STATISTICS 402B
Spring 2016
Homework Set#8
1. A 12 rep of a 25 factorial experiment was run in a CRD and the following data were obtained. The defining
relation used was I=ABCDE.
Trt.
e
a
b
abe
Obs.
14.8
14.5
18.1
19.4
Trt.
c
ace
bce
abc
Obs.
18.4
15.7
27.3
28.2
Trt.
d
ade
bde
abd
Obs.
16.0
15.1
18.9
22.0
Trt.
cde
acd
bcd
abcde
Obs.
19.8
18.9
29.9
27.4
(a) Display the alias pattern. (You may use the = or + symbols to denote aliased effects.)
(b) Create a JMP data table representing this design. Must have 6 columns labelled A,B,C,D,E, and
Y, and 16 rows for each line of data. Use the appropriate +, − signs to represent each treatment
combination.
(c) Use JMP to estimate all main effects and 2-factor interactions assuming that all 3-factor and higher
order interactions are negligible.
(d) Obtain a normal probability plot of the above effects.
(e) Discuss the results by interpreting the important effects
(f) What is the resolution of this design? What does it tell you about the design?
2. Construct a 26−2 fractional factorial design with as high a resolution as possible. Display the aliasing
pattern assuming 3-fi and higher order interactions are zero and determine the fraction to be run using
Method II.
3. A 1/8th fraction of 26 factorial design was chosen in an experimental study to determine the effects of six
factors A, B, C, D, E, and F. They used the generators I=ABD, I=ACE, and I=BCF.
(a) Give the complete defining relation of this design.
(b) Derive the treatment combinations to be used in this experiment?
(c) Is this design a “saturated” design? Explain.
(d) What is the resolution of this design?
(e) Assuming that 3-factor and higher order interactions are negligible, give the alias pattern of the main
effects and 2-factor interactions.
(f) To reduce the ambiguities resulting from this alias structure, another 1/8th fraction was added. This
design was obtained by reversing the signs for all factors in the design matrix used for the first fraction.
Show the treatment combinations used in this design.
(g) Give the alias structure of the second fraction (again assuming 3-factor and higher order interactions
are negligible).
(h) Give the alias structure of the combined design assuming 3-factor and higher order interactions are
negligible.
(i) What is the resolution of the combined design?
Note: Need to present written answers to each part, with calculation shown for parts that you are required to
do hand computation. Use the JMP output to obtain numbers for answering other parts. Attach edited JMP
output when you use the JMP output to extract numbers as part of the analysis.
Due Friday, April 29th, 2016 (turn-in at the beginning of class)
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