NAME _______________________
PLS 205 Final [Total Points in Exam = 100]
March 12, 2014
Due Date: Tuesday, March 17, by 5:00 pm; 122 Robbins Hall
Include your SAS programs, include only the critical parts of the SAS output, and discuss each result.
NO POINTS WILL BE AWARDED TO OUTPUTS WITHOUT A SENTENCE EXPLAINING
THE CONCLUSION.
Clarification questions should be directed to Miguel and Dr. Dubcovsky by e-mail only. No consultation
with other students is allowed during the exam period (including SAS programming questions). Exams
with more than one unlikely identical mistake will receive zeroes, and the incident will be referred
to the Office of Student Judicial Affairs.
Problem 1
[25 points]
A grower would like to test if fruit size in blueberry is affected by fungicide application, insecticide
application, and insect pollination. The treatments the grower experimented with are:
Fungicide – regular fungicide application or no fungicide application
Insecticide – regular insecticide application or no insecticide application
Pollination – 25% of the flowers pollinated or 100% of the flowers pollinated
To conduct the experiment the grower picked 4 field sections with 1.8 m wide x 12 m long dimensions.
Each field section was divided into two 1.8 m x 6 m subsections and the fungicide treatments were
randomly assigned to each subsection. Each subsection was divided into 1.8 m x 3 m sub-sub section and
the insecticide treatment was randomly assigned to these sections. Finally the sub-sub sections were
divided into sections of 1.8 m x 1.5 m where the pollination treatments were randomly assigned. To apply
the 25% pollination treatment, the grower covered the plants with a bee proof net when the flowering for
the plants reached 25%. To insure that the flowers were being pollinated the grower installed bumble bee
colonies within each cage. When the plants were ready to harvest the grower weighed all of the ripe fruit
in bulk from each 1.8 m x 1.5 m section and divided the number by the total number of ripe fruit weighed
to get an average fruit weight. While harvesting one of the workers accidentally fell on a box of berries
corresponding to the Full fungicide, None insecticide, 25% pollination, in block 2. This data was removed
and is indicated by the word MISSING. The data is summarized below:
Block
1
1
1
1
1
Fungicide
Full
Full
Full
Full
None
Insecticide
None
None
Full
Full
None
Pollination
25
100
25
100
25
Response
0.687
0.361
0.87
0.558
0.442
1
1
1
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
None
None
None
Full
Full
Full
Full
None
None
None
None
Full
Full
Full
Full
None
None
None
None
Full
Full
Full
Full
None
None
None
None
None
Full
Full
None
None
Full
Full
None
None
Full
Full
None
None
Full
Full
None
None
Full
Full
None
None
Full
Full
None
None
Full
Full
100
25
100
25
100
25
100
25
100
25
100
25
100
25
100
25
100
25
100
25
100
25
100
25
100
25
100
0.382
0.39
0.462
MISSING
0.401
0.592
0.566
0.518
0.381
0.395
0.626
0.713
0.377
0.584
0.655
0.442
0.382
0.394
0.472
0.706
0.36
0.617
0.557
0.447
0.382
0.393
0.475
1. [5 points] Use the table in the appendix to describe the experimental design.
2. [5 points] Perform the appropriate ANOVA and report the significance of the different treatments and
interactions. THERE IS NO NEED TO TEST ASSUMPTION.
3. [5 points] Perform the appropriate tests based on your results for question 2.
4. [5 points] Report the appropriate means for Fungicide and Insecticide at the different levels of
pollination.
5. [5 points] Report the recommendations you will give on the application of fungicide and insecticide
based on all the previous statistical analyses.
Problem 2
[20 points]
An agronomist wants to test the effect of four treatments (two tillage practices and two cover crop
methods) on processing tomato yields and to extend his conclusions to the Central Valley. The two tillage
practices include Standard tillage (ST) vs. Conservation tillage (CT) and the two cover crop treatments
include No Cover crop (NO) vs. Cover crop (CC). The researcher also wants to test if there are significant
interactions between the cover crop and tillage.
