Experimental Design in Agriculture
CROP 590
Final Exam, Winter, 2013
Name____________________
Please show your work!
8 pts
8 pts
1) You wish to compare ten varieties of sugarbeets in a field for which no uniformity
data is available. The last time you conducted a trial in this field, the Mean Square
Error from your ANOVA was 57,600 (yield was measured in kg/ha) using a standard
plot size of 15 m2 and four replications. You intend to use the standard plot size
again and four blocks to facilitate field operations and data collection. What is the
magnitude of the difference (in kg/ha) that you could expect to detect 80% of the
time, using a significance level of 5%?
2) When the results of ANOVA indicate that there are significant differences among
treatment means, generally there are additional questions that the researcher would
like to ask about the treatment effects. For each of the types of experiments
described below, choose a suitable approach (A-D) for comparing means. For full
credit, each option should be used once.
A
B
C
D
Orthogonal contrasts
Dunnett’s test
Orthogonal polynomial contrasts or regression
Tukey’s test
Experiment
Response of pigeonpeas to four levels of
Phosphorous application
A comparison of 12 new herbicides for
controlling weeds in rice, to identify the
most effective herbicide(s) for licensing
Yield of soybeans inoculated with 5 strains
of Rhizobium in comparison to a control
(no inoculant)
A study to investigate possible interactions
between 3 irrigation methods and several
planting arrangements as they affect
disease severity in peanuts
Good approach for comparing means
1
8 pts
3) The use of the Bonferroni adjustment is said to be a “conservative” approach for
making multiple comparisons among unstructured treatment means. Explain how
that influences the comparisonwise error rate, the experimentwise (family) error rate,
and the power of the test.
4) A large vineyard decided to conduct an experiment using a Randomized Block
Design to determine the best rates of an insecticide to apply to their grapes. The
experiment was conducted on a north facing site and on a south facing site to ensure
that results would apply to all of their major grape production environments. They
considered the sites and insecticides to be fixed effects and the blocks to be random.
Their across site ANOVA and Expected Mean Squares are outlined below.
Source
df
Site
1
MS1
σ2e + 6σ2Block(Site) + 24Ө 2Site
Block(Site)
6
MS2
σ2e + 6σ2Block(Site)
Insecticide
5
MS3
σ2e + 8Ө2Insecticide
Site*Insecticide
5
MS4
σ2e + 4σ2Site x Insecticide
30
MS5
σ2e
Error
Mean Square
Expected Mean Square
Based on the Expected Mean Squares shown above:
3 pts
3 pts
a) What is the appropriate ratio of mean squares to calculate the F value for sites?
b) What is the appropriate ratio of mean squares to calculate the F value for
insecticides?
2
5) An experiment was conducted to determine the effects of inoculation with two
bacterial strains on dry weight of two cultivars of perennial grasses. A control
treatment (no inoculum) was also applied to each cultivar. The treatments were
arranged in a split-plot design with cultivar as the main plot and inoculation treatment
as the subplot. The experiment was replicated in four complete blocks.
10 pts
a) Complete the ANOVA (fill in the shaded areas):
Source
Total
Block
Cultivar
Inoculation
Error b
6 pts
6 pts
df
23
3
1
SS
188.24
55.92
2
110.90
0.10
9.21
12
MS
F
18.64
2.68
3.49
0.05
0.77
0.07
b) Using the F table in the back of this exam, what are your conclusions regarding
the effects of cultivar and inoculation treatments on dry weight of grasses?
6) You are reading an article that was published in 1965. The authors were evaluating
the effect of growth promoters on Douglas Fir seedlings. Measurements were taken
at monthly intervals over the first two years of growth, and time of sampling was
analyzed as a sub-plot factor in a split-plot analysis. What type of analysis should be
considered for this data set today? What are the advantages of the current methods
of analysis compared to the split-plot in time?
3
7) A plant breeder conducted trials to compare six meadowfoam varieties at four sites,
as shown in the table below. The experimental design was a Randomized Block
Design with four blocks. Large seeds and high oil content are desired characteristics.
The weight of 1,000 seeds (TSW) was measured from bulk seed samples harvested
from each plot.
Varieties
MF166
MF179
