Question

in a seven-factor experiment (a, , g), suppose a quarter-replicate is actually carried out. if the defining effects are abcde and cdefg, what is the third nonestimable effect?

Answer 1

The third nonestimable effect derived from multiplying the defining effects abcde and cdefg, and simplifying by eliminating repeated factors, is abdfg.

Step-by-step explanation:

In the context of a seven-factor fractional factorial experiment, the defining relationship helps us to identify the nonestimable effects. The defining relationship is built from the defining effects provided. In this case, the defining effects are abcde and cdefg. To find the third nonestimable effect, we can multiply the two given defining effects.

Multiplying abcde by cdefg we get abcefg. But, since each letter represents a factor in the experiment and a factor multiplied by itself is equivalent to the factor not being in the equation (since factors are their own inverses), we can simplify this by eliminating the c and e (which appear twice) to get abdfg. This is the third nonestimable effect, as it is a combination that we cannot estimate due to the quarter replicate's defining relationship.