Show that, in a 23 design, 8 i=1 (Xi X) 2 = 8 [A]2 + [B]2 + [C]2 + [AB]2 + [AC]2 + [BC]2
Chapter 9, Problem 9.5-2(choose chapter or problem)
Show that, in a 23 design, 8 i=1 (Xi X) 2 = 8 [A]2 + [B]2 + [C]2 + [AB]2 + [AC]2 + [BC]2 + [ABC]2 . Hint: Since both the right and the left members of this equation are symmetric in the variables X1, X2, ... , X8, it is necessary to show only that the corresponding coefficients of X1Xi, i = 1, 2, ... , 8, are the same in each member of the equation. Of course, recall that X = (X1 + X2 ++ X8)/8.
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