Experimental Design in Agriculture
CROP 590
Final Exam, Winter, 2014
Name___________________
Please show your work!
Part I. Short Answer
1) An agronomist wants to measure the effect of irrigation (none, once, and twice during
the cropping season) and nitrogen fertilizer (25, 50, and 75 kg/ha) on the yield of
durum wheat. He decides to use a factorial set of treatments and a strip plot design,
with 4 blocks.
8 pts
8 pts
a) Complete the ANOVA by filling in the shaded cells (use the F table at the end of
this exam). What are your conclusions from the ANOVA?
Source
df
SS
MS
Block
3
1.08
0.36
Irrigation
2
3.34
1.67
Block*Irrigation
6
1.8
0.30
Nitrogen
2
3.02
1.51
Block*Nitrogen
6
1.74
0.29
Irrigation*Nitrogen
4
0.24
0.06
Error
12
Total
35
F
F critical
12.42
b) What means would you report from this experiment? Calculate the appropriate
standard errors for those means.
1
8 pts
6 pts
2) An experiment was conducted to determine the effects of inoculation with four
bacterial strains on dry weight of a perennial grass species. The experiment was
replicated in four complete blocks. The researcher intended to obtain additional
harvests from the same plots for several years. A colleague advised him to treat the
harvest time as a sub-plot factor in a split-plot analysis. The researcher then asks for
your opinion. What type of analysis should be considered for this data set? Explain
why you are recommending that analysis.
3) The effect of storage temperature on seed viability was studied in a Completely
Randomized Design (CRD). Three samples were stored at each of four
temperatures: 10, 30, 50, and 70 F. At the end of a one year storage period the
samples were tested for germination percentage. The estimate of MSE from the
ANOVA was 19.0 with 8 df.
8 pts
a) Complete the table of orthogonal polynomial contrasts by filling in the shaded
cells.
Storage temperature F
6 pts
10
30
50
70
Mean
58
31
18
13
ki2
Li
SSL
Fcalc
Linear
-3
-1
1
3
20
-148
3285.6
172.926
Quadratic
1
-1
-1
1
Cubic
-1
3
-3
1
20
-6
5.4
0.28421
b) What do these results tell you about the relationship between storage
temperature and seed viability?
2
6 pts
4) Consider a split-plot design with 4 levels of factor A (main plots) and 2 levels of factor
B (sub-plots). Assume that there is a soil gradient from high clay on the west to low
clay on the east side of the field. Circle the design below that is most likely to
effectively control experimental error due to this field effect.
3
5) Researchers in state X wished to determine the best varieties of a new annual crop
to recommend for commercial production. Five varieties were evaluated at three
locations over a two year period (a total of six sites). A randomized block design was
used at each site with three blocks. Yield data were collected from each of the six
trials.
After performing an analysis at each site to check for outliers and confirm that
assumptions for the ANOVA were satisfied, PROC GLIMMIX was used to determine
if variances across sites met the assumption of homogeneity of variance needed for
a combined analysis.
The output is shown below:
Covariance Parameter Estimates
Cov Parm
Group
Estimate Standard Error
Residual (VC) Site Hilltown 2018
7.9417
3.9708
Residual (VC) Site Hilltown 2019
34.2160
17.1080
Residual (VC) Site Springfiield 2018
21.5927
10.7963
Residual (VC) Site Springfield 2019
20.3512
10.1756
Residual (VC) Site Waterbury 2018
21.7168
10.8584
Residual (VC) Site Waterbury 2019
11.8882
5.9441
Tests of Covariance Parameters
Based on the Restricted Likelihood
Label
common variance
4 pts
DF -2 Res Log Like ChiSq Pr > ChiSq Note
5
324.77
4.92
0.4260 DF
a) The covariance parameter estimate of 34.2160 represents (choose one):
i) The mean yield in Hilltown in 2019
ii) The MSE from the ANOVA for yield for Hilltown in 2019
iii) The covariance of yield in Hilltown in 2018 and 2019
iv) The Mean Square for varieties in Hilltown in 2019
5 pts
b) What conclusion can be drawn about the homogeneity of variance assumption
from the Chi Square test shown above?
4
Question 5, continued.
The Random statement with a /test option was used in PROC GLM to generate
Expected Mean Squares for an across site analysis:
Source
Type III Expected Mean Square
Site
Var(Error) + 3 Var(Site*Variety) + 5 Var(Block(Site)) + 15 Var(Site)
Block(Site)
Var(Error) + 5 Var(Block(Site))
Variety
Var(Error) + 3 Var(Site*Variety) + Q(Variety)
Site*Variety Var(Error) + 3 Var(Site*Variety)
6 pts
c) Based on the results above, what would be the appropriate ratio of Mean
Squares to use to test for significant differences among varieties?
d) Are the blocks nested within sites? Explain your answer.
