A fractional factorial experiment with 16 test runs was conducted to determine the effects of several factors on the antioxidant capacity in carotenoid extracts of the bacterium Thermus filiformis (“Evaluation of Biomass Production, Carotenoid Level and Antioxidant Capacity Produced by Thermus Filiformis Using Fractional Factorial Design,” Braz. J. Microbiol., 2012: 126–134). The variables studied were temperature (at 65°C and 75°C), pH (at 7 and 8), tryptone (at 5 and 10 g/L), yeast extract (at 5 and 10 g/L), and Nitsch’s trace elements (2 and 5 mL/L). The Nitsch’s trace elements factor was aliased with the highest-order interaction term.
a. What are k and p for this 2k2p design?
b. Determine the alias structure of the design.
c. Suppose that it is reasonable to assume that all interactions consisting of three or more factors are negligible. In this case, will any of the estimates of the remaining effects be aliased with one another?