Wheeler
Ross
MF183
Starlight
Sites
D_06_07
H_05_06
H_06_07
P_05_06
To determine if an across site analysis could be conducted, she used PROC
GLIMMIX to determine if the assumption of homogeneity of variance was met. The
output is shown below:
Covariance Parameter Estimates
Cov Parm
Group
Estimate Standard Error
Residual (VC) Site D_06_07 0.03786
0.01383
Residual (VC) Site H_05_06 0.01734
0.006332
Residual (VC) Site H_06_07 0.03642
0.01330
Residual (VC) Site P_05_06 0.06685
0.02441
Tests of Covariance Parameters
Based on the Restricted Likelihood
Label
common variance
DF -2 Res Log Like ChiSq Pr > ChiSq Note
3
25.7919
6.49
0.0901 DF
4 pts
a) Calculate Fmax from the estimates of the residuals above. The critical Fmax is
4.01 with k=4 and df=15.
5 pts
b) What can she conclude about the homogeneity of variance assumption from the
Fmax test and from the Chi Square test shown above?
4
Question 7, continued.
The results of the combined ANOVA across sites is shown below:
The GLM Procedure
Tests of Hypotheses for Mixed Model Analysis of Variance
Dependent Variable: TSW
Source
DF Type III SS Mean Square F Value Pr > F
Sites
Error
3 32.453611
14.371
10.817870
1.888864
82.30 <.0001
0.131439
Error: MS(Rep(Sites)) + MS(Sites*Variety) - MS(Error)
Source
DF Type III SS Mean Square F Value Pr > F
Rep(Sites)
12
1.209971
0.100831
2.55 0.0087
Sites*Variety
15
1.053395
0.070226
1.77 0.0606
Error: MS(Error) 60
2.377104
0.039618
Source DF Type III SS Mean Square F Value Pr > F
Variety
Error
5
8.136718
1.627344
15
1.053395
0.070226
23.17 <.0001
Error: MS(Sites*Variety)
5 pts
c) Give a brief interpretation of these results. Can she make generalizations about
the relative performance of varieties across sites?
5 pts
d) Calculate the standard error of a mean for a variety averaged across sites.
5
8) An experiment was conducted to determine how two growth regulators (GR1 and
GR2) affect the response of sorghum to nitrogen fertilizer (remember HW7). A graph
of the yield data for each of the growth regulators across the four nitrogen levels is
shown below. The F tests for the main effects of growth regulators (GR) and nitrogen
(N) as well as the interactions of GR and N were all significant in the ANOVA.
GR2
GR1
A total of seven orthogonal contrasts were evaluated, including three for the
interactions of GR and N. Based on the appearance of this graph, circle the
interaction contrasts that you would expect to be significant (there can be more than
one):
6 pts
i.
GR1 vs GR2 x N linear
ii. GR1 vs GR2 x N quadratic
iii. GR1 vs GR2 x N cubic
6
9) Minimum tillage is commonly practiced in the southeastern US in order to maintain
soil organic matter, conserve soil moisture, and reduce erosion. Cover crops are also
grown frequently to provide additional biomass during the winter months and to
reduce soil compaction. The cover crops are controlled with chemicals before cotton
is planted in the spring. A research scientist would like to conduct an experiment to
determine the best combinations of tillage practices and cover crops to promote the
growth and productivity of the cotton crop. He asks for your help in planning an
experimental design that will meet his research objectives.

The cover crops he wishes to study include winter pea, crimson clover, and rye.

The planter for the cover crops is 15 ft wide.

He would like to compare no-till, deep tillage, and conventional tillage.

The tillage equipment is 38 ft wide.

Equipment is available to plant the cotton crop in the same direction that the tillage is
applied.

He estimates that he needs a minimum plot size of 2000 sq ft for each of the
combinations of cover crop and tillage treatments to meet his objectives, with 3
replications.

The field he intends to use is 250 ft wide and 400 ft in length. Turning his planting or
tillage equipment around in the field requires a space of at least 20 ft. The roadways
on all sides of the field can also be used to turn around equipment.
5 pts
a) List the treatments of the experiment. Be sure to include any necessary controls.
8 pts
b) What type of experimental design will you use? Defend your choice and include
any basic assumptions you have made.
7
Question 9, continued.
10 pts
c) Draw a diagram to indicate the field layout. Show how the entire experiment will
fit in the field. For one replication, show how the treatments will be randomized
and assigned to experimental units.
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