Experimental Design in Agriculture
CSS 590
Final Exam, Winter, 2015
Name_______KEY___________
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
98
Amendment
2
1420
710
Error a
6
48
8
Cultivar
3
69
23
5.75
Amendment x Cultivar
6
84
14
3.5
27
108
4
Error b
6 pts
MS
F
88.75
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.
The Amendment x Cultivar interactions are significant (3.5 is greater than Fcritical = 2.46).
The main effects of amendments is highly significant (88.75>>5.14). The main effect of
cultivars is significant (5.75>2.96). However, the main effects should be interpreted with
caution due to the presence of the interactions. The effect of the soil amendment depends
on the cultivar.
6 pts
b) How would you report the results? Calculate the appropriate standard error(s)
for the means.
You would need to report the means for each combination of cultivar and soil amendment.
The standard error of the mean would be
se 
MSE

r
4
1
4
The relatively large effects of the amendments suggests that it might be possible to draw
general conclusions about them in spite of the interactions with cultivars. You would want
to explore this further by graphing the means and trying to understand the nature of the
interaction.
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.
Use a repeated measures analysis when you are taking repeated observations from
the same experimental units over time. There is likely to be some correlation in
errors from one harvest to the next, and the repeated analysis adjusts for that. In
order for a split-plot to be valid, you have to be able to assume that correlations in
errors among the sub-plot observations are equal. That is not likely to be the case
for repeated measures in time, because observations that are made at close time
intervals are likely to be more similar than those that are taken at distant time
intervals. With a repeated measures analysis, patterns in the covariance structure
can be taken into account. An autoregressive covariance structure is often
appropriate for repeated measures in time.
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?
MS3/MS4
6 pts
b) To determine if there are differences among the Years?
MS1/MS2
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.
Question 1 – circle the best answer
6 pts
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
Question 2 – circle the best answer
6 pts
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
-
-
-
Any additional blocking factors will impose more constraints on your randomization and will
remove degrees of freedom from error, thereby reducing the power of the significance
tests. Blocking will only be beneficial if it is effective in reducing experimental error.
Designs with multiple plot sizes may be necessary in particular circumstances, but
complicate the statistical analysis and mean comparison tests, and generally result in fewer
degrees of freedom for error (because there are several error terms).
Missing plots are more problematic with complex designs than with simple designs such as a
CRD.
Three-way and higher order factorials can become very difficult to interpret, particularly if
interactions are significant.
Greater complexity in planning, implementation, data collection and analysis provides more
opportunities for mistakes. There must be a clear benefit to justify the use of a more
complex design.
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?
The residual in his analysis includes variation among plots treated alike (true experimental error)
and variation among quadrats within each plot (sampling error). Pooling the two sources of
variation together will give you too many degrees of freedom in the error term, and will
probably provide an estimate of error that is too small, thereby inflating the Type I error rate.
One approach is to calculate the means for each plot and perform ANOVA on the means. The
other option is to keep the data for individual quadrats in the data set, but specify that the
appropriate error for testing methods is the block*method interaction. In an RBD, this term
represents the error among experimental units to which the treatments were randomly applied.
An analysis including the individual quadrats would have the benefit of providing an estimate of
sampling error, which could provide insights about the plot size that would be needed to meet
experimental objectives.
Correct ANOVA including subsamples: Source
Total
Block
Method
Block*Method
Sampling Error
4
df
29
4
2
8
15
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
1) What type of experimental design will you use? Justify your choice. Indicate any
basic assumptions that you have made.
I will use a strip plot design, due to the fact that both the insecticide and the plant
spacing treatments are best applied in a single pass through the field (i.e. it is
difficult to change treatments in the middle of a pass).
We have to assume that the insect pressure is uniform throughout the field, and
that spraying one plot won’t affect other insecticide treatments nearby.
5 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.
Insecticide – 1) no spray
2) one spray at the recommended time
3) two sprays – recommended time plus a later spray
Plant spacing - 6”, 9” and 12”
The no spray treatment is needed as a control so that we know the extent of insect damage
in the field when insects are not controlled, and to see if spraying is effective.
This will be a complete 3 x 3 factorial.
Due to the limited error degrees of freedom for a strip-plot experiment and the large errors
associated with insect counts, I will use 5 replications. A randomized complete block design
will be used to facilitate the application of the treatments (and there is really no practical
option for using a CRD because the treatment factors are applied in perpendicular strips).
5
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.
Source
Total
Block
Insecticide
Block * insecticide (error a)
Spacing
Block * spacing (error b)
Insecticide * spacing
Residual
df
44
4
2
8
2
8
4
16
4) Draw a diagram to indicate the field layout. For one replication, show how the
treatments will be randomized and assigned to experimental units.
N
8 pts
6"
20 ft
BLOCK 1
9" 12"
one spray
6"
BLOCK 2
12" 9"
no spray
5 ft alley
no spray
two sprays
5 ft alley
two sprays
one spray
An additional 3 Blocks
would also be included.
The planter would drive in
the north –south direction.
The sprayer would drive
down the alleys (eastwest), spraying on one side
at a time. Because the
boom extends for 10 ft
over the plots, two passes
would be needed (up one
alley and down the next) to
spray the entire 20-ft plot.
6 ft
The center of each plot would be harvested to reduce border effects due to differences in
plant density in neighboring plots. The ends of the plots adjacent to the alleys could also be
trimmed back before harvest.
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