To conduct the experiment the researcher randomly picks six random locations in the Central Valley in
California. In each location he selects one field, divides it in four homogeneous sections with 4 large plots
in each section. In each location he randomly assigns each of the four possible cover by tillage treatment
combinations to one of the 4 large plots available within each section. The researcher measures tomato
yield in each plot and records the yield in tons per acre. The data is reported below:
Location
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
Block
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
Tillage
ST
ST
ST
ST
ST
ST
ST
ST
ST
ST
ST
ST
CT
CT
CT
CT
CT
CT
CT
CT
CT
CT
CT
CT
ST
ST
ST
Crop
NO
NO
NO
NO
NO
NO
CC
CC
CC
CC
CC
CC
NO
NO
NO
NO
NO
NO
CC
CC
CC
CC
CC
CC
NO
NO
NO
Yield
54
65
42
49
55
33
58
68
54
47
48
46
52
62
51
51
59
34
69
64
55
61
52
59
54
59
41
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
ST
ST
ST
ST
ST
ST
ST
ST
ST
CT
CT
CT
CT
CT
CT
CT
CT
CT
CT
CT
CT
ST
ST
ST
ST
ST
ST
ST
ST
ST
ST
ST
ST
CT
CT
CT
CT
CT
CT
CT
CT
NO
NO
NO
CC
CC
CC
CC
CC
CC
NO
NO
NO
NO
NO
NO
CC
CC
CC
CC
CC
CC
NO
NO
NO
NO
NO
NO
CC
CC
CC
CC
CC
CC
NO
NO
NO
NO
NO
NO
CC
CC
48
50
32
53
71
64
47
56
41
50
55
52
63
57
42
58
69
66
55
60
48
55
54
36
52
51
38
52
70
51
51
58
40
63
55
51
53
62
35
56
73
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
loc1
loc2
loc3
loc4
loc5
loc6
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
CT
CT
CT
CT
ST
ST
ST
ST
ST
ST
ST
ST
ST
ST
ST
ST
CT
CT
CT
CT
CT
CT
CT
CT
CT
CT
CT
CT
CC
CC
CC
CC
NO
NO
NO
NO
NO
NO
CC
CC
CC
CC
CC
CC
NO
NO
NO
NO
NO
NO
CC
CC
CC
CC
CC
CC
59
58
63
58
51
50
51
49
57
28
52
61
56
47
48
41
52
58
46
53
53
41
59
65
57
56
52
57
[Don’t worry about testing the assumptions]
1. [5 points] Perform appropriate analysis of variance on the data. Report the results of the analysis and
answer the following questions:
a) Are there significant differences in yield between tillage methods or cover crop methods?
b) Is the interaction between tillage and cover crop significant?
c) Are the effects of tillage, cover crop, and their interaction consistent across locations? If yes,
show an interaction plot for the significant interaction.
2. [5 points] Create two plots using SAS, R, or Excel where the first plot shows the main effects of tillage
and the second plot shows the main effects of the crop treatments. Based on this result and the previous
ANOVA provide your conclusion and recommendations for the complete Central Valley.
3. [5 points] Please report the means of the main effects of tillage and cover crop. Is the difference
between standard tillage and conventional tillage larger than the difference between no cover crop
and cover crop? Does the largest difference correspond to the most significant result? If not
explain why.
4. [5 points] Using the same model as in question 1, estimate the variance components for all of the
random effects in your model. Which of these random effects had the largest variance?
Problem 3
[25 points]
A table grape breeder has developed two potential varieties and would like to release the variety that
produces the largest berries upon application of gibberellic acid (GA), as well as confirm that these two
new varieties are better than the traditional variety Thompson Seedless. The breeder selects three
homogeneous sections in a vineyard and plants 18 10-plant plots in each section. Within each section he
randomly assigns two plots to one of the 9 combinations of the three varieties and three GA treatments (0
ppm, 10 ppm, and 20 ppm). At harvest, he randomly picks 50 berries per plant per plot and weighs them
in bulk. The average individual berry weights (g) calculated for each plot are reported below:
Section
Variety
TS
1
Var1
Var2
TS
2
Var1
Var2
TS
3
Var1
Var2
GA application rate (ppm)
0
10
20
4.15
4.90
5.45
4.19
4.81
5.17
4.84
5.28
6.39
4.77
5.37
6.10
4.92
5.64
5.66
4.58
5.29
6.01
4.27
4.83
5.90
4.83
4.95
5.76
5.21
6.02
6.06
5.24
5.50
6.56
5.34
5.79
5.95
5.11
5.29
6.29
5.01
5.25
5.67
4.80
5.35
5.87
5.61
6.20
6.78
5.06
6.13
6.70
5.58
5.57
6.33
5.44
5.91
6.24
1. [3 points] Describe the experimental design in detail using the table in the appendix.
2. [2 points] Test all three required ANOVA assumptions for this design.
3. [4 points] Perform ANOVA with the correct model and discuss the results.
4. [3 points] Present an interaction plot of GA concentration by variety on the effect of berry weight.
Comment on the interaction plot in light of the ANOVA results.
5. [5 points] Are any of the components of the GA*Variety interaction significant?
6. [6 points] Based on your answer to question 5, answer the following questions based on the appropriate
analyses:
a. Was there a significant difference in berry weight between Thompson Seedless and the two new
varieties?
b. Was there a significant difference in berry weight between the two new varieties?
c. How would you describe the response of berry weight to GA concentration?
7. [2 points] What recommendations would you make to the breeder if the difference in cost between the
10 and 20 ppm GA applications is small?
Problem 4
[5 points]
Two levels of Nitrogen (N0 and N1) and two levels of Potassium (K0 and K1) are tested in a 2 x 2
factorial organized in a RCBD with three blocks. A third factor, Varieties (A, B, and C) is added as a split
plot of the Nitrogen Potassium combinations. Show an actual field layout of how you would design this
experiment.
Problem 5
[25 points]
Black point is a common disease of wheat in the Sacramento region. The incidence of the disease is
estimated as the % of grains with a black discoloration at the end of the grain. A researcher wants to test
the differences in resistance among four specific varieties (designated 1 to 4) and three fungicides
(designated 1-3). He selects three homogeneous blocks of land and divides each in 4 large plots, and
randomizes the four varieties separately in each block. He plants the field in a North-South direction,
changing variety in each plot. By head emergence he cut two aisles in a West-East direction dividing each
block in three horizontal sections. He then drives his tractor in a West-East zigzag applying only one
fungicide in each pass through the block. The order in which the three fungicides will be applied is
randomized independently in each of the blocks. A design of the field is included below. Since Black
point is affected by lodging (the falling spikes are more likely to show the disease), the researcher records
the lodging of each of the 12 plots in each block after the fungicide was applied and before harvesting.
The data for the percentage of grains with black point and the % lodging in each plot is included in the
Table below the graph of the field.
Block
1
2
3
1
2
3
1
2
3
Fung
1
1
1
2
2
2
3
3
3
Var.1
Y
X
39.6
14
52.5
17
47.1
15
54.5
16
63.5
17
63.0
16
60.4
17
68.6
19
67.4
18
Var.2
Y
X
55.2
15
55.2
16
61.5
16
76.7
16
60.6
15
68.0
16
78.5
16
62.7
14
80.6
18
Var.3
Y
X
38.9
15
58.3
16
45.5
16
73.4
16
53.3
15
67.2
16
63.7
15
66.2
17
73.1
17
Var.4
Y
X
38.6
15
46.3
16
51.3
16
56.4
15
63.2
16
59.6
15
65.3
16
50.2
13
70.4
18
1. [5 points] Are there significant differences among varieties and among fungicides in the
percentage of black point, once the values were adjusted for lodging?
2. [5 points] Are the differences the same if the values are not adjusted for lodging? If different
provide a potential explanation of the source of the discrepancies.
3. [3 points] Were the responses to fungicides different at the different varieties when the values
were corrected for lodging?
4. [5 points] Based on the previous answer (and using the adjusted values) use the most sensitive
fixed range mean comparison test controlling the experiment wise error rate to compare all four
varieties and all three fungicides separately. What would be your recommendation?
5. [4 points] Test all the required assumptions required to perform the test on the adjusted values (no
need to show Tukey 1-df test for multiplicative effects)
6. [3 points] Was the test with the adjusted values more efficient than the test with the unadjusted
values? Quantify the difference.
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?
Number of
Levels
Fixed or
Random
YES / NO
YES / NO
Description