Homework # 3 (on Design) – due by Thursday October 2 at 5pm
Problems students are to do
-
- students registered for BIOL/STAT 336 (UG) – do
problems 2, 3 and 4
- students registered for STAT 435 (G) – do problems 1 - 5
Please type up your answers or write very neatly - no need to attach a copy of the output. Use the attached Outputs. Summarize all results comparing treatments using the under-line method, and interpret these results.
1. As part of a pollution study,
lead levels at five monitoring sites in Chicago were measured. Grass
specimens from three areas within each monitoring site were collected and their
lead levels, in mg/g dry weight, measured in duplicate as presented
below. Does lead pollution differ with monitoring site and areas within
monitoring site? Please report all necessary assumptions, (exact) test
statistics and p-values, and results of relevant diagnostics, along with a
thorough analysis of the data. Be sure to identify the type of design.
See this
file.
NB
- if we find that Sites are
significant, our next step would be to perform a MCP/MSP to determine which
sites differ - this is done here by
averaging the sub-samples, doing the one-way analysis, and performing the
SNK/MCP.
|
Site |
A |
A |
A |
B |
B |
B |
C |
C |
C |
D |
D |
D |
E |
E |
E |
|
Area |
1 |
2 |
3 |
1 |
2 |
3 |
1 |
2 |
3 |
1 |
2 |
3 |
1 |
2 |
3 |
|
|
40.0 |
37.5 |
22.5 |
31.0 |
42.5 |
32.5 |
27.5 |
11.0 |
15.0 |
25.0 |
11.0 |
14.0 |
12.5 |
9.0 |
10.0 |
|
|
40.0 |
37.5 |
20.0 |
37.5 |
43.0 |
36.5 |
30.0 |
10.0 |
14.0 |
25.0 |
11.0 |
15.0 |
10.0 |
8.0 |
9.0 |
2. The female flower (A) and the
seed (B) of two African plants are widely used in traditional medicine for the
treatment of people with certain diseases. It has been claimed, however,
that use of these traditional remedies in combination can temporarily impair
vision by reducing the patient's field of vision. The measurements
provided in the following table were collected from 18 subjects randomly
assigned in groups of two to different combinations of flower and seed
concentrations. How do the plants appear to affect field of vision?
Again, report all necessary assumptions, (exact) test statistics and p-values,
the results of relevant diagnostics, along with a thorough analysis of the
data, and be sure to identify the type of design and the appropriate analysis
in your analysis. See this file.
Flower (A) Seed
(B) Field of
Vision
0.25 g 0.001
g
67 66
0.005
g
65 61
0.009
g
62 64
2.5
g
0.001 g
68 65
0.005
g
68 61
0.009 g
55 53
5.0
g
0.001 g
65 64
0.005
g
62 63
0.009
g
49 47
3. A horticulturalist studied
the germination of tomato seed with four different temperatures (25C, 30C, 35C
and 40C) such that each run of the experiment included only two different
temperatures because there were only two growth chambers available for the study.
The two experimental temperatures were randomly assigned to the chambers for
each run, but the researcher feels certain there may be run-to-run
variability. The data that follow are germination rates of the tomato
seed. Be sure to thoroughly identify the design (including all parameters
and verify any claims concerning the design) and thoroughly analyze the data
(after giving necessary assumptions) including subsequent analyses. What
is the commonly used term for "runs" in this experiment? See this file.
Run
25C
30C
35C 40C
1
24.65
--
--
18.62
2
--
24.11
--
17.08
3
22.31
21.25
--
--
4
--
--
17.95 18.93
5
28.90
--
18.27
--
6
-- 25.53
20.91
--
4. Associative effects
occur in animal diets when feedstuffs are combined and diet utilization or
animal performance is different from that predicted from a sum of the
individual ingredients. The addition of roughage to the diets of ruminant
animals had been shown to influence various diet utilization factors such as
ruminal retention time. However,
information about the relative associative effects of different roughage was
scarce, especially in mixed feedlot diets. An animal scientist
hypothesized roughage source could influence utilization of mixed diets of beef
steers by altering ruminal digestion of other diet ingredients. The basic
mixed diet for the beef steers was a 65% concentrate based on steam flaked milo
and 35% roughage. Three roughage treatments were used with
(A) 35% alfalfa
hay as a control treatment
(B) 17.5% wheat
straw and 17.5% alfalfa and
(C) 17.5%
cottonseed hulls and 17.5% alfalfa.
Twelve beef steers were available for the study. Each of the three
roughage diets was fed to
the steers in one of six
possible sequences of the three diets
(seq 1: A -> B -> C,
seq 2: B -> C -> A,
seq 3: C -> A -> B,
seq 4: A -> C -> B,
seq 5: B -> A -> C,
seq 6: C -> B -> A ).
Each diet in each sequence was fed to two steers for 30 days. The steers
were allowed a period of 21 days to adapt to a diet change before any data were
collected. The Neutral Detergent Fiber (NDF) digestion coefficient, which
indicates the percent of dietary fiber digested by the steer, was calculated
for each steer on each diet. The data are given below, with each row
corresponding to a different steer and the variables are sequence, treatment,
NDF, treatment, NDF, treatment and NDF for each steer in each of the 3 periods.
Thoroughly analyze the data and report all assumptions, findings and results of
diagnostics. As always, report exact test statistics and p-values. See this file.
abc a 50 b 61 c 53
abc a 55 b 63 c 57
bca b 44 c 42 a 57
bca b 51 c 46 a 59
cab c 35 a 55 b 47
cab c 41 a 56 b 50
acb a 54 c 48 b 51
acb a 58 c 51 b 54
bac b 50 a 57 c 51
bac b 55 a 57 c 55
cba c 41 b 56 a 58
cba c 46 b 58 a 61
5. Discuss the uses of
blocking in biostatistical studies - Why is it used and useful? Why is it not
used more? What are its
drawbacks? In what sense (if any) is blocking used in CODs and split-plot
designs? How is the analysis of a RCBD with one blocking and one treatment
factor different from a two-way ANOVA with two treatment factors?