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I need to prove the following identities for a factorial design experiment of the form $2^k$.

  1. $\overline{Y}(AB+)-\overline{Y}(AB-)=0.5$[$A(B+)-A(B-)$]
  2. $A(B+)=A+AB$
  3. $A(B-)=A-AB$
  4. $A=\frac{[A(B+)+A(B-)]}{2}$

($\overline{Y}(AB+)$ is the mean of all observations where A*B has a positive sign, A(B+) is the effect of A when B is positive +, and so on..)

I know that for a factorial design experiment of the form $2^3$ $AB=[A(B+)-A(B-)]/2$, but I'm not sure it's applicable for a $2^k$ factorial design experiment. We've mostly talked about the $2^2$ factorial design experiment and briefly mentioned the $2^k$ factorial design

M.H
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Manko
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  • Maybe this should be cross-posted to statistics.stackexchange.com. (I remember doing exercises on this kind of thing, but I never learned it particularly well and I've forgotten everything except that this subject exists and is where applied statistics relies most heavily on combinatorics.) – Michael Hardy Jun 01 '13 at 17:25

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