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Incomplete Factorial design

2 messages · giovanni parrinello, Spencer Graves

Spencer Graves
# 
I assume that means you have two treatments, say A and B, can be 
either absent or present.  The standard analysis codes them as -1 or +1 
for absent or present, respectively.  If you have observations in all 4 
cells, you can write the following equation: 

      y(A,B) = b0 + b1*A + b2*B + b12*A*B + error. 

      This equation has 4 unknowns, b1, b1, b2 and b12.  If you have all 
4 cells in the 2x2 table, then you can estimate all 4 unknowns.  If you 
have data for only 3 cells, the standard analysis pretends that b12 = 0 
and estimates the other three.  If you have only 2 cells, say (both 
absent) and (both present), the standard analysis can estimate b0 plus 
either of b1 or b2.  However, in fact, these really estimate (b0+b12) 
and (b1+b2).  To understand this, consult any good book that discusses 
confounding with 2-level fractional factorial designs. 

      To do this in R, use "lm", as

      fit <- lm(y~A+B, data.frame(y=..., A=..., B=..,)

      hope this helps. 
      spencer graves
parrinel at med.unibs.it wrote: