Experimental Design in Agriculture
CROP 590
Winter, 2013
Second Midterm
Name:
Please show your work.
1) A study was conducted to determine if three varieties of a crop had different levels of
resistance to an insect pest. Twenty-two single-row plots of each variety were grown in a
Completely Randomized Design under field conditions. Insect larvae were extracted
from 10 plants in each plot using Berlese funnels and the total numbers of larvae were
recorded for each plot. A residual plot for this experiment is shown below.
6 pts
6 pts
a) Do the data appear to meet the assumptions necessary for the Analysis of Variance?
Explain your answer and indicate which assumption(s) (if any) may have been
violated.
b) Assuming that any further investigation of ANOVA assumptions supports your
answer to the previous question, list two approaches that you could take to proceed
with a valid analysis of this data set.
1
2) You wish to evaluate four commercially available soil amendments for use as fertilizers
in organic strawberry production in the Willamette Valley. Five strawberry growers agree
to collaborate with you in the study. On each farm, a one-acre strawberry field is divided
into four sections of equal size and the four soil amendments are randomly assigned to
one of the ¼-acre sections. On each farm, you harvest three quadrats from each of the
four sections for evaluation of fruit quality.
3 pts
a) Are there any blocks used in this study? If so, what are they?
3 pts
b) What are the experimental units?
6 pts
c) Consider the following components of this study and indicate whether you think they
are random or fixed effects:
i.
farms
ii. soil amendments
iii. quadrats
3 pts
d) You intend to analyze all of your data including the fruit weights from each quadrat
using PROC GLM in SAS. What would be the appropriate error term to use to
determine if there are significant differences among the soil amendments (FERT)?
(circle the correct answer)
i.
The Error Mean Square from the default analysis of the full model
ii. The Mean Square for Blocks
iii. The Sampling Error
iv. The Block*FERT interaction Mean Square
2
3) An animal scientist wishes to test the effects of five different feeding regimens on the
weight gain of pigs. Only five pigs are available for this research.
15 pts
6 pts
a) Can you suggest a design that would permit her to address the research question of
interest under these conditions? Show the sources of variation and degrees of
freedom for the ANOVA for this design.
b) The scientist asks her assistant to provide a randomization that is appropriate for the
design you suggested in part a. How would you verify that this is a valid
randomization for this design (i.e., what features would you look for)?
3
4) A Sugar Company conducted an experiment to compare two varieties of sugar cane in
combination with three levels of nitrogen (150, 210, and 270 lbs. N per acre
respectively). The experiment was run in 4 complete blocks.
16 pts
a) Fill in the shaded cells to complete the following ANOVA. (There is an F table at the
end of this exam)
ANOVA
Source
Blocks
Variety
Nitrogen
Error
Total
df
3
SS
249
216
16
400
15
23
MS
83.0
216.0
8.0
F
4.82
0.18
F crit
3.68
3.68
44.8
1553
Mean Yield (tons)
6 pts
6 pts
N-150
N-210
N-270
Mean
Variety 1
Variety 2
65
69
69
63
73
57
69
63
Mean
67
66
65
66
b) Interpret the results from this experiment. What can you say about the response of
sugarcane to Nitrogen fertilizer? (you do not need to calculate contrasts, but discuss
trends).
c) Is there a significant difference between the varieties at the highest N level?
4
5) You are conducting an experiment to evaluate the effectiveness of two new herbicides
for control of broadleaf weeds in barley. A widely used herbicide (standard) is included
for comparison. You also want to determine if addition of a surfactant to improve leaf
penetration of these herbicides will provide better weed control without causing injury to
the barley crop. A Randomized Complete Block Design is used with four blocks. The
treatments are as follows:
1) Standard herbicide
2) New herbicide A
3) New herbicide B
4) Standard herbicide + surfactant
5) New herbicide A + surfactant
6) New herbicide B + surfactant
Write orthogonal contrast coefficients that would address the following questions:
1. Does the use of the new herbicides improve barley yields in comparison to the
standard?
