Experimental Design in Agriculture
CROP 590
Winter, 2013
Second Midterm
Name:
KEY
Please show your work.
1) A study was conducted to determine if three varieties of a crop had different levels of
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.
Possible outlier? (but this is
not the main problem)
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.
No. The variance appears to increase with the means (predicted values), creating a
funnel shape which is common for count data. The assumption of homogeneity of
variance is therefore not met. There may also be greater dispersion of residuals
above zero (skewness), which could violate the assumption of normality.
6 pts
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.
- Use an appropriate transformation (e.g., a log transformation) so that the residuals
have a common variance and follow a normal distribution
- Use a Generalized Linear Mixed Model based on the actual distribution of the data
(e.g. Poisson)
- Use a nonparametric test (e.g. ranks) (but this would have less power)
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
3 pts
a) Are there any blocks used in this study? If so, what are they?
The farms are the blocks.
b) What are the experimental units?
The ¼-acre sections on each farm.
6 pts
c) Consider the following components of this study and indicate whether you think they
are random or fixed effects:
i.
3 pts
farms
random
ii. soil amendments
fixed
iii. quadrats
random
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
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.
She could use a Latin Square Design and give all five feeding regimens to each pig.
The pigs would be one blocking factor (rows) and the sequence of the feeding
regimen could be a second blocking factor (columns). There would need to be a
waiting period between the time the pigs finish one regimen and begin the next to
avoid carryover effects.
Source
6 pts
df
Total
t2-1
24
Pigs
t-1
4
Sequence
t-1
4
Feeding Regimen
t-1
4
Error
(t-1)(t-2)
12
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)?

A randomization process should have been used to assign the regimens to pigs
and sequences

Each animal would receive each regimen once

The order in which the regimens are given would be unique for each pig

At any point in time, each of the five regimens would be assigned to one and only
one pig
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
VxN
Error
Total
df
3
1
2
2
15
23
SS
249
216
16
400
672
1553
MS
83.0
216.0
8.0
200.0
44.8
F
4.82
0.18
4.46
F crit
4.54
3.68
3.68
Mean Yield (tons)
N-210
N-270
Variety 1
Variety 2
65
69
69
63
73
57
69
63
Mean
67
66
65
66
Mean
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).
Variety 1
Variety 2
There is a significant interaction between
variety and nitrogen, so conclusions should
be based on the two-way table of means.
The yield of sugar cane in this study
depended upon the variety grown and the
rate of applied nitrogen. The yield of
Variety 2 decreased as the rate of
application increased, while variety 1
showed a positive response to the higher
application rates.
75
70
Sugar Yield (tons)
6 pts
N-150
65
60
55
50
N-150
N-210
N-270
Nitrogen Application
c) Is there a significant difference between the varieties at the highest N level?
6 pts
sed = sqrt(2*44.8/4) = 4.73
t(0.05,15 df) = 2.131
LSD for A*B means = 2.131*4.73 = 10.09;
Mean1-Mean2 = 73-57 = 16;
16 > 10.09
Yes, the varieties differ at the highest N level.
Could also use a t test (or compare confidence intervals or use contrasts)
t
Y1  Y2
73  57

 3.38
2MSE
2 * 44.8
r
4
3.38>2.131 so the means are different.
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
-2
1
1
-2
1
1
2
-1
-1
-1
1
1
1
3
0
-1
1
0
-1
1
4
0
1
-1
0
-1
1
12 pts
4 pts
a) Describe how you would verify that these contrasts are orthogonal to each other (give
one example).
The sum of cross-products of the coefficients for all pairs of contrasts should be zero.
For example, for contrast 1 vs contrast 2:
(-1)(-2) + (-1)(1) + (-1)(1) + (1)(-2) + (1)(1) + (1)(1) = 0
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?
No, a complete set would consist of t-1 = 5 contrasts. We would need one more 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.
SSL  MSL 
r    j Yj 
j
2
2

r * L2 4*1012

 3400.333
2
12
j
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