Fractional Factorial Designs..

 Here we are dealing with 2-k fraction of 2n Design. So we have less number
 of Runs to deal with..  Instead of Confounding Scheme here we have Defining
 Relations. 

 eg. In 24-1 expt with  Defining Relation  I=ABCD, we wont be able to estimate
     the factor  ABCD,  and neither we  could estimate many other factors.. but
     we can estimate the alias  effects... and I will show you that if you had
     the rest half of fraction then you could have estimated many other effects.

 Reference : Example-8.1, Montgomery.
 

 
  
 Construction of Design
 
 proc factex;
  factors C B A D;
  size fraction=2; for 2-2 fraction use 4
  model res=4; 
  examine confounding aliasing(3);
  output out=part1;
 run;
 
  data part2;
   input rate @@;
   datalines;
   45 100 45 65 75 60 80 96
   ;

  data filter;
   merge part1 part2;
  run;


 Analysis of this Design.

  proc glm data=filter;
   class A B C D;
   model rate=A|B|C|D@2 /ss1;
   estimate 'L(a)' A -1 1;
   estimate 'L(b)' B -1 1;
   estimate 'L(c)' C -1 1;
   estimate 'L(d)' D -1 1;
  run;
 
 An atlernate method for analysis.

   %adxgen
   %adxff
   %adxinit
   %adxffa(filter,rate,C B A D,4);

 This gives the estimates as half of the 
 value of L(a) shown in the previous code. 



 Note : Here we are getting L(a) and not the effect estimate of A.
 
        The defining equation is :  A = BCD
				=>  L(a) = A + BCD

 So if you use the other fraction of the design, then we will get

				    A = -BCD
				=>  L'(a) = A - BCD
				=>  A  = (L(a) + L'(a))/2
				&  BCD = (L(a) - L'(a))/2

 
 Go for Residual analysis, Factor screening & Profile Plots in the usual way.
 There is nothing special you need to do for this.

 Resolution (R) : A design is said to be of resolution R if all k-fi's are not aliased
                  with less than (R-k)-fi's.

		  ie. if 2-fi's are not aliased with any other 2-fi's & Main effects but are
		  aliased with 3-fi's then we say that the design in Resolution-5.