15.12 Consider Exercise 15.11. Suppose there was some experimental difficulty in making the runs. In fact, the total experiment had to be halted after only 4 runs. As a result, the abbreviated experiment is given by Life a 43 b 35 c 44 abc 39 With only these runs, we have the signs for contrasts given by A B C AB AC BC ABC a + − − − − + +
b − + − − + − +
c − − + + − − +
abc + + + + + + +
Comment. In your comments, determine whether or not the contrasts are orthogonal. Which are and which are not? Are main effects orthogonal to each other? In this abbreviated experiment (called a fractional factorial), can we study interactions independent of main effects? Is it a useful experiment if we are convinced that interactions are negligible? Explain.