chapter 1

Chapter 11: Multifactor Analysis of Variance55.a.Effect %Iron 1 2 3EffectContrast SS7 18 37 174 684A 11 19 137 510 144 1296B 7 62 169 50 36 81AB 12 75 341 94 0 0C 21 79 9 14 272 4624AC 41 90 41 22 32 64BC 27 165 47 2 12 9ABC 48 176 47 -2 -4 1D 28 4 1 100 336 7056AD 51 5 13 172 44 121BD 33 20 11 32 8 4ABD 57 21 11 0 0 0CD 70 23 1 12 72 324ACD 95 24 1 0 -32 64BCD 77 25 1 0 -12 9ABCD 99 22 -3 -4 -4 1contrastWe use estimate = when n = 1 (see p 472 of text) to getp2144 14436272α ˆ1 = = = 9.00 , β 2. 254ˆ1 = = , δˆ1 = = 17. 00 ,2 161616336⎛γ ˆ1 = = 21.00 . Similarly, ⎞ ⎛⎜αβ ⎟ = 0 , ⎞ ⎛ ⎞⎜αδ ⎟ = 2. 00 , ⎜αγ ⎟16⎝ ⎠ ⎝ ⎠ ⎝ ⎠= 2. 75 ,⎛ ∧ ⎞ ⎛⎜ βδ ⎟ = .75 , ∧ ⎞⎛ ⎞⎜ βγ ⎟ = . 50 , and ⎜δγ ∧⎟ = 4. 50.⎝ ⎠ ⎝ ⎠⎝ ⎠111111111111b.20DCeffect10ACD0-2-10z-percentile12The plot suggests main effects A, C, and D are quite important, and perhaps theinteraction CD as well. (See answer section for comment.)347