2. Are yields higher when a surfactant is used?
3. Is there a difference between herbicide A and herbicide B?
4. Does the difference between herbicides A and B depend on the presence or
absence of a surfactant?
Fill in the appropriate coefficients below the corresponding treatment combinations:
TRT#
1
Standard
2
New A
3
New B
4
Standard+
Surfactant
5
New A +
Surfactant
6
New B +
Surfactant
Means
Contrast #
1
25.4
70.8
72.5
68.3
75.7
69.4
12 pts
2
3
4
4 pts
a) Describe how you would verify that these contrasts are orthogonal to each other (give
one example).
3 pts
b) Is this a complete set of orthogonal contrasts? If not, how many additional contrasts
would be required to make a complete set?
5 pts
c) For the first contrast that you defined, calculate the Sums of Squares for the contrast
using the means provided in the Table.
5
F Distribution 5% Points
Denominator
df
1
1 161.45
2 18.51
3 10.13
4
7.71
5
6.61
6
5.99
7
5.59
8
5.32
9
5.12
10
4.96
11
4.84
12
4.75
13
4.67
14
4.6
15
4.54
16
4.49
17
4.45
18
4.41
19
4.38
20
4.35
21
4.32
22
4.3
23
4.28
24
4.26
25
4.24
26
27
28
29
30
Student's t Distribution
Numerator
(2-tailed probability)
2
3
4
5
6
7
199.5 215.71 224.58 230.16 233.99 236.77
19 19.16 19.25
19.3 19.33 19.36
9.55
9.28
9.12
9.01
8.94
8.89
6.94
6.59
6.39
6.26
6.16
6.08
5.79
5.41
5.19
5.05
4.95
5.88
5.14
4.76
4.53
4.39
4.28
4.21
4.74
4.35
4.12
3.97
3.87
3.79
4.46
4.07
3.84
3.69
3.58
3.5
4.26
3.86
3.63
3.48
3.37
3.29
4.10
3.71
3.48
3.32
3.22
3.13
3.98
3.59
3.36
3.2
3.09
3.01
3.88
3.49
3.26
3.1
3
2.91
3.8
3.41
3.18
3.02
2.92
2.83
3.74
3.34
3.11
2.96
2.85
2.76
3.68
3.29
3.06
2.9
2.79
2.71
3.63
3.24
3.01
2.85
2.74
2.66
3.59
3.2
2.96
2.81
2.7
2.61
3.55
3.16
2.93
2.77
2.66
2.58
3.52
3.13
2.9
2.74
2.63
2.54
3.49
3.1
2.87
2.71
2.6
2.51
3.47
3.07
2.84
2.68
2.57
2.49
3.44
3.05
2.82
2.66
2.55
2.46
3.42
3.03
2.8
2.64
2.53
2.44
3.40
3.00
2.78
2.62
2.51
2.42
3.38
2.99
2.76
2.6
2.49
2.4
6
df
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
0.4
0.05
0.01
1.376 12.706 63.667
1.061 4.303 9.925
0.978 3.182 5.841
0.941 2.776 4.604
0.920 2.571 4.032
0.906 2.447 3.707
0.896 2.365 3.499
0.889 2.306 3.355
0.883 2.262
3.25
0.879 2.228 3.169
0.876 2.201 3.106
0.873 2.179 3.055
0.870
2.16 3.012
0.868 2.145 2.977
0.866 2.131 2.947
0.865
2.12 2.921
0.863
2.11 2.898
0.862 2.101 2.878
0.861 2.093 2.861
0.860 2.086 2.845
0.859 2.080 2.831
0.858 2.074 2.819
0.858 2.069 2.807
0.857 2.064 2.797
0.856 2.060 2.787
0.856 2.056 2.779
0.855 2.052 2.771
0.855 2.048 2.763
0.854 2.045 2.756
0.854 2.042 2.750