Forms information about aliased model terms in analysis of variance (R.W. Payne).
|Controls printed output (
||Treatment model for the design; if this is not set, the default is taken from any existing setting defined by the
||Block model for the design; if this is not set, the default is taken from any existing setting defined by the
||Limit on number of factors in a treatment term; default 3|
||Defines a restriction on the units for the analysis; default * i.e. none|
||Model terms whose aliased terms are to be identified; the default is to take all the terms in the treatment model|
||New factors, with levels (and labels) that exclude those that Saves the aliased terms|
When a term is aliased in an analysis of variance, it is listed in the Information summary produced by
under the heading “Aliased model terms”. However,
ANOVA does not indicate the terms with which it is aliased. This information can be obtained using procedure
The block structure of the design can be specified by the
BLOCKSTRUCTURE option. If this is not set, the default is taken from any existing setting defined by the
BLOCKSTRUCTURE directive. Similarly, the treatments are specified by the
TREATMENTSTRUCTURE option, with a default taken from any existing setting defined by the
TREATMENTSTRUCTURE directive. As in
FACTORIAL option sets a limit on the number of factors in a treatment term; default 3. The
RESTRICTION option can supply a variate to define a restriction on the units of the design. (Units where the variate contains a zero value are excluded from the analysis.)
The terms whose aliasing is to be investigated are specified by the
TERMS parameter. If this is not specified, all the terms in the treatment model are investigated.
The terms to which they are aliased can be saved using the
ALIASEDTERMS parameter. They are saved in a formula structure if a single term has been specified by
TERMS, or in a pointer containing a formula structure for each term if it has specified several.
Printed output is controlled by the
||to print the analysis-of-variance table; and|
||to print the terms to which each term is aliased (default).|
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
A restriction can be specified using the
CAPTION 'FALIASTERMS 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 TREATMENTS A*B*C+D ANOVA [PRINT=aovtable,information] Y CAPTION !T('The aov table and information summary show that D is aliased;',\ 'FALIASTERMS indicates that the aliasing is with B, C and B.C ') FALIASTERMS 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] Y FALIASTERMS [RESTRICTION=Blocks<4] D