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.
 

 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.
 
Now we should merge these two REPLICATIONS to get the final layout. Note : here we are not merging the data sets, I am augmenting on the bottom of another dataset.. data part1; set rep11 rep21; run;
  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.
 
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