81 103  64 132 133
108 126 149  70 144 124 121  96  61 100  91  97
109  99  63  70  80  94 126  82  90 100 116  62
 96  60  89 102 112  86  68  64 132 124 129  89
118  53 113  74 104  86  89  82  97  99 119 121 :
" Define the treatment structure: factorial effects of V and N."
TREATMENTS Variety*Nitrogen
" Subplots nested within whole-plots nested within blocks."
BLOCK      Blocks/Wplots/Subplots
AOVANYHOW  [PRINT=aovtable,information] Yield

CAPTION    'AOVANYHOW example 2',\
           'Unbalanced design with almost all information within blocks.';\
SPLOAD     '%GENDIR%/Data/Product.gsh'
AOVANYHOW  [PRINT=aovtable,information] Y
Updated on June 20, 2019

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