STA 6207 – Data Analysis Assignment 1
Data were generated from the cell means model with normal and independent errors:
Yij   i  eij
eij ~ NID(0, 2 )
i  1,,4
j  1,,5
1)
2)
3)
4)
Based on your random sample, give least squares estimates of the 4 population means (by hand).
Obtain the analysis of variance (by hand).
Give an unbiased estimate of 2 (by hand)
Test whether the 4 population means are equal by writing out the null and alternative hypotheses, the
test statistic, and rejection region ( =0.05 significance level).
5) Give 95% confidence intervals for each of the population means (by hand)
6) Conduct the analysis using PROC GLM in SAS.
7) Give a plot of the responses versus treatment.
8) The true parameter values are 1=60, 2=40, 3=75, 4=45, =15. How many replicates per treatment
would we need for the power of the F-test to be 0.99?
9) Derive the least squares estimates of {i}
10) Derive the expected mean squares for treatments and error.
n
a
m
i
e
j
CARTWRIGHT
COL
COOPER
CUTLER
DOTSON
ELLIS
GALATI
GORSUCH
GRAGE
GU
GUO
HSU
KAO
KRISHNASWAMI
KRSKA
LI G
LI YA
LI YI
LI Z
POPESCU
ROGERS
STRAUBER
SUN
TAN
WANG
WU
XU
YAP
ZHENG
DIAZ
MOUSSEAU
RILEY
KIM
COLEE
Extra6
y
1
1
42
65
33
50
74
42
60
77
57
59
90
74
63
66
76
61
68
67
66
75
49
59
71
39
83
57
62
85
46
64
61
63
56
54
66
y
1
2
51
79
60
72
77
73
97
47
64
57
53
71
54
53
56
52
69
61
55
81
70
75
36
53
89
43
74
68
63
41
43
82
90
84
72
y
1
3
62
80
61
36
71
38
48
61
66
74
23
47
53
57
54
70
55
60
69
62
60
45
45
71
53
51
36
32
34
67
64
47
48
68
73
y
1
4
59
47
77
74
70
70
65
42
15
62
63
43
82
61
38
66
71
64
70
58
68
49
50
59
56
49
60
79
56
66
70
67
20
55
77
y
1
5
30
37
53
62
90
77
58
89
28
50
41
46
47
67
82
50
64
84
78
79
71
60
43
64
80
76
78
79
45
46
45
60
52
78
25
y
2
1
63
10
21
29
34
44
47
43
88
27
61
57
13
7
37
42
6
49
41
35
50
36
47
49
54
69
32
53
42
44
41
36
63
52
40
y
2
2
36
41
18
13
30
37
32
33
18
45
48
35
34
41
34
60
40
48
25
41
60
50
58
58
22
31
15
28
28
10
52
19
15
39
13
y
2
3
49
41
59
52
39
35
47
35
29
56
26
54
46
25
48
28
70
17
46
38
68
25
31
56
51
26
47
62
29
35
47
37
43
20
37
y
2
4
27
25
39
41
20
26
68
34
57
54
21
38
36
42
29
15
49
57
13
30
46
52
17
29
54
33
65
37
45
21
44
21
65
37
32
y y
y
y
y
y y y y y y
2 3
3
3
3
3 4 4 4 4 4
5 1
2
3
4
5 1 2 3 4 5
52 69 58 101 54 84 63 55 37 45 18
27 75 80 82 78 66 55 56 16 25 44
29 74 63 73 63 65 41 43 43 50 53
19 43 93 70 88 75 72 46 31 68 65
37 59 91 85 105 54 50 75 30 53 40
20 60 75 67 60 99 32 50 38 47 71
54 83 73 55 102 69 62 61 35 25 50
34 78 91 62 65 84 44 32 56 42 23
38 82 91 80 60 96 59 46 27 62 52
31 56 74 39 72 63 15 29 33 59 46
49 55 81 70 53 60 12 29 53 49 68
35 77 102 77 81 73 28 34 47 52 45
55 78 76 86 76 87 31 70 42 57 59
39 70 82 77 75 89 21 15 50 59 42
63 62 91 79 55 39 47 54 21 50 47
7 61 80 65 93 90 39 27 34 41 76
49 75 99 52 67 74 33 58 44 34 32
56 72 63 40 59 80 22 59 40 73 69
38 75 80 85 76 74 46 22 32 50 38
50 83 94 112 70 98 67 53 39 14 41
30 104 84 58 56 71 24 57 51 68 56
27 73 100 68 51 66 41 28 52 39 54
24 77 60 75 102 87 33 44 51 58 51
60 69 65 72 87 84 76 47 68 37 47
36 73 76 60 91 75 40 54 14 47 38
59 68 101 76 91 55 24 31 50 39 61
15 62 77 70 70 68 29 35 48 52 63
20 92 97 63 84 70 72 20 46 14 32
38 72 75 78 68 78 34 50 34 49 89
36 74 67 74 91 42 69 30 59 53 48
46 55 69 98 77 75 42 54 62 53 54
50 54 73 77 78 70 42 27 45 46 40
48 76 95 54 95 45 54 27 45 47 42
26 94 59 91 80 69 44 57 41 56 66
45 80 85 48 80 58 36 36 36 44 24