Suppose we want to get a design : 23 in 2 blocks with all f.i. estimable. But for getting 2n f.e. in 2k blocks we have to confound at least 2k-1 f.i. with blocks. So we need to replicate the design and get the CONFOUNDING SCHEME in such a manner that all the f.i.'s are estimable. Reference : example-7.3 Montgomery. The most important part is the construction of design.
Layout for Replication-I
proc factex;
factors C B A;
size design=8;
model estimate=(A|B|C@2); forcing to confound ABC
blocks nblocks=2;
output out=rep1 blockname=block ;
run;
data rep11;
set rep1;
do i=1 to 8;
rep =1;
end;
output;
keep rep block A B C;
Now this design "rep11" is the layout of replication-1
and in this design ABC is confounded with blocks.
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Layout of Replication-II
proc factex;
factors C B A;
size design=8;
model estimate=(A B C A*C B*C A*B*C); AB confounded
blocks nblocks=2;
output out=rep2 blockname=block ;
run;
data rep21;
set rep2;
do i=1 to 8;
rep =2;
end;
output;
keep rep block A B C;
Now this design "rep21" is the layout of replication-2
and in this design AB is confounded with blocks.
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Now get the response and get merge the two datasets... data part2; input height @@; datalines; -3 2 2 1 0 -1 -1 6 1 0 1 1 -1 3 0 5 ; data fillh; merge part1 part2; run; | Following is the analysis.. proc glm data=fillh; class rep block A B C; model height=rep block(rep) A|B|C /ss1 ; run; Now you can do the Residual analysis and profile plots as usual...... There is no problem in that. |