Description
1. 2
p
factorial experiments. Read the description of the study in Exercise 40 (Chapter 11,
Section 11.1, “In a study of processes used to remove impurities …”). An ANOVA
table for analyzing the dataset is given below. Follow the instructions below.
Source DF SS MS F P-Value
A 1 0.168 0.168 0.08 0.788
B 1 1.940 1.940 0.87 0.366
C 1 8.161 8.161 3.64 0.074
D 1 13.082 13.082 5.84 0.028
A*B 1 3.419 3.419 1.53 0.235
A*C 1 0.263 0.263 0.12 0.736
A*D 1 0.911 0.911 0.41 0.533
B*C 1 0.738 0.738 0.33 0.574
B*D 1 0.781 0.781 0.35 0.563
C*D 1 6.771 6.771 3.02 0.101
A*B*C 1 0.020 0.020 0.01 0.926
A*B*D 1 0.775 0.775 0.35 0.565
A*C*D 1 0.622 0.622 0.28 0.606
B*C*D 1 1.758 1.758 0.78 0.389
A*B*C*D 1 0.004 0.004 0.00 0.967
Error 16 35.851 2.241
Total 31 75.264
a. Identify the effects (main and interactions) that are significant at the =0.10 level.
b. Compute the coefficient of determination R
2 and give a brief
interpretation. (See Formula 11K and pages L-71 to L-72) of lecture
notes.)
c. Computed R2
adj, the adjusted R2,
(See Formula 11K and pages L-71 to L72) of lecture notes.)
d. Assume that only the main and interaction effects of C and D are important
(two-way interaction model). Complete the ANOVA table below in this
case.
Source DF SS MS F P-Val
C 1 8.161 8.161 ? 0.036
D ? ? ? ? 0.010
C*D 1 6.771 6.771 ? 0.055
Error ? ? ?
Total 31 75.264
Hint: You can derive the missing values from the previous ANOVA table.
e. Compute R
2
adj for the ANOVA table in part (d).
f. Assume that only the main effects of C and D (two-way additive model) are
important. Below is the corresponding ANOVA table. Compute R
2
adj
g. Based on the R
2
adj values, which of the 3 fitted models do you
prefer? Give a short explanation for your choice.
2. A Fractional Factorial Design. In a study of p=5 factors with two levels each, only 8 different
combinations of levels of A, B, C, D, and E will be run (i.e. q=2 and the experiment is a
quarter fractional). Use A, B, D as the independent factors and with generators
C = ABD and E = AD
A. List out the 8 treatments will be run.
B. Which treatments, used in the experiment, have all of B and D at their low levels?
C. What effects will be aliased with the A main effect?
