Finds out information about aliased model terms in analysis of variance (R.W. Payne).
Options
TREATMENTSTRUCTURE = formula |
Treatment model for the design |
|---|---|
BLOCKSTRUCTURE = formula |
Block model for the design |
FACTORIAL = scalar |
Value used in the FACTORIAL option of ANOVA if not the default |
DESIGN = pointer |
Design structure for the analysis |
Parameter
TERM = factors |
Factors defining the aliased model term |
|---|
Description
When a term is aliased in an analysis of variance, it is listed in the Information summary (produced by ANOVA [PRINT=information]) under the heading “Aliased model terms” (see the Guide to the Genstat Command Language, Part 2, Section 4.7.1). However ANOVA does not indicate the terms with which it is aliased. This information can be obtained using procedure ALIAS.
The aliased term is specified by setting the TERM parameter to the list of factors that define it. The structure of the design can be specified either by options BLOCKSTRUCTURE and TREATMENTSTRUCTURE (together with option FACTORIAL, if necessary); alternatively you can save the design structure from the original analysis and supply this using the DESIGN option – this is the only way of specifying the design if there are weights or if the analysis is restricted. If an undeclared structure is specified for DESIGN (and BLOCKSTRUCTURE and TREATMENTSTRUCTURE are also specified), it will be set to the design structure for the analysis.
Note: this procedure has been replaced by FALIASTERMS, but is retained for use in earlier programs. FALIASTERMS has a more convenient syntax, and allows you to save details of the aliased terms.
Options: TREATMENTSTRUCTURE, BLOCKSTRUCTURE, FACTORIAL, DESIGN.
Parameter: TERM.
Method
The procedure calculates a set of dummy effects for the aliased model term, and then forms and analyses a variate in which only these effects are present. The analysis detects the model terms to which the term is aliased as those that have non-zero sums of squares.
Action with RESTRICT
None of the options nor parameters are vectors. To indicate that the analysis is of a restricted set of units you must use the DESIGN option to specify the design structure from the original analysis.
See also
Directives: ANOVA, FPSEUDOFACTORS.
Procedure: AEFFICIENCY, FALIASTERMS.
Commands for: Analysis of variance, Design of experiments.
Example
CAPTION 'ALIAS example'; STYLE=meta
FACTOR [NVALUES=32; LEVEL=2] A,B,C & [LEVEL=4] D,Blocks & [LEVEL=8] Plots
GENERATE A,B,C & D & Blocks,Plots
VARIATE [VALUES=13,17,25,33,18,19,22,14,26,23,31,29,25,21,18,34,\
23,19,33,36,25,23,29,18,31,30,37,33,29,27,20,36] Y
BLOCKSTRUCTURE Blocks/Plots
TREATMENTSTRUCTURE A*B*C+D
ANOVA [PRINT=aovtable,information] Y
CAPTION !T('The aov table and information summary show that D is aliased;',\
'ALIAS indicates that the aliasing is with B, C and B.C ')
ALIAS [BLOCKSTRUCTURE=Blocks/Plots; TREATMENTSTRUCTURE=A*B*C+D] D
PRINT !T('The printout below confirms this:',\
'D level 1 corresponds to B level 1 and C level 1,',\
'D level 2 corresponds to B level 1 and C level 2,',\
'D level 3 corresponds to B level 2 and C level 1,',\
'D level 4 corresponds to B level 2 and C level 2.');\
JUSTIFICATION=left
& [RLWIDTH=3; ORIENTATION=across] D,B,C; FIELDWIDTH=2; JUST=left
PRINT !T('Use RESTRICT to analyse only the first 3 blocks;',\
'the main effect D is still aliased, exactly as before...');\
JUSTIFICATION=left
RESTRICT Y; Blocks < 4
ANOVA [PRINT=aovtable,information; DESIGN=DB1to3] Y
CAPTION 'The design must now be specified for ALIAS using the DESIGN option.'
ALIAS [DESIGN=DB1to3] D