Assignment:
Questions:
1. (a) An investigator was interested in comparing the effectiveness of five different types of fertilizers (F1, F2, F3, F4 and F5) for increasing sunflower yields. The fertilizers were given to five different types of sunflower varieties. The investigator was informed that the experimental area was not homogenous. The yield of sunflower was measured in kg per acre after harvesting the crop.
(i) What experimental design would be the most appropriate to address the research question?
(ii) How many experimental units are required for the investigation?
(iii) Identify the treatment and outcome variables for the investigation.
(iv) Draw a sketch of the experimental design which was proposed in (i).
(b). The following table shows the yields of sunflower on the effect of application of different fertilizers (F1, F2, F3, F4 and F5). The objective in applying fertilizer is to increase the yields.
Table below: Field plan for fertilizer use and the yields per plot is shown below.
|
F1
190
|
F5
80
|
F4
100
|
F2
240
|
F1
170
|
|
F3
200
|
F4
110
|
F5
110
|
F1
220
|
F2
270
|
|
F2
290
|
F5
280
|
F2
210
|
F4
110
|
F3
190
|
|
F4
90
|
F1
180
|
F3
100
|
F3
245
|
F4
120
|
|
F5
80
|
F3
300
|
F1
230
|
F5
130
|
F2
250
|
(i) Looking at Table shown, what experimental design was used to investigate the effectiveness of fertilizer in sunflower yields? Briefly explain your choice.
(ii) Calculate the mean yields for each of the different fertilizers (F1, F2, F3, F4 and F5) and plot the mean yields in an appropriate graph.
(iii) How many sources of variation would you report for your proposed design of experiment and what are the associated degrees of freedom?
(iv) How would you define the precision of an experimental design. Using a numerical example show that the precision increases as the standard deviation decreases when repeating the experiment.
2. Table below: Time to follow-up in study, or until disease develops for 40 subjects.
|
Subject
|
Years
|
Disease
|
Subject
|
Years
|
Disease
|
|
1
|
4.5
|
N
|
21
|
6.5
|
Y
|
|
2
|
3.9
|
Y
|
22
|
5.9
|
N
|
|
3
|
12.3
|
N
|
23
|
14.3
|
Y
|
|
4
|
14
|
Y
|
24
|
16
|
Y
|
|
5
|
4.5
|
Y
|
25
|
6.5
|
N
|
|
6
|
6.9
|
N
|
26
|
8.9
|
N
|
|
7
|
1.2
|
N
|
27
|
3.2
|
N
|
|
8
|
4.5
|
N
|
28
|
6.5
|
Y
|
|
9
|
2.3
|
Y
|
29
|
4.3
|
N
|
|
10
|
3.3
|
N
|
30
|
5.3
|
Y
|
|
11
|
5.4
|
Y
|
31
|
7.4
|
N
|
|
12
|
12
|
N
|
32
|
14
|
N
|
|
13
|
10.5
|
N
|
33
|
12.5
|
N
|
|
14
|
11.2
|
N
|
34
|
13.2
|
Y
|
|
15
|
13.9
|
Y
|
35
|
15.9
|
N
|
|
16
|
10.5
|
N
|
36
|
12.5
|
Y
|
|
17
|
9.6
|
Y
|
37
|
11.6
|
Y
|
|
18
|
1.2
|
Y
|
38
|
3.2
|
Y
|
|
19
|
2.4
|
Y
|
39
|
4.4
|
Y
|
|
20
|
7.3
|
N
|
40
|
9.3
|
N
|
2. (a) Assuming that all subjects in Table entered the study at the same time and are followed up until they leave the study (end of follow-up) or develop the disease, find the total observation time for the 40 subjects and estimate the incidence density. Give the answer per 10,000 person-years.
(b) It is more usual for follow-up studies to be of limited duration where not all the subjects will develop the disease during the study period. Calculate the incidence density for the same 40 subjects if they were observed for only the first six years, and compare this with the rate obtained.
(c) Twenty years after the American National Health And Nutrition examination Survey - NHANES, 1971-75 Gu et al was trying to find out if there was a difference in mortality between 1971 and 1993 of those claimed themselves diabetic in 1971 compared to the healthy population. The following table shows some of their results:
|
Male
|
Diabetic
|
Non-diabetic
|
The standard population of 1990
|
|
|
Population
|
Number of death
|
Population
|
Number of death
|
|
25-44 years
|
454
|
10
|
34461
|
154
|
325,000
|
|
45-64 years
|
1222
|
60
|
28412
|
706
|
186,000
|
|
65-74 years
|
1484
|
157
|
18189
|
1371
|
73,000
|
(i) Calculate the standardized mortality of the diabetic population (per thousand)
(ii) Calculate the relative mortality risk of the diabetic compared to the non-diabetic population in each age groups.
3. A study was designed to evaluate the relative risk of developing skin cancer in people who exposed with different levels of solar exposure. In a large cohort observed for 10 years in a follow-up study, a cumulative incidence of 10 skin cancer was observed in 8020 people who had either no or mild level of solar exposer, 22 cases in 5020 people who had moderate level of solar exposer, and 42 cases in 3840 people who had high level of solar exposer.
(i) What would be the prevalence of skin cancer in the total sample (report the prevalence per 1000 people)
(ii) Construct a contingency table (3×2) to present the data
(iii) Calculate the relative risk of developing skin cancer in people who had solar exposure at (a) moderate level, and (b) high level, compared to those who had either no or mild level of solar exposure.
(iv) How many people could be saved from the skin cancer if none was exposed with high level of solar exposure?