A 2 4-1 fractional factorial design using
I=ABCD, was used to improve the response rate to a credit card mail
marketing offer, with the following factors:
A=annual fee (Current, Lower)
B=account opening fee (No, Yes)
C=Initial interest rate (Current, Lower)
D=Long-term interest rate (Low, High)
They ran the experiment initially as a full factorial (data
follows).
Let’s assume that they would first run the experiment as a
fractional factorial instead, with I=ABCD.
Perform the analysis for a ½ fractional factorial using an alpha
level of .05, and answer the questions below,
Then perform the analysis for the full factorial, using an alpha
of .05.
Test Cell
A=Annual Fee
B=Account-opening fee
C=Initial interest rate
D=Long-term interest rate
Orders
Response Rate
1
-
-
-
-
184
2.45
2
+
-
-
-
252
3.36
3
-
+
-
-
162
2.16
4
+
+
-
-
172
2.29
5
-
-
+
-
187
2.49
6
+
-
+
-
254
3.39
7
-
+
+
-
174
2.32
8
+
+
+
-
183
2.44
9
-
-
-
+
138
1.84
10
+
-
-
+
168
2.24
11
-
+
-
+
127
1.69
12
+
+
-
+
140
1.87
13
-
-
+
+
172
2.29
14
+
-
+
+
219
2.92
15
-
+
+
+
153
2.04
16
+
+
+
+
152
2.03
Analyze the full factorial experiment, removing 3rd
order and above interactions. What are the significant
factors at alpha = ..05?
A is significant? Yes or No
B is significant? Yes or No
C is significant? Yes or No
D is significant? Yes or No
AB is significant? Yes or No
AC is significant? Yes or No
AD is significant? Yes or No
BC is significant? Yes or No
BD is significant? Yes or No
CD is significant? Yes or No
Analyze the full factorial experiment. What are the
p-values?
A?
B?
C?
D?
AB?
AC?
AD?
BC?
BD?
CD?
ABC?
ABD?
BCD?
ABCD?
What levels of each factor would you recommend?
A: Current or Lower
B: No or Yes
C: Current or Lower
D: Low or High