Design And Analysis Of Experiments Chapter 8 | Solutions

ABC: confounded with block — contrast is the block difference. ABC contrast = (+1,-1,-1,+1,-1,+1,+1,-1)?? Wait, sign pattern for ABC = A B C = (1): +++ → +1; a: +-- → -1; b: -+- → -1; ab: --+ → +1; c: -++ → -1; ac: +-+ → +1; bc: ++- → +1; abc: --- → -1. So ABC: +1, -1, -1, +1, -1, +1, +1, -1.

B: -25-22+20+30-24-28+32+35 = (-47+20=-27; -27+30=3; 3-24=-21; -21-28=-49; -49+32=-17; -17+35=18) ✅

:

BC: (+1,+1,-1,-1,-1,-1,+1,+1) = 25+22-20-30-24-28+32+35 = (47-20=27; 27-30=-3; -3-24=-27; -27-28=-55; -55+32=-23; -23+35=12) ✅

| Block | (1) | a | b | ab | c | ac | bc | abc | |-------|-----|---|---|----|---|---|----|-----| | 1 | 25 | | | 30 | | 28 | 32 | | | 2 | | 22 | 20 | | 24 | | | 35 |

C: -25-22-20-30+24+28+32+35 = (-47-20=-67; -67-30=-97; -97+24=-73; -73+28=-45; -45+32=-13; -13+35=22) ✅

y = [25, 22, 20, 30, 24, 28, 32, 35]