Assignment 7 Comparing a Number of Entities and ANOVA

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SYSEN 5300
Assignment 7 Comparing a Number of Entities and ANOVA
For all of the questions in this assignment, show the steps of your calculation. And only use JMP
(see “Assignment 7 JMP Tips.pdf”) or other statistical software to check your results.
Question 1: Comparing two entities. (30 points)
A civil engineer tested two different types (A and B) of special reinforced concrete beams. There
were nine test beams (5 of type A and 4 of type B) and the engineer measured the strength of
each. From the following strength data (in coded units) he wanted to decide whether there was
any real difference between the two types. What assumptions did he need make in order to
perform a statistical test to draw conclusions? Calculate the test statistics, p-value, and draw a
conclusion based on your calculations.
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Question 2: Comparing a number of entities. (40 points)
Paint used for marking lanes on highways must be very durable. In one experiment, paints from
four different suppliers, labeled by GS, FD, L, and ZK, were tested on six different highway
sites, denoted by 1, 2, 3, 4, 5, 6. After a considerable length of time, which included different
levels of traffic and weather, the averages of wear of the samples at the six sites were as follows:
Type A: 67
Type B: 45
80
71
106
87
1
2
Sites 3
4
5
6
GS
69
83
74
61
78
69
Paint Suppliers
FD
L
59
55
65
65
64
59
52
59
71
67
64
58
ZK
70
75
74
62
74
74
The objective was to compare the wear of the paints from the four different suppliers.
(a) As implied in the question, factors such as suppliers, sites, levels of traffic and
weather all have an impact on the wear of the paint. In the Design of Experiment
(DOE) above, how are the effects of the factors other than the effect of suppliers
treated for the experiment to be valid?
(b) Make an ANOVA. Show both the table for the decomposition of total deviations and
the table for the analysis of variance.
Hint: make two tables in the form of those shown in slide 32 of lecture notes
(“Comparing a number of entities”).
(c) Make graphical checks on violation of the assumptions based on which ANOVA is
interpreted. Do you think these data contain bad values?
Hint: See slide 29 of lecture notes (“Comparing a number of entities”).
(d) Draw your conclusions from the analysis about the durability of the paint from the
four suppliers.
Question 3: Comparing a number of entities. (30 points)
Six burn treatments A, B, C, D, E, F were tested on six subjects (volunteers). Each subject had
six positions on arm where a burn could be applied for testing (each arm with two below the
elbow and one above). A standard burn was administered at each position and the six treatments
were arranged on all subjects and positions as shown in the table below. After the treatment each
burn was covered by clean gauze. Treatment C was a control with clean gauze but without other
treatment. The data are the number of hours for a clearly defined degree of partial healing to
occur.
I
II
Positions
on arm
III
IV
V
VI
1
A
32
B
29
C
40
D
29
E
28
F
37
2
B
40
A
37
D
56
F
59
C
50
E
42
Subjects
3
C
72
F
59
A
53
E
67
B
100
D
67
4
D
43
E
53
B
48
A
56
F
46
C
50
5
E
35
D
32
F
37
C
38
A
29
B
33
6
F
50
C
53
E
43
B
42
D
56
A
48
(a) What is the design called? How should the six treatments be arranged on the six
subjects and six positions for the experiment to be valid?
Hint: See slide 38 of lecture notes (“Comparing a number of entities”).
(b) Make an ANOVA. Show both the table for the decomposition of total deviations and
the table for the analysis of variance.
Hint: make two tables in the form of those shown in slide 39 of lecture notes
(“Comparing a number of entities”).
(c) What are your conclusions from the analysis
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