STATISTICS 402 - Assignment 7
Due April 17, 2015
The Federal Aviation Administration does an experiment on the ability to detect targets on a radar
screen. Two factors are manipulated, the amount of background noise or “ground clutter” (levels
1-Low, 2-Medium and 3-High) and the type of filter placed over the radar screen (Type 1 and
Type 2). Treatments (A, B, C, D, E and F) are made by factorial crossing levels of ground clutter
with levels of the type of filter. For each of the treatment combinations a signal representing an
aircraft is introduced and the intensity increased until the radar operator is able to detect the
signal. A lower intensity is desirable because it means the radar operator can detect a weaker
signal. A total of 36 observations are collected, six for each treatment combination.
1) Suppose the experiment is run as completely randomized design.
a) Explain how to assign treatments to experimental units for the experiment if it is run as a
completely randomized design? Be sure to answer this question within the context given
above.
The data for a completely randomized experiment are given below.
A
Type 1, 1-L
94
102
106
98
96
98
B
Type1, 2-M
101
106
105
96
100
98
C
Type 1, 3-H
113
112
108
98
110
104
D
Type 2, 1-L
79
78
86
72
78
75
E
Type 2, 2-M
87
90
97
80
86
88
F
Type 2, 3-H
93
91
95
83
90
91
b) Analyze the data and give a complete analysis of variance table including all sources of
variation, degrees of freedom, sums of squares, mean squares, F statistics and P-values.
c) Are there statistically significant treatment effects? Support your answer statistically.
d) Are there statistically significant factor effects? Support your answer statistically.
e) Is there statistically significant interaction between the factors? Support your answer
statistically.
f) Is there a “best” combination of type of filter and amount of background noise or “ground
clutter”? Support your answer statistically.
2) Different operators have different abilities to detect signals so operators contribute to
variation in the intensity values. Suppose the experiment is run as a randomized complete
block design with six operators.
a) Explain how to assign treatments to experimental units for the experiment if it is run as a
randomized complete block design? Be sure to answer this question within the context
given above.
The data for a randomized complete block experiment are given on the next page. Note: this is
the same data as given in problem 1 except for the inclusion of the Operator variable.
1
Operator
1
2
3
4
5
6
A
Type 1, L
94
102
106
98
96
98
B
Type1, M
101
106
105
96
100
98
C
Type 1, H
113
112
108
98
110
104
D
Type 2, L
79
78
86
72
78
75
E
Type 2, M
87
90
97
80
86
88
F
Type 2, H
93
91
95
83
90
91
b) Analyze the data and give a complete analysis of variance table including all sources of
variation, degrees of freedom, sums of squares, mean squares, F statistics and P-values.
c) Are there statistically significant treatment effects? Support your answer statistically.
d) Are there statistically significant factor effects? Support your answer statistically.
e) Is there statistically significant interaction between the factors? Support your answer
statistically.
f) Is there a “best” combination of type of filter and amount of background noise or “ground
clutter”? Support your answer statistically.
g) Has blocking on Operator been effective? Support your answer statistically.
3) The setup for each experimental treatment takes time so that only six treatments can be done
in one day. There are differences from day to day due to temperature and humidity, in
addition to the differences from operator to operator, that may affect the intensity values.
a) Given this information, why would a Latin Square design be appropriate?
The data for a Latin square experiment are given below. Note: this is the same data as given
in problem 2 except for the inclusion of the Day variable.
Operator 1
Operator 2
Operator 3
Operator 4
Operator 5
Operator 6
Day 1
A
94
B
106
C
108
D
72
F
90
E
88
Day 2
C
113
A
102
B
105
F
83
E
86
D
75
Day 3
B
101
E
90
F
95
A
98
D
78
C
104
Day 4
E
87
D
78
A
106
B
96
C
110
F
91
Day 5
F
93
C
112
D
86
E
80
A
96
B
98
Day 6
D
79
F
91
E
97
C
98
B
100
A
98
b) Analyze the data and give a complete analysis of variance table including all sources of
variation, degrees of freedom, sums of squares, mean squares, F statistics and P-values.
c) Are there statistically significant treatment effects? Support your answer statistically.
d) Has including the second blocking factor, Day, been effective? Support your answer
statistically.
2