Experimental Design in Agriculture
CSS 590
Final Exam, Winter, 2015
Name______________________
Part 1. Short answer, multiple choice, brief discussion questions
1) An experiment was conducted to determine the effects of two soil amendments on
dry weight of four cultivars of a perennial grass species. A control treatment (no
amendment) was also applied to each cultivar. The treatments were arranged in a
split-plot design with soil amendment as the main plot and cultivar as the subplot.
The experiment was replicated in four complete blocks.
Complete the ANOVA (fill in the shaded areas):
11 pts
Source
df
SS
Total
Block
47
3
2023
294
Amendment
MS
F
98
2
8
Cultivar
Error b
6 pts
6 pts
3
69
27
84
14
108
4
a) Using the F table in the back of this exam, what are your conclusions regarding
the effects of soil amendment and cultivar treatments on dry weight of this grass
species? Justify your answer.
b) How would you report the results? Calculate the appropriate standard error(s)
for the means.
1
Question #1 cont’d.
8 pts
c) The researcher would like to obtain additional harvests from the same plots for
several years. What approach would you recommend for conducting a combined
analysis of the data across years? Explain the rationale for your choice.
2) An experiment was conducted to determine the optimum time to apply a plant
growth regulator to reduce lodging in oats. The growth regulator was applied at
three growth stages (ZGS22, ZGS26, and ZGS30). A control treatment (no growth
regulator) was also included. The experiment was conducted for three years to see if
the optimum application time and effect of the growth regulator are consistent
across a range of environmental conditions. The experimental design was a
randomized complete block design with four replications.
Source
df
Mean Square
Expected Mean Square
Year
2
MS1
σ2e + 4σ2Rep(Year) + 16σ2Year
Rep(Year)
6
MS2
σ2e + 4σ2Rep(Year)
Growth Stage
3
MS3
σ2e + 4σ2Year*GS + 12Ө2GS
Year*Growth Stage
6
MS4
σ2e + 4σ2 Year*GS
Error
27
MS5
σ2e
Based on the Expected Mean Squares given in the table above, what would be
appropriate ratio of Mean Squares to use to calculate an F value
6 pts
a) To determine if there are differences among the Growth Stage Treatments?
6 pts
b) To determine if there are differences among the Years?
2
3) You are a food technologist and you have developed three new methods for making
orange juice. You wish to evaluate consumer acceptance of juice made with these
new methods. You also want to compare the new juice products to two types of
orange juice that are currently on the market (fresh squeezed brand X and frozen
brand Y). You suspect that different age groups may have different preferences. Ten
panelists in each of three age groups are identified to participate in the study (10
young, 10 middle-aged, and 10 elderly adults). Each of the panelist will be given the
five types of orange juice in random order and asked to rate them for various quality
parameters on a questionnaire that you have provided.
Answer the two questions below regarding the linear model for this experiment.
“Products” refer to the five types of orange juice.
6 pts
Question 1 – circle the best answer
a) Panelists and Age groups are cross-classified
b) Panelists are nested in Products
c) Age groups and Products are cross-classified
d) There are no nested effects in the model
6 pts
Question 2 – circle the best answer
a) Panelists are fixed effects
b) Products are fixed effects
c) Age is the only fixed effect in the model
d) All effects in the model are random
4) A fellow graduate student is planning an experiment, and seems to think that more
complex experimental designs are better than simple designs. How would you
convince him that it is best to use the simplest possible design that will meet the
objectives of the experiment? Include at least three reasons that you would give him
to justify your position.
9 pts
3
5) You are studying the effect of three cultivation methods on fresh weight of spinach.
You decide to use a Randomized Block Design with 5 Blocks. This is your first
experience collecting data of this sort, and you are not sure about the appropriate
plot size needed to obtain an acceptable level of precision. For a preliminary
analysis, you collect samples from two quadrats in each plot, and you then ask your
assistant to enter the data and calculate the ANOVA. He provides you with the
output below:
The GLM Procedure
Dependent Variable: weight
Source
DF Sum of Squares Mean Square F Value Pr > F
Model
6
16.35733333
2.72622222
Error
23
8.92266667
0.38794203
Corrected Total 29
25.28000000
7.03 0.0002
R-Square Coeff Var Root MSE weight Mean
0.647046
11.12232
0.622850
5.600000
Source DF Type III SS Mean Square F Value Pr > F
9 pts
block
4
4.16333333
1.04083333
2.68 0.0570
method
2 12.19400000
6.09700000
15.72 <.0001
Looking at the degrees of freedom and F ratios, you realize that the analysis has not
been done correctly. How would you explain the mistake to your assistant? What
should be done to obtain a correct analysis?
4
Part 2. Experimental Design Question
You are planning an experiment to estimate yield losses due to an insect pest on an
oilseed crop. The current practice is to spray with an insecticide one time during the
cropping season. You would like to know if an additional spray one month later could
provide a higher level of control and reduce yield losses. To avoid driving over the crop,
the insecticide is generally applied to your research plots by driving through an alley
that separates the plots. The boom on the sprayer can be adjusted to spray insecticide
on one or both sides of the tractor. When fully extended on both sides, the width of the
boom is 25 feet. The movement of the tractor with sprayer is perpendicular to the
direction of planting. The alley must be at least 4 feet wide to avoid driving over the
ends of the plots.
You expect that the width of spacing between rows can affect the damage due to the
insect and the capacity of the plants to compensate for the insect damage. Adjusting the
row width on the planter is time consuming and must be done before or after planting
any particular pass of the planter through the field. The planter can be adjusted to a 6”,
9” or 12” row spacing and can plant individual plots that are 20 feet long. The planter is
6-feet wide.
Design an experiment that would meet your objectives
6 pts
5 pts
1) What type of experimental design will you use? Justify your choice. Indicate any
basic assumptions that you have made.
2) List the treatments of the experiment. Be sure to include any necessary controls.
Explain why you have chosen this particular set of treatments.
5
8 pts
8 pts
3) Break out the ANOVA in terms of Sources of Variation and degrees of freedom.
Indicate the Mean Squares that would be used to calculate the F ratios for testing
the treatment main effects and interactions for the design that you have chosen.
4) Draw a diagram to indicate the field layout. For one replication, show how the
treatments will be randomized and assigned to experimental units.
6
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
4.23
3.37
2.98
2.74
2.59
2.47
2.39
27
4.21
3.35
2.96
2.73
2.57
2.46
2.37
28
4.20
3.34
2.95
2.71
2.56
2.45
2.36
29
4.18
3.33
2.93
2.70
2.55
2.43
2.35
30
4.17
3.32
2.92
2.69
2.53
2.42
2.33
7
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