chapter 1

Chapter 11: Multifactor Analysis of Variance44.a. The eight treatment conditions which have even number of letters in common with abcdand thus go in the first (principle) block are (1), ab, ac, bc, ad, bd, cd, and abd; the othereight conditions are placed in the second block.b. and c.2x , x = 105, 160 , so SST = 1153.75. The two block totals are 639....= 1290ΣΣΣΣ ijkl2 22639 651 1290and 651, so SSBl = + − = 9. 00 , which is identical (as it must be8 8 16here) to SSABCD computed from Yates algorithm.Condition/Effect Block( contrast)SS = f(1) 1 --A 2 25.00 1.93B 2 9.00 < 1AB 1 12.25 < 1C 2 49.00 3.79AC 1 2.25 < 1BC 1 .25 < 1ABC 2 9.00 --D 2 930.25 71.90AD 1 36.00 2.78BD 1 25.00 1.93ABD 2 20.25 --CD 1 4.00 < 1ACD 2 20.25 --BCD 2 2.25 --ABCD=Blocks 1 9.00 --Total 1153.75162SSE = 9 .0 + 20.25 + 20.25 + 2.25 = 51.75 ; d.f. = 4, so MSE = 12.9375,F 7.71, so only the D main effect is significant.. 05,1,4=340