: A (2^3) design with 2 replicates, each in 2 blocks. In replicate I, confound ABC; in replicate II, confound AB. Estimate all effects.
AC: (+1,-1,+1,-1,-1,+1,-1,+1) = 25-22+20-30-24+28-32+35 = (25-22=3; 3+20=23; 23-30=-7; -7-24=-31; -31+28=-3; -3-32=-35; -35+35=0) ✅
: Estimate main effects and interactions, accounting for blocking. design and analysis of experiments chapter 8 solutions
Compute: 25 1 +22 (-1)+20*(-1)+30 1 +24 (-1)+28 1 +32 1 +35*(-1) = 25 -22 -20 +30 -24 +28 +32 -35 = (25-22=3; 3-20=-17; -17+30=13; 13-24=-11; -11+28=17; 17+32=49; 49-35=14).
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: Main effects A, B, C positive; interactions AB, BC positive; AC negligible. Block effect significant but aliased with ABC. Example 3: (2^4) Design in 4 Blocks (Confounding ABC and ABD) Problem : Construct a (2^4) design (A, B, C, D) in 4 blocks of 4 runs each, confounding ABC and ABD. Find all confounded effects.
AB: (+1,-1,-1,+1,+1,-1,-1,+1) = +25-22-20+30+24-28-32+35 = (25-22=3; 3-20=-17; -17+30=13; 13+24=37; 37-28=9; 9-32=-23; -23+35=12) ✅ : A (2^3) design with 2 replicates, each in 2 blocks
Actually, let's structure properly: