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NAME _______________________
BIOL 933 Final [Total Points in Exam = 96]
November 19, 2015
Due Date: Tuesday, December 8, at the beginning of lecture
Include your R scripts, include only the critical parts of the R output, and discuss each result. No points
will be awarded to outputs without a sentence explaining the conclusion. Clarification questions should be
directed only to Iago by e-mail (iago.hale@unh.edu). No consultation with other students is allowed
during the exam period, including R programming questions. Exams with more than one unlikely
identical mistake will receive zeroes, and the incident will be referred to the Associate Dean of the
Graduate School.
Question 1
[24 points]
Rising demand for organic rice led a group of four innovative growers to collaborate with a recent
BIOL933 graduate to design an experiment to optimize the germination and establishment of wet-seeded
rice plants under various reduced tillage and seed treatment regimes [see background below].
4 grower's
fields,
each divided into
four equal areas…
…to which seed trtmts are
Each field is then
re-divided into 4 areas… allocated and broadcast.
T2
T4
T4
T4
T4
T4
T3
T3
T3
T3
T3
T1
T1
T1
T1
T1
S1
T2
S4
T2
S3
T2
S2
T2
…to which tillage
trtmts are assigned.
the number of established
rice plants are counted in
four random 1 m2 plots
Each grower's field was divided into four areas [see diagram above] to which four tillage regimes were
randomly applied to the previous season's cover crop before the rice was planted. In keeping with the
organic spirit, this cover crop was purple vetch, a green manure acting as a source of nitrogen for the rice
field. The four tillage regimes:
T1
T2
T3
T4
Full till (the cover crop was completely incorporated into the soil via three passes with a disc)
High-partial till (the cover crop was incorporated partially via two passes with a disc)
Low-partial till (the cover crop was incorporated partially by a single pass with a disc)
No till (the cover crop was mown and the residue left to break down under the flooded conditions)
1
Once cultivated, the fields were flooded and again divided into four areas. Working in partnership with
the private company Seed Dynamics, the researchers prepared sixteen large batches of rice seed.
Specifically, they prepared four separate batches of each of the following pelletization treatments:
S1
S2
S3
S4
Round-Thin (round, thin-walled pellets)
Round-Thick (round, thick-walled pellets)
Torpedo-Thin (torpedo-shaped, thin-walled pellets)
Torpedo-Thick (torpedo-shaped, thick-walled pellets)
S2
S1
S3
S4
These large batches were then broadcast by airplane onto the farmers' fields, one batch of each treatment
allocated at random among the four areas of each field. At the time of tillering, high-resolution aerial
digital photographs were taken of the fields. Within each pellet-tillage combination, four 1 m2 areas were
chosen at random and the number of established rice plants counted. The data table below shows the
results of these four measures for each pellet-tillage combination across all four growers' fields. Some
plant counts were lost, due to their being recorded illegibly.
Name of
Grower
Farmer
Smith
Farmer
Watanabe
Farmer
Carlson
Farmer
Gottlieb
Area
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
T1
S1
262
255
251
257
239
240
238
245
270
266
268
249
273
284
285
293
S2
230
228
216
231
231
222
230
224
221
233
217
223
237
236
244
239
S3
279
268
271
281
253
247
248
242
258
.
260
253
272
267
269
278
T2
S4
272
277
279
273
249
242
254
244
255
260
263
266
278
273
276
279
S1
262
249
252
248
247
247
244
240
244
236
248
256
260
247
254
257
S2
234
237
234
232
228
230
232
231
213
209
215
215
237
240
246
245
S3
281
278
271
270
252
267
.
256
244
237
246
254
266
268
273
272
T3
S4
269
277
279
278
264
263
266
268
254
263
262
249
291
296
295
301
S1
273
269
276
273
262
256
265
266
253
248
254
249
276
282
285
277
S2
230
221
229
228
219
219
219
224
222
221
220
224
249
248
246
252
S3
275
278
273
272
247
250
250
255
258
258
248
263
282
281
281
272
T4
S4
271
273
271
271
261
248
253
259
270
262
262
266
.
284
287
282
S1
267
262
266
261
243
244
243
250
253
248
250
258
264
261
265
268
S2
223
223
218
218
223
224
226
231
230
235
224
228
240
244
238
241
S3
.
267
266
270
263
252
253
260
267
270
272
265
272
273
273
275
Background For organic growers, planting rice by a method known as "wet-seeding" can be an effective
non-chemical strategy to control weeds, especially red rice, an aquatic weedy relative of cultivated rice. In
wet-seeding, the rice seed is broadcast from an airplane onto a flooded field, the flooded conditions acting
as a weed suppressor up until the moment of planting. Immediately after broadcasting, the field is drained
so that the rice seed can germinate. Once the young plants begin to tiller (i.e. branch), the fields are
flooded once again, with the hope that the rice plants were given enough advantage to outcompete the
weeds.
That sounds great, but there are some problems with wet-seeding. Because the seeds are not drilled directly
into the ground, germination rates can be low due to suboptimal soil contact and plant density can be quite
non-uniform due to seed drift in the water. To help with both of these issues, the rice seed are usually
pelletized (i.e. encased in a thin shell, usually a mixture of clay, water, and binder) and soaked prior to
broadcasting. The pelletization lends weight and momentum to the seed, theoretically improving soil
contact and reducing drift, while the pre-soaking gives the seed a head start on germination.
2
S4
284
278
278
271
252
252
258
252
252
252
252
254
277
281
279
278
1.1
[5 points] Describe in detail the design of this experiment [see appendix].
1.2
[8 points] Generate the appropriate ANOVA table for this experiment. Test for normality of
residuals. Test for homogeneity of variances among both Tillage and Seed treatments. If done
correctly, you will find non-significant results for all these tests [i.e. do not transform the data!].
1.3
[1 point each, unless otherwise stated] Now use the most sensitive method that controls MEER to
answer the following set of questions:
a. Are there significant differences in the number of established plants per m2 between plots
receiving full cultivation versus plots receiving reduced cultivation (partial and no till)?
b. Is there a significant difference between partial and no till?
c. Is there a significant difference between high-partial and low-partial till?
d. Does a significant difference in the number of established plants result from using roundversus torpedo-shaped seed pellets?
e. What about between thin- and thick-walled seed pellets?
f. [5 points] Is there an interaction between seed pellet shape and wall thickness? Create
an interaction plot and perform and interpret the appropriate follow-up analyses. [i.e.
Perform a simple effects analysis, because you should find this interaction to be
significant.]
1.4
[1 point] What Tillage-Seed treatment combination would you recommend to achieve maximum
plant establishment?
3
Question 2
[22 points]
The objective of this experiment is to optimize the creaminess of homemade ice cream without negatively
affecting taste. To avoid the formation of crunchy ice crystals during churning, homemade ice cream
technicians have two time-honored strategies: Add plenty of sugar and put in a little alcohol. The reason
for this is that both the sugar and the alcohol act to lower the freezing temperature of the cream mixture,
preventing crystallization. Too much sugar, however, makes for a distastefully sweet final product. And
too much alcohol can keep the cream mixture indefinitely in a liquid state, as well as lend it off-flavors.
So the question is: What is the minimum amount of sugar and alcohol that one can get away with?
The researchers used a standard recipe as their starting point in laying out the treatments. Since the
standard recipe calls for 1 cup of sugar and 2 tablespoons of vodka (vodka is the liquor of choice due to
its neutral taste), the researchers decided to bracket these quantities, like so:
S1:
S2:
S3:
S4:
1/2 cup sugar
3/4 cup sugar
1 cup sugar
5/4 cup sugar
V1:
V2:
V3:
V4:
1 tablespoon vodka
1.5 tablespoons vodka
2 tablespoons vodka
2.5 tablespoons vodka
They then made three separate batches of each of the sixteen treatment combinations and, using an IceCrystalometer, measured the density of ice crystals* in each batch (crystals/cm3). The data for the
experiment are shown in the table below. Note that two of the batches were eaten by a researcher before
they could be measured.
[For this study, "ice crystals" means frozen granules measuring larger than 0.5 mm in diameter.]
ICE
CREAM!
S1
S2
S3
S4
1
31.50
9.55
7.69
5.40
V1
Batch
2
33.38
12.17
9.78
9.68
3
30.19
9.69
6.90
4.43
1
22.04
6.39
3.04
3.59
V2
Batch
2
20.70
2.81
0.49
0.06
3
24.07
7.28
5.95
4.84
V3
Batch
1
2
20.54
23.21
0.29
2.03
0.02
2.26
2.90
3.13
3
.
1.12
.
0.13
1
23.86
3.18
3.81
3.70
V4
Batch
2
18.37
0.66
0.33
0.11
3
21.29
1.44
1.89
3.76
2.1
[3 points] Describe in detail the design of this experiment [see appendix].
2.2
[5 points] Present an appropriate ANOVA table, showing the correct F tests for the main effect of
Sugar, the main effect of Vodka, and their interaction.
2.3
[6 points] Assign treatment ID's to the 16 Sugar-Vodka combinations and show that the
Linear:Linear component of the Sugar:Vodka interaction is significant, even though the overall
interaction (from 2.3 above) is NS. Make sure to use adjusted means (i.e. the lsmeans package!).
2.4
[6 points] Present a ranked table of adjusted means for the 16 treatment combinations. Based on
Tukey significance groupings, what is the minimum amount of sugar and alcohol one can use
without significantly increasing ice crystal density, relative to the "best" combination? (Work smart
here; you don't need to generate a complete Tukey means separation table to answer this question.)
2.5
[2 points] Is the analysis in 2.4 appropriate given the results from 2.3? Why or why not?
4
Question 3
[25 points]
Septoria tritici blotch (STB) is a fungal disease of wheat leaves characterized by patches of necrosis (dead
tissue) spotted with pycnidia (small spore-producing spots), as shown below.
pycnidia
wheat leaf
It is difficult to quantify the severity of an STB infection quickly by
eye, so an enterprising disease researcher decided to develop a
computer program that would scan infected wheat leaves, digitize their
images, and automatically calculate the density of pycnidia (i.e. the
number of pycnidia per cm2 of leaf). When the program was
completed, the researcher realized he needed to calibrate it by
determining which combination of light intensity (during scanning)
and contrast (during image digitization) would yield the most
consistently accurate readings.
To accomplish this, the researcher harvested 81 leaves from STB-infected wheat plants and randomly
gave 27 to each of his three assistants. Each assistant then randomly assigned his or her leaves, one-byone, to nine different intensity-contrast combinations:
1
2
3
Low intensity, low contrast
Low intensity, med contrast
Low intensity, high contrast
4
5
6
Med intensity, low contrast
Med intensity, med contrast
Med intensity, high contrast
7
8
9
High intensity, low contrast
High intensity, med contrast
High intensity, high contrast
Each assistant then used the computer program to evaluate the pycnidial densities of their leaves,
measuring each leaf two separate times at its assigned intensity-contrast combination.
Finally, using a dissecting microscope, each assistant painstakingly counted the number of pycnidia on
each of his or her 27 leaves and calculated the "true" pycnidial density of each leaf manually. By then
taking the difference between the "true" and computer-generated pycnidial densities for each leaf, the
researcher created a variable which effectively measures the accuracy of the different intensity-contrast
combinations. The complete dataset for this experiment can be found on Page 7 of this exam.
3.1
[5 points] Describe in detail the design of this experiment [see appendix].
3.2 [4 points] Assign treatment ID's to the 9 intensity-contrast combinations and present an ANOVA
table containing the proper F test for this treatment factor. Check normality and homogeneity of
variances among the treatment levels and state why it is necessary to transform the data.
3.3 [4 points] Transform the data using the appropriate power transformation. [Note: Before searching
for an appropriate transforming power, add 12 to each data point. Why is this necessary? Why is 12 a
reasonable number to use?]
3.4 [4 points] Using the same model as in 3.2, check all relevant assumptions with the transformed
data and verify that they are now satisfied. Present res*pred plots for both the original and transformed
data and comment.
[Tip: You will find Shapiro-Wilk to be just barely nonsignificant here. It's OK, go on…]
5
3.5 [8 points] Perform an ANOVA on the transformed data, present the ANOVA table, and carry out
all possible pairwise comparisons using the most sensitive fixed-range test available to you that controls
MEER. Present a means separation table and state which intensity-contrast combinations yield the most
accurate results.
[Tip: Think about what "most accurate" means here. Once you determine what the mean
would be for a perfectly accurate treatment, construct a 95% confidence interval about
that mean and see which treatments fall within it.]
6
Assistant 1
Program
Setting
Leaf
1
1
Low Intensity
Low Contrast
2
3
1
2
Low Intensity
Med Contrast
2
3
1
3
Low Intensity
High Contrast
2
3
1
4
Med Intensity
Low Contrast
2
3
1
5
Med Intensity
Med Contrast
2
3
1
6
Med Intensity
High Contrast
2
3
1
7
High Intensity
Low Contrast
2
3
1
8
High Intensity
Med Contrast
2
3
1
9
High Intensity
High Contrast
2
3
Computer
Count
39.4
39.4
57.0
57.8
29.0
29.4
21.0
21.2
25.1
24.3
37.6
37.9
34.5
34.5
21.9
22.2
29.0
29.2
36.9
37.3
66.1
65.9
37.7
38.2
38.7
38.9
29.2
30.3
58.6
58.4
35.2
34.8
30.1
30.5
26.8
26.7
30.3
30.2
56.9
56.4
38.4
38.1
27.3
26.1
54.4
54.5
36.1
35.6
31.1
30.8
25.1
24.7
29.4
29.4
"True"
Count
31.0
45.1
19.2
22.5
27.0
36.2
40.7
26.6
33.9
25.2
51.0
23.2
32.8
24.7
53.6
34.1
34.1
27.0
31.2
53.9
33.4
31.7
56.5
36.0
38.1
33.6
35.0
Assistant 2
Diff
Computer
Count
8.4
8.4
11.9
12.7
9.8
10.2
-1.5
-1.3
-1.9
-2.7
1.4
1.7
-6.2
-6.2
-4.7
-4.4
-4.9
-4.7
11.7
12.1
15.1
14.9
14.5
15.0
5.9
6.1
4.5
5.6
5.0
4.8
1.1
0.7
-4.0
-3.6
-0.2
-0.3
-0.9
-1.0
3.0
2.5
5.0
4.7
-4.4
-5.6
-2.1
-2.0
0.1
-0.4
-7.0
-7.3
-8.5
-8.9
-5.6
-5.6
38.8
38.4
31.5
31.7
58.0
57.3
37.8
37.4
31.8
32.1
5.9
6.3
33.4
34.2
21.1
21.3
33.1
33.5
39.4
38.8
31.8
32.3
44.3
43.8
30.5
30.4
42.9
42.5
46.2
46.5
24.9
24.2
40.4
39.4
33.6
33.0
30.1
29.8
23.5
23.5
37.3
37.0
24.8
25.0
33.2
33.8
30.3
30.5
14.0
13.9
38.6
38.3
35.4
35.2
7
"True"
Count
34.8
24.7
46.1
35.7
35.1
10.0
37.1
28.6
40.0
24.4
30.0
37.5
23.4
33.6
41.4
26.6
37.7
32.9
37.5
25.8
27.9
30.5
39.2
33.7
22.9
47.7
43.1
Assistant 3
Diff
Computer
Count
4.0
3.6
6.8
7.0
11.9
11.2
2.1
1.7
-3.3
-3.0
-4.1
-3.7
-3.7
-2.9
-7.5
-7.3
-6.9
-6.5
15.0
14.4
1.8
2.3
6.8
6.3
7.1
7.0
9.3
8.9
4.8
5.1
-1.7
-2.4
2.7
1.7
0.7
0.1
-7.4
-7.7
-2.3
-2.3
9.4
9.1
-5.7
-5.5
-6.0
-5.4
-3.4
-3.2
-8.9
-9.0
-9.1
-9.4
-7.7
-7.9
41.1
41.1
38.9
38.3
45.2
45.1
24.6
24.4
16.7
16.2
37.2
37.5
13.4
12.9
23.6
23.5
37.4
36.9
36.4
36.3
42.5
42.2
35.2
34.8
20.8
20.3
31.0
31.9
37.4
37.2
37.4
37.7
22.1
21.3
22.1
21.9
36.0
36.4
29.1
28.9
44.6
44.6
27.3
28.0
32.7
33.1
36.0
36.1
20.0
20.9
38.9
38.8
5.7
5.2
"True"
Count
43.3
37.8
41.9
31.3
20.7
35.0
20.5
30.5
46.7
20.5
29.9
27.2
20.1
26.7
29.7
38.4
23.8
23.3
32.0
30.2
44.0
33.0
38.2
41.4
31.3
47.3
14.7
Diff
-2.2
-2.2
1.1
0.5
3.3
3.2
-6.7
-6.9
-4.0
-4.5
2.2
2.5
-7.1
-7.6
-6.9
-7.0
-9.3
-9.8
15.9
15.8
12.6
12.3
8.0
7.6
0.7
0.2
4.3
5.2
7.7
7.5
-1.0
-0.7
-1.7
-2.5
-1.2
-1.4
4.0
4.4
-1.1
-1.3
0.6
0.6
-5.7
-5.0
-5.5
-5.1
-5.4
-5.3
-11.3
-10.4
-8.4
-8.5
-9.0
-9.5
Question 4
[25 points]
A researcher from Pacific Ethanol suspects that excess N fertilization can result in cell wall structure
modifications that reduce the amount of extractable cellulosic ethanol from maize biomass in production
areas in central Indiana. He obtains a list of all maize growers from the region, randomly selects four, and
makes them offers they cannot refuse. The researcher then selects 30 acres of homogeneous land within
each of the four farms. To nine small plots within these 30 acres, he randomly assigns three replications
of three different nitrogen application levels (0, 150, and 300 lbs N / acre). At the end of the season, he
records the total biomass produced per plot (tons of dry matter), as well as the total amount of ethanol
extracted (gallons) from each plot. The results are presented below:
0 lb/ac N
Farm
1
2
3
4
Biomass
80.5
80.8
80.4
80.1
80.2
80.3
80.9
80.6
80.0
80.8
80.9
80.7
Total
Ethanol
4102.5
4110.8
4149.1
4143.3
4144.8
4156.9
4129.8
4176.2
4143.2
4084.1
4176.3
4123.7
150 lb/ac N
Biomass
86.3
86.3
86.8
86.0
86.9
86.8
85.8
85.9
85.4
86.8
86.9
86.6
Total
Ethanol
4372.9
4371.0
4374.7
4284.3
4460.0
4469.4
4311.6
4376.7
4390.8
4411.7
4441.7
4423.2
300 lb/ac N
Biomass
92.9
92.9
92.4
89.0
88.1
88.7
89.9
89.8
89.4
92.3
92.2
92.4
Total
Ethanol
4401.3
4367.5
4411.7
4292.9
4236.6
4232.9
4299.1
4416.9
4283.5
4489.5
4468.6
4538.2
4.1
[5 points] Describe in detail the design of this experiment [see appendix].
4.2
[4 points] Is the differences in total ethanol yield among N treatments significant? What about
among farms? Do the differences among N treatments vary significantly across farms?
4.3
[6 points] Now use total biomass per plot as a covariable and answer the same questions posed
above in 4.2. How does the inclusion of the covariable affect the interpretation of the interaction
between Farms and N Level?
4.4
[2 points] Present a table of the adjusted and unadjusted ethanol means for the three N Levels. In
light of the objective of the study, explain the differences you observe between the adjusted and
unadjusted means. Are these conclusions valid for the entire production region across central
Indiana? Why or why not?
4.5
[5 points] Show that the data meet the assumptions of normality, homogeneity of variances across
N levels, and homogeneity of regression slopes across N levels.
4.6
[3 points] Characterize the relationship (linear, quadratic, etc.) between the response variable
ethanol yield per unit biomass and nitrogen. Present a plot to illustrate this relationship.
BIOL933
8
2015 Final Exam
* Bonus Extra Credit Question *
[6 percentage points]
Welcome to your new favorite game (it's sweeping the nation):
"Name That Design!"
Read the description of the following experiment and answer the questions.
Four friends who have not taken BIOL933 each believe (strongly) that their
grandmother's apple pie recipe is the best in the world. To put an end to the
argument, they decide to have a taste test. This is what they do:
First, they go shopping together so that everyone uses the same ingredients
(e.g. butter, flour, sugar, types of apples, etc.) because they want to compare
recipes, not quality of ingredients. Each person then lovingly prepares one pie
according to his or her grandmother's recipe. They time things such that all four pies come out of their
ovens at 6 PM on the same day.
One of the friends feels strongly that her pie will taste best fresh out of the oven, but another thinks that
his pie will taste best after sitting for a day. Another believes that her pie needs ice cream in order to
bring out its flavors. To accommodate all of these concerns and also to see how such things affect taste,
they decide to divide each pie into four quarters and randomly assign four "serving times" among them (7
PM, 10 PM, 8 AM the next day, 6 PM the next day). They also decide to divide each quarter into two
large slices and randomly assign "ice cream" to the two slices (with ice cream, without ice cream). At 7
PM, an unbiased fifth friend prepares the assigned eight slices (2 from each pie, with and without ice
cream) on eight different plates, labeled simply A – H. The four friends share these slices, taking tastes of
each; each person then assigns to each slice an overall score of 1 to 10. They repeat this ritual at the other
three serving times.
NOTE: Answer all questions based on how the experiment was actually conducted,
not on the stated intentions of the experimenters.
Answer questions 5.1 – 5.7 using the following multiple choice options. If none are applicable, or if it is
not clear from the experimental description, say so.
Select all that apply and provide information where indicated by "…".
a.
b.
c.
d.
e.
f.
Treatments
Blocks
Replications of …
Subsamples of …
Sub-subsamples of …
Main plots
5.1
What are the recipes?
5.2
What are the serving times?
BIOL933
g.
h.
i.
j.
k.
9
Subplots
Strip plots
Sub-subplots
Sub-sub-subplots
Repeated measures of …
2015 Final Exam
5.3
What are the ice cream assignments?
5.4
What are the tasters?
5.5
What are the pies?
5.6
What are the quarters of the pies?
5.7
What are the halves of the quarters of the pies?
_____
5.8
What is the replication level of Recipes? Of Serving Times? Of Ice Cream Assignments?
5.9
As it was conducted, this study allocates the most power to detecting differences among:
a.
b.
c.
d.
Recipes
Serving times
Ice cream assignments
Individual preferences of the tasters
5.10 In terms of the recipes themselves (the stated object of the study), is this experiment a CRD, an
RCBD, a LS, or is it uncertain?
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
Subsamples?
Covariable?
BIOL933
Number of
Levels
Fixed or
Random
Description
YES / NO
YES / NO
10
2015 Final Exam
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