Suppose a 27 design is arranged in 8 blocks with the generators B𝟏 = 𝟏𝟐𝟑, B𝟐 = 𝟒𝟓𝟔, B𝟑 = 𝟏𝟔𝟕. (a) Find all the interactions that are confounded with block effects and use these to compute...

Suppose a 27 design is arranged in 8 blocks with the generators B𝟏 = 𝟏𝟐𝟑,

B𝟐 = 𝟒𝟓𝟔, B𝟑 = 𝟏𝟔𝟕.

(a) Find all the interactions that are confounded with block effects and use

these to compute the gi

(b) for i ≥ 2 and to determine the order of estimability.

(b) An alternative scheme is the one given in Table 4.1 with k = 7 and q = 3.

Compute the gi

(b) for i ≥ 2 and determine the order of estimability for

the second scheme.

(c) Compare the two schemes and show the clear advantages of the second

scheme.