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7/28/2019 Design and Analysis of Experiments HW#18
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Individual Homework #18
Design and Analysis of Experiments
1.
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7/28/2019 Design and Analysis of Experiments HW#18
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Since there is not any replication there is not degrees of
freedom
left for error. A normal probability plot shows that Car, Pr and
Sp
are important variables but Bl is not. So a model with three
varibles
will be tried.
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7/28/2019 Design and Analysis of Experiments HW#18
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It looks like interactions are not important.
Regression model: y = 1.0+ 1.5*Car + 1.125*Pr + 0.875*Sp
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7/28/2019 Design and Analysis of Experiments HW#18
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Residuals appear to meet assumptions of constant variance and
normally
distributed.
2. c)Randomization protocol: The two blocks are separated and
assigned
a random number (Column with #) and then the order of the set
of
numbers is randomized and the new order is taken as the order
in
which the runs will be done (random order column).
Run ID A B C D ABD
Technici
an
1 -1 -1 -1 -1 -1 1
2 1 -1 -1 -1 1 2
3 -1 1 -1 -1 1 2
4 1 1 -1 -1 -1 1
5 -1 -1 1 -1 -1 1
6 1 -1 1 -1 1 2
7 -1 1 1 -1 1 2
8 1 1 1 -1 -1 1
9 -1 -1 -1 1 1 2
10 1 -1 -1 1 -1 1
11 -1 1 -1 1 -1 1
12 1 1 -1 1 1 2
13 -1 -1 1 1 1 2
14 1 -1 1 1 -1 1
15 -1 1 1 1 -1 1
16 1 1 1 1 1 2
Run ID A B C D ABD
Technici
an #
Random
order
1 -1 -1 -1 -1 -1 1 403 3774
4 1 1 -1 -1 -1 1 1896 1896
5 -1 -1 1 -1 -1 1 3708 5327
8 1 1 1 -1 -1 1 7211 4191
10 1 -1 -1 1 -1 1 4191 403
11 -1 1 -1 1 -1 1 5327 8392
14 1 -1 1 1 -1 1 3774 3708
15 -1 1 1 1 -1 1 8392 7211
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7/28/2019 Design and Analysis of Experiments HW#18
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Run ID A B C D ABD
Technici
an #
Random
order
2 1 -1 -1 -1 1 2 3901 8983
3 -1 1 -1 -1 1 2 8983 8249
6 1 -1 1 -1 1 2 2376 3901
7 -1 1 1 -1 1 2 8249 49389 -1 -1 -1 1 1 2 2289 8888
12 1 1 -1 1 1 2 8888 2376
13 -1 -1 1 1 1 2 7374 2289
16 1 1 1 1 1 2 4938 7374
d)
Run ID A B C D ABD BCD
(ABD)*(B
CD) Technician1 -1 -1 -1 -1 -1 -1 1 1
2 1 -1 -1 -1 1 -1 -1 2
3 -1 1 -1 -1 1 1 1 4
4 1 1 -1 -1 -1 1 -1 3
5 -1 -1 1 -1 -1 1 -1 3
6 1 -1 1 -1 1 1 1 4
7 -1 1 1 -1 1 -1 -1 2
8 1 1 1 -1 -1 -1 1 1
9 -1 -1 -1 1 1 1 1 4
10 1 -1 -1 1 -1 1 -1 3
11 -1 1 -1 1 -1 -1 1 1
12 1 1 -1 1 1 -1 -1 2
13 -1 -1 1 1 1 -1 -1 2
14 1 -1 1 1 -1 -1 1 1
15 -1 1 1 1 -1 1 -1 3
16 1 1 1 1 1 1 1 4
e)A*B*D*B*C*D = B2*A*C*D = A*C*D The interaction between A, C
and D is
confounded.
