Transcript Mearsures of Sample Mean -- Super

Mearsures of Sample Mean -- Super-Drowsy drug Study
Presented by : Yong(Eric) Xu, (Yan Yan) Minna Wu
Date
: Oct 4, 2006
1.
Executive Summary:
Baker and The Federal Trade commission (FTC) both computed the
percentage reduction of time to fall asleep (“sleep latency”) after using the
Super-drowsy drug and had two different results. We found that Baker’
conclusion was more accurate than FTC’s.
2. Introduction
The Able Company claimed in TV advertisement that taking its product
Super Drowsy drug reduced the time it took to fall asleep by 46%.
Thereafter Baker acquired Able and conducted a new study.
Baker selected a group of people and recorded the average times to fall asleep for
one week with no drugs and one week taking drugs.
3. Methods
●
Baker’s method to calculate the percentage reduction of sleep latency
Average time for week 2(taking drug)
Average % reduction = 1 Average time for week 1 (before taking drug)
= 46.5%
●
FTC’s method to calculate the percentage reduction of sleep latency
(i). calculated the percentage of reduction for each person
∑ % of reduction for each person
(ii). Average % reduction =
total # of people
= 40.9%
4. Conclusion
--
Baker’s conclusion is more precise than FTC’s.
0.0
-0.5
-1.0
dd$per
0.5
1.0
From below plot, we can see that the average percentage reduction increases by the sleep
latency with smaller variance, which implies that the average percentage reduction is not
constant. We should weight the sleep latency to get a more precise average.
Baker’s method gives greater weight to larger sleep latencies and FTC’s method doesn’t.
Thus, Baker’s method is correct in the Super-Drowsy Drug study.
20
40
60
80
dd$week1
100
120
140
5. Suggestion
Split the people into two groups randomly, one group take the Superdrowsy drug and the other group takes the placebo pills. Then compare the
response of the two groups.
6. Reference
M.O. Finkestein and B. Levin, Statistics for Laywers, 2nd edition
7. Appendix -- Sleep study data
Obs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
week1
61.07
46.07
84.64
31.07
54.64
26.79
58.93
13.93
71.79
82.5
37.5
35.36
37.5
114.64
35.36
73.93
17.5
94.29
22.5
58.93
46.07
31.07
62.14
20.36
56.79
week2
20.36
37.5
64.07
9.67
28.93
11.79
31.07
9.64
35.36
33.21
24.64
46.07
9.64
16.07
9.64
36.36
11.79
20.36
9.64
30
100.71
9.64
20.36
13.93
32.14
Average sleep latency in minutes)
Obs
week1
week2
26
16.07
7.5
27
33.21
26.79
28
51.43
20.36
29
28.93
17.21
30
139.29
37.5
31
78.21
39.64
32
43.93
35.36
33
111.43
7.5
34
56.79
31.07
35
106.07
43.93
36
98.57
77.14
37
43.93
70
38
114.64
26.79
39
39.64
33.21
40
91.07
31.07
41
18.21
20.36
42
63.21
18.21
43
37.5
20.36
44
41.79
22.5
45
40
43.93
46
50.36
41.79
47
48.21
60
48
63.21
50.36
49
54.64
20.36
50
73.93
13.93
Obs
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
week1
41.79
22.5
39.64
78.21
46.07
46.07
61.07
39.64
56.79
34.29
43.93
31.07
46.07
22.5
50.36
41.79
36.36
65.36
37.5
48.21
102.86
86.79
31.07
week2
11.79
22.5
18.21
26.79
16.07
28.93
33.21
28.93
18.93
32.14
24.64
24.64
24.64
9.64
41.79
18.21
18.21
78.21
31.5
9.64
43.93
43.93
9.64