Stat HW10 Solutions
Explanation of problem: We are interested in 7 factors and how they interact to affect our
response variable. We have resource constraints that we have to deal with: availability of lab
time and a tight budget for costs associated with the experiment. We need to look at ways to
design our experiment that allow us to stay within these constraints. We will use our knowledge
of experimental design along with what Minitab’s design functions to do so.
Number of levels per factor: A, 2; B, 2; C, 3; D, 4; E, 2; F, 2; G, 3
Number of preferred observations per treatment combination: 2
1) If we did a full factorial design with the 7 factors with the levels of factors and number of
observations per treatment combination stated above, how many total observations would
we need to collect?
N = (2*2*3*4*2*2*3)*2 = 576*2 = 1152
2) If we did a 2k design for the 7 factors with the number of observations per treatment
combination stated above, how many total observations would we need to collect?
N = 27*2 = 128*2=256
3) We might consider a fractional factorial design for the 7 factors. Use Minitab to find the
number of total observations and indicate the design generators for each of the following:
a) A resolution III design with n=2 N = 16
Fractional Factorial Design
Factors: 7 Base Design: 7, 8 Resolution: III
Runs: 16 Replicates: 2 Fraction: 1/16
Blocks: 1 Center pts (total): 0
b) A ¼ fraction resolution IV design with n=2 N = 64
Fractional Factorial Design
Factors: 7 Base Design: 7, 32 Resolution: IV
Runs: 64 Replicates: 2 Fraction: 1/4
Blocks: 1 Center pts (total): 0
4) Which design requires the fewest total observations?
The 1/16th fraction, resolution III design.
5) Which designs allow us to test and interpret all of the interactions?
Both the full factorial and the 27 factorial allow us to test and interpret all of the
interactions.