5 pts
A summary of the results of the combined ANOVA across sites is shown below:
Source
Mean
Square
2014.37
F Value
5
Type III
SS
10072
16.62
<.0001
12
1038.85
86.5712
4.41
0.0001
4
1072.25
268.061
4.94
0.0062
Site*Variety
20
1084.69
54.2347
2.76
0.002
Error
48
941.652
19.6178
Site
Block(Site)
Variety
DF
5
Pr > F
6 pts
e) Use the ANOVA on the previous page and the graph below to give a brief
interpretation of these results. Can generalizations be made about the relative
performance of varieties across sites? Can you note any trends that might
warrant further investigation?
Variety D
Variety E
Variety B
Part II. Experimental Design Question
A researcher has developed a new herbicide that can control a parasitic weed in red
clover fields in the Willamette Valley. The herbicide can be applied as a seed treatment
on clover, or as a post-emergence spray, but optimum rates have not been established.
Widely grown varieties of clover may differ in their tolerance to the herbicide. The
6
researcher would like to develop recommendations for use of the herbicide. Assume that
the primary reason for growing the crop is for seed production.
The parasite is prevalent on several acres of land that are available with a cooperative
farmer who grows clover near Salem.
Design an experiment that would meet the objectives of the researcher.
1) What type of experimental design will you use? Justify your choice. Indicate any
basic assumptions that you have made.
6 pts
2) List the treatments of the experiment. Be sure to include any necessary controls.
Explain why you have chosen this particular set of treatments.
6 pts
3) Break out the ANOVA in terms of Sources of Variation and degrees of freedom.
6 pts
7
4) Identify two meaningful questions that this experiment might address that are not
adequately evaluated from an ANOVA. Indicate the coefficients that would be
needed for each of the treatment means to estimate Sums of Squares for the
corresponding contrasts. Show how you would determine if the two contrasts are
orthogonal (or not). (There is a table of orthogonal polynomial contrast coefficients at
the end of this exam that can be used for reference.)
6 pts
6 pts
Continue on next page if needed.
8
F Distribution 5% Points
Denominator
Numerator
df
1
2
3
4
5
6
7
1 161.45 199.5 215.71 224.58 230.16 233.99 236.77
2 18.51 19.00 19.16 19.25 19.30 19.33 19.36
3 10.13
9.55
9.28
9.12
9.01
8.94
8.89
4
7.71
6.94
6.59
6.39
6.26
6.16
6.08
5
6.61
5.79
5.41
5.19
5.05
4.95
5.88
6
5.99
5.14
4.76
4.53
4.39
4.28
4.21
7
5.59
4.74
4.35
4.12
3.97
3.87
3.79
8
5.32
4.46
4.07
3.84
3.69
3.58
3.50
9
5.12
4.26
3.86
3.63
3.48
3.37
3.29
10
4.96
4.10
3.71
3.48
3.32
3.22
3.13
11
4.84
3.98
3.59
3.36
3.20
3.09
3.01
12
4.75
3.88
3.49
3.26
3.10
3.00
2.91
13
4.67
3.80
3.41
3.18
3.02
2.92
2.83
14
4.60
3.74
3.34
3.11
2.96
2.85
2.76
15
4.54
3.68
3.29
3.06
2.90
2.79
2.71
16
4.49
3.63
3.24
3.01
2.85
2.74
2.66
17
4.45
3.59
3.20
2.96
2.81
2.70
2.61
18
4.41
3.55
3.16
2.93
2.77
2.66
2.58
19
4.38
3.52
3.13
2.90
2.74
2.63
2.54
20
4.35
3.49
3.10
2.87
2.71
2.60
2.51
21
4.32
3.47
3.07
2.84
2.68
2.57
2.49
22
4.30
3.44
3.05
2.82
2.66
2.55
2.46
23
4.28
3.42
3.03
2.80
2.64
2.53
2.44
24
4.26
3.40
3.00
2.78
2.62
2.51
2.42
25
4.24
3.38
2.99
2.76
2.60
2.49
2.40
26
27
28
29
30
9
Student's t Distribution
(2-tailed probability)
df
0.40
0.05
0.01
1 1.376 12.706 63.667
2 1.061 4.303 9.925
3 0.978 3.182 5.841
4 0.941 2.776 4.604
5 0.920 2.571 4.032
6 0.906 2.447 3.707
7 0.896 2.365 3.499
8 0.889 2.306 3.355
9 0.883 2.262 3.250
10 0.879 2.228 3.169
11 0.876 2.201 3.106
12 0.873 2.179 3.055
13 0.870 2.160 3.012
14 0.868 2.145 2.977
15 0.866 2.131 2.947
16 0.865 2.120 2.921
17 0.863 2.110 2.898
18 0.862 2.101 2.878
19 0.861 2.093 2.861
20 0.860 2.086 2.845
21 0.859 2.080 2.831
22 0.858 2.074 2.819
23 0.858 2.069 2.807
24 0.857 2.064 2.797
25 0.856 2.060 2.787
26 0.856 2.056 2.779
27 0.855 2.052 2.771
28 0.855 2.048 2.763
29 0.854 2.045 2.756
30 0.854 2.042 2.750
10