3. The coating experiment, described in Excercise 7 of Chapter 7, was to study the effect of different
spray parameters on thermal spray coating properties. In the experiment, the authors attempted to
produce high-quality alumina (Al2O3) coatings by controlling the fuel ratio (factor A at 1:2.8 and
1:2.0), carrier gas flow rate (factor B at 1.33 and 3.21 L s-¹), frequency of detonations (factor C
at 2 and 4 Hz), and spray distance (factor D at 180 and 220 mm). To quantify the quality of
the coating, the researchers measured multiple response variables. In this example we will examine
the porosity (vol. %). The data are shown in the table below and can be downloaded from http:
//deanvossdraguljic.ietsandbox.net/DeanVossDraguljic/SAS-data.html.
A
B
с
D
Yijkl
A
B
C
D
2
2
2
2
5.95
2
2
2
1
2
2
1
2
1
4.57 4.03 2.17
1
2
2
2
1
2
2
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
2
Yijkl 12.28 9.57 6.73 6.07 8.49 4.92 6.95 5.31
1
2
2
3.43
2
1
2
1
1.02
2
1
1
2
4.25
2
1
1
1
2.13
1
1
1
1
(a). [3pts]. Run a model with ALL main-effects and two-way interaction effects. Write down the SAS code
copy the ANOVA table from SAS.
and
(b).[2pts] The 95% confidence interval for the difference between the two main effects of B is (
(c).[2pts] Do you believe there are significant interaction effects between B and C? Answer yes or no.
(d).[3pts] Generate an interaction plot for the B*C interaction. State how the plot supports your answer in
c. [Hint: use 1smeans B*C to get the least squares estimates, then plot it using any software of your choice.]
(e).[3pts] The 90% confidence upper limit for the error variance o² is
Show your work.
Fig: 1
