Forms a new experimental design from the product of two designs (R.W. Payne).
|Controls printing of the design (
||Whether to analyse the design by
||How to combine the designs (
||Block formula for design 1|
||Treatment formula for design 1|
||Block formula for design 2|
||Treatment formula for design 2|
APRODUCT forms an experimental design by taking the product of two other designs. The
METHOD option controls whether the product is formed by nesting the second design within the first, or by crossing the two designs together. For example, suppose that the first design has a single factor
Units in the block structure and a single treatment factor
A, while the second design is a Latin square with block structure
Rows*Colums and treatment factor
B. If we nest the second design within the first, we would obtain a design with block structure
Units/(Rows*Columns) in which each unit of the first design has been subdivided into a row by column array of subplots to contain a Latin square of the sort defined by the second design. Nesting is thus useful when you want to subdivide the units of a design and apply further treatments (in this case those defined by the factor
B) to the resulting subplots. Similarly, if we cross the two designs, the new design will have a block structure of
Units*Rows*Columns, in which we have duplicated the second design for every level of Units. Crossing is useful if you need to introduce a new blocking structure into an existing design. For example, the
Units factor might represent different time periods or different locations in which the latin square design was to be used, and the factor
A the different systematic conditions that might apply on each occasion.
With both nesting and crossing, the new design will contain a unit for every combination of the block factors in the two original designs, and so every combination of the treatment factors in the first design will occur with every combination of the treatment factors in the second design. The treatment structure is thus defined for the new design by crossing the treatment structures of the two original designs, to estimate all the original treatment terms and their interactions. So, in the example above, the treatment structure is defined to be
APRODUCT redefines the values of the factors as required for the new design, and executes
TREATMENTSTRUCTURE directives with the new block and treatment formulae. The new formulae can then be accessed, outside the procedure, using the
GET directive or procedure
design to print the new design, and the
ANALYSE option can be set to
yes to produce a skeleton analysis of variance from
TF2 define the block structure and treatment structure of the first and then the second design.
None of the factors must be restricted, and any existing restrictions will be cancelled.
CAPTION 'APRODUCT example',\ !t('Design 1 is a design with no blocking (the single',\ 'block factor Rep merely identifies the different units),',\ 'Design 2 is a Latin square with 4 rows and 4 columns.');\ STYLE=meta,plain FACTOR [VALUES=1...6; LEVELS=6] Rep & [VALUES=2(1...3); LEVELS=3] A FACTOR [NVALUES=16; LEVELS=4] Row,Column,B;\ VALUES=!(4(1...4)),!((1...4)4),!(1,2,3,4, 2,3,4,1, 3,4,1,2, 4,1,2,3) APRODUCT [PRINT=design; ANALYSE=yes; METHOD=nest;\ BF1=Rep; TF1=A; BF2=Row*Column; TF2=B]