Produces further output for an unbalanced design (after AUNBALANCED
) (R.W. Payne).
Options
PRINT = string tokens 
Controls printed output from the analysis (aovtable , effects , means , residuals , %cv ); default aovt , mean 

PFACTORIAL = scalar 
Limit on number of factors in printed tables of predicted means; default 3 
FPROBABILITY = string token 
Printing of probabilities for variance ratios in the analysisofvariance table (yes , no ); default no 
TPROBABILITY = string token 
Printing of probabilities for ttests of effects (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 , ese ); default diff 
LSDLEVEL = scalar 
Significance level (%) for least significant differences; default 5 
RMETHOD = string token 
Type of residuals to plot (simple , standardized ); default simp 
PMEANTERMS = formula 
Treatment terms for which predicted means are to be printed; default * implies all the treatment terms

Parameter
SAVE = identifiers 
Save structure (from AUNBALANCED ) containing details of the analysis for which further output is required; if omitted, output is from the most recent use of AUNBALANCED 

Description
This procedure can be used, following the use of procedure AUNBALANCED
, to produce further output for the analysis of variance of an unbalanced design.
The output to be printed is controlled by the PRINT
option, with settings: aovtable
to print the analysisofvariance table, effects
to print the effects (as estimated by Genstat regression), means
to print tables of predicted means with standard errors, residuals
to print residuals and fitted values, and %cv
to print the coefficient of variation. The default is to print the analysisofvariance table and tables of means.
The model is fitted sequentially, first any covariates and then the treatments. Thus, the sum of square in each line of the analysisofvariance table is for the term concerned, eliminating the effects of terms in earlier lines and ignoring the effects of terms lower in the table. In particular, the sums of squares for covariates are ignoring treatments, and not after eliminating treatments (as with the ANOVA
directive).
Tables of means are calculated using the PREDICT
directive. The first step (A) of the calculation 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, 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 
standard errors of the means (relevant for comparing them with zero); 
ese 
approximate effective standard errors – these are formed by procedure SED2ESE with the aim of enabling good approximations to the standard errors for differences to be calculated by the usual formula of sed_{i}_{,j} = √( ese_{i}^{2} + ese_{j}^{2} ). 
The default is differences
. The LSDLEVEL
option sets the significance level (as a percentage) for the least significant differences.
The PFACTORIAL
option limits the number of factors in terms for which predicted means are printed. Probabilities can be printed for variance ratios by setting option FPROBABILITY=yes
, and probabilities for ttests of effects by setting option TPROBABILITY=yes
. Finally, there is a PLOT
option which 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. By default, simple residuals are plotted, but you can set option RMETHOD=standardized
to plot standardized residuals instead. The PMEANTERMS
option can be used to specify the treatment terms for which predicted means are to be printed; by default, they are printed for all the treatment terms (subject, of course, to the PFACTORIAL
option).
The SAVE
parameter can be set to the save structure from the analysis for which further output is required. If SAVE
is not set, output will be produced for the most recent analysis from AUNBALANCED
; however, none of the Genstat regression directives (MODEL
, TERMS
, FIT
, ADD
, DROP
and so on) must then have been used in the interim.
Options: PRINT
, PFACTORIAL
, FPROBABILITY
, TPROBABILITY
, PLOT
, COMBINATIONS
, ADJUSTMENT
, PSE
, LSDLEVEL
, RMETHOD
, PMEANTERMS
.
Parameter: SAVE
.
Method
The output is produced mainly using the directives RKEEP
and PREDICT
.
Action with RESTRICT
If the yvariate originally analysed by AUNBALANCED
was restricted, only the units not excluded by the restriction will have been analysed.
See also
Procedures: AUNBALANCED
, AUGRAPH
, AUPREDICT
, AUMCOMPARISON
, AUKEEP
.
Commands for: Analysis of variance.
Example
CAPTION 'AUDISPLAY example',\ 'Data from Genstat 5 Release 1 Reference Manual, page 340.';\ STYLE=meta,plain FACTOR [NVALUES=36; LEVELS=3; VALUES=12(1...3)] Block FACTOR [NVALUES=36; LABELS=!t(baresoil,emerald,emergo)] Leachate & [LABELS=!t('1','1/4','1/16','1/64')] Dilution VARIATE [NVALUES=36] Nhatch,Nnohatch READ Leachate,Dilution,Nhatch,Nnohatch 1 2 109 318 3 4 54 350 3 1 * 415 2 2 783 212 3 3 652 1375 2 4 490 816 1 3 95 1219 2 1 1012 66 1 4 166 943 3 2 1059 313 1 1 257 1006 2 3 1058 234 2 4 507 1119 1 2 194 840 1 3 175 1707 1 1 326 609 3 4 142 980 2 3 286 230 3 2 546 313 2 2 * 301 2 1 2471 112 3 3 76 489 1 4 208 503 3 1 * 325 1 1 322 913 1 2 255 2246 3 2 1774 1446 2 2 999 193 2 4 388 1836 3 4 221 1800 1 3 220 1902 2 1 2821 187 3 1 1486 463 3 3 717 1473 1 4 143 941 2 3 968 550 : CALCULATE Logit%h = LOG(Nhatch/Nnohatch) BLOCKSTRUCTURE Block TREATMENTSTRUCTURE Leachate*Dilution AUNBALANCED [PRINT=*] Logit%h AUDISPLAY