BIOL933
Fall 2015
Homework 5
Topic 8
Due Thursday, October 22, at the beginning of lecture. Answer all parts of the questions completely,
and clearly document the procedures used in each exercise. To ensure maximum points for yourself,
invest some time in presenting your answers in a concise, organized, and clear manner.
Question 1
An ecology student studied the effect of different treatments on the growth of toothed dodder (Cuscuta
denticulata), a parasitic flowering plant whose host is creosote bush (Larrea tridentate) in the Mojave
Desert. The student blocked 4 distinct regions were she wanted to carry out her experiments in order to
control variation (Blocks I to IV). In each block, she randomized her 5 treatments (A to E) along with a
control (K), in which she applied no treatment. One month after applying the treatment, she measured the
surviving number of vines of Cuscuta per creosote bush in 10 bushes per plot. The averages of these
measurements are presented below.
A
B
C
D
E
K
I
25.49
16.05
17.67
26.19
22.79
28.82
II
21.12
16.33
16.43
23.39
19.81
22.30
III
17.78
11.78
11.16
17.21
16.61
19.96
IV
31.20
22.97
21.63
33.37
29.30
37.85
1.1
Describe in detail the design of this experiment [see appendix at the end of this problem set].
1.2
Test all necessary assumptions and produce a Res*Pred plot.
1.3
Explain why a log transformation is appropriate for these data.
1.4
Test all necessary assumptions using log10() transformed data and produce a Res*Pred plot.
Compare this plot with the one generated previously.
1.5
Perform an ANOVA on the transformed data, present a Tukey mean comparison of detransformed
means, and interpret the effect of the treatments on the parasitic Cuscuta.
1.6
Based on the Tukey table from 1.4 above, how would you report the upper and lower bounds of the
95% confidence interval about the mean of Treatment D?
HW5 (Topic 8)
1
Question 2
Saponins are natural tensoactives (surfactants) derived from the tree Quillaja saponaria, indigenous to
Chile. They have been used for over 100 years in the production of photographic films, as foaming
agents in food and beverages, and as adjuvants in animal vaccines, cosmetics, etc. A researcher is
interested in studying the effect of two solvents (A and B) on the extraction of saponins from the bark of
Quillay. Four different extraction processes were tested: Method A used only solvent A, Method B used
only solvent B, Method C combined both solvents A and B, and Method D used no solvents. The
extractions were done in four different facilities (1 - 4) throughout the central valley of Chile. Eight trees
were sent to each facility and there they randomized the 8 tress into the 4 extraction methods. The % w/w
of saponins to total water soluble compounds is presented below:
Method
A
B
C
D
Facility 1
30.2
35.2
26.0
22.8
33.0
35.6
16.4
17.2
Facility 2
38.5
35.2
31.8
34.2
47.7
38.1
19.3
19.5
Facility 3
35.2
39.7
35.4
34.1
50.9
43.4
26.2
24.4
Facility 4
40.9
49.5
31.7
31.0
54.4
56.0
24.6
23.0
[Little tidbit for the interested: Quillaja saponaria in grown today as a crop,
and it is illegal to use the bark from naturally growing trees for their saponin.]
2.1
Describe in detail the design of this experiment [see appendix at the end of this problem set].
2.2
Test all necessary assumptions using the full exploratory model (i.e. a model that contains the
Block*Treatment interaction) and produce a Res*Pred plot.
2.3
Transform the data with the most appropriate power transformation, present new assumption test
values, and produce a new Res*Pred plot. Compare this plot with the one generated previously.
2.4
Using the transformed data, again retain the Block*Treatment interaction term in your model and
answer the following questions. Choose the most sensitive method of analysis that controls MEER
for all questions, taken as a group. [Tip: Be sure to use the right error term (MSBlock*Trtmt!]
a.
b.
c.
d.
2.5
Is there a significant treatment effect?
Is there a significant effect of Solvent A on saponin yield?
Is there a significant effect of Solvent B on saponin yield?
Is the effect of Solvent A different at the different levels of Solvent B? Present a graph
with the 4 treatments and comment how the graph confirms your result.
Present a table of the detransformed Method means. With the analysis you've done, are you able to
recommend one Method as superior to the others? Why or why not?
Those interested in delving deeper may wish to consider these additional questions:
How does the use of a transformed scale affect your interpretation of the interaction results?
With this explanation in mind, speculate as to why I asked you to retain the Block*Treatment
interaction term in your model.
To be clear, you are not expected to provide answers to these questions for this HW.
HW5 (Topic 8)
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BRAIN TEASER (FOR THE INTERESTED -- NOT REQUIRED!)
Consider this thought experiment:
In trying to develop more cost-effective low-emissivity (low-e) windows, a researcher studies the effect
of two different thin metal films (A and B) on reducing the infrared transmission properties of glass
(measured as a fraction of total incident radiation). The two films are arranged in four different
treatments:
Treatment 1
Treatment 2
Treatment 3
Treatment 4
No film
Film A only
Film B only
Both film A and film B
A0B0
A1B0
A0B1
A1B1
When analyzing the data from the experiment, the researcher finds he must carry out a power
transformation to bring the data in line with the ANOVA assumptions. Specifically, the transformation
he uses is:
Transformed Datai = (Original Datai)1.8
He finds a significant interaction between the two films in the transformed data (see table of means
below).
Table of Means of the Transformed Data
A0B0
A1B0
A0B1
A1B1
0.883
0.687
0.712
0.305
The question: Is this interaction real, is it an artifact of the transformation, or is it uncertain? Why?
It's easy to get confused with this, so here's a hint: Consider what a non-interacting
original data set would look like (go ahead and generate a sample set) and then what the
above transformation would do to it. What does that tell you about the data provided?
HW5 (Topic 8)
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Appendix
When you are asked to "describe in detail the design of this experiment," please do so by completing the
following template:
Design:
Response Variable:
Experimental Unit:
Class
Variable
1
2
↓
n
Block or
Treatment
No. of
Levels
Subsamples?
YES / NO
HW5 (Topic 8)
Description
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