44.

a. In a 24 experiment, suppose two blocks are to be used, and it is decided to confound the ABCD interaction with the block effect. Which treatments should be carried out in the first block [the one containing the treatment (1)], and which treatments are allocated to the second block?

b. In an experiment to investigate niacin retention in vegetables as a function of cooking temperature (A), sieve size (B), type of processing (C), and cooking time (D), each factor was held at two levels. Two blocks were used, with the allocation of blocks as given in part

(a) to confound only the ABCD interaction with blocks. Use Yates’s procedure to obtain the ANOVA table for the accompanying data.

Treatment xijkl Treatment xijkl

(1) 91 d 72 a 85 ad 78 b 92 bd 68 ab 94 abd 79 c 86 cd 69 ac 83 acd 75 bc 85 bcd 72 abc 90 abcd 71

c. Assume that all three-way interaction effects are absent, so that the associated sums of squares can be combined to yield an estimate of 2

, and carry out all appropriate tests at level .05.