chapter 1

Chapter 11: Multifactor Analysis of Variance45.a. The allocation of treatments to blocks is as given in the answer section, with block #1containing all treatments having an even number of letters in common with both ab andcd, etc.216,898b. x.....= 16, 898 , so SST = 9,035,054 − = 111,853. 8832block × replication. The eighttotals are 2091 ( = 618 + 421 + 603 + 449, the sum of the fourobservations in block #1 on replication #1), 2092, 2133, 2145, 2113, 2080, 2122, and2222091 2122 16,8982122, so SSBl = + ... + − = 898. 88 . The remaining SS’s4 4 32as well as all F ratios appear in the ANOVA table in the answer section. WithF. 01,1,12=9.33, only the A and B main effects are significant.46. The result is clearly true if either defining effect is represented by either a single letter (e.g.,A) or a pair of letters (e.g. AB). The only other possibilities are for both to be “triples” (e.g.ABC or ABD, all of which must have two letters in common.) or one a triple and the otherABCD. But the generalized interaction of ABC and ABD is CD, so a two-factor interaction isconfounded, and the generalized interaction of ABC and ABCD is D, so a main effect isconfounded.47. See the text’s answer section.341