Problems students are to do -
- students registered for Biol/Stat 336 (undergraduate)
credit please do problems 1, 3 and 4 below
- students registered for Math 488 (graduate) credit
please do problems 1 - 5 below
Please type up your answers or write very
neatly - no need to attach a copy of the output. Use
the attached Outputs.
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. 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 subsamples,
doing the one-way analysis, and requesting a MCP.
See this file.
| 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 remidies
in combination can temporarily impair vision by reducing the patient's
field of vision. The measurements provid-
ed in the following table were collected from 18 subjects randomly
assigned in groups of two to different com-
binations 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, theresults
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
temperature 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 para-
meters and verify any claims concerning the design) and thoroughly
analyse 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 perform-
ance 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, treat-
ment, NDF, treatment, NDF, treatment and NDF for each steer in each
of the 3 periods. Thoroughly analyse
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 it's 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?