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 analysis-of-variance table (yes, no); default no |
TPROBABILITY = string token |
Printing of probabilities for t-tests 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 analysis-of-variance 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 analysis-of-variance 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 analysis-of-variance 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 sedi,j = √( esei2 + esej2 ). |
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 t-tests 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 y-variate 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