In a 2^5??1design (such as the one in Exercise 12) what does the estimate of the main effect of factor A actually represent?

i. The main effect of A.

ii. The sum of the main effect of A and the BCDE interaction.

iii. The difference between the main effect of A and the BCDE interaction.

iv. The interaction between A and BCDE.

Exercise 12.

The article ??An Application of Fractional Factorial Designs?? (M. Kilgo, Quality Engineering, 1988:19??23) describes a 2^5??1 design (half-replicate of a 2⁵ design) involving the use of carbon dioxide (CO₂) at high pressure to extract oil from peanuts. The outcomes were the solubility of the peanut oil in the CO₂ (in mg oil/liter CO₂), and the yield of peanut oil (in percent). The five factors were A: CO₂ pressure, B: CO₂ temperature, C: peanut moisture, D: CO₂ flow rate, and E: peanut particle size. The results are presented in the following table.

Treatment Solubility Yield Treatment Solubility Yield 29.2 63 d ade bde abd e 22.4 23 a 23.0 21 37.2 74 b 37.0 36 31.3 80 abe 139.7 99 48.6 33 23.3 24 cde 22.9 63 38.3 66 acd 36.2 21 bce 42.6 71 bcd 33.6 44 abc 141.4 54 abcde 172.6 96