Experimental Design in Agriculture
CROP 590
Final Exam, Winter, 2016
Name _______
________
_
Part I. Short answer – please show your work
1) An experiment is conducted to evaluate the yield of seven oat cultivars at four
locations that represent a sample of the environments in which the cultivars are
likely to be grown. The experimental design at each location is a randomized
complete block design with three replications.
Source
df
Mean Square
Expected Mean Square
Location
3
MS1
σ2e + 7σ2Rep(Loc) + 21σ2Loc
Rep(Loc)
8
MS2
σ2e + 7σ2Rep(Loc)
Cultivar
6
MS3
σ2e + 3σ2Loc x Cultivar + 12Ө2Cult
Loc*Cultivar
18
MS4
σ2e + 3σ2 Loc x Cultivar
Error
48
MS5
σ2e
3 pts
a) Based on the Expected Mean Squares given in the table above, what would be the
appropriate ratio of Mean Squares to use to calculate an F value to determine if
there are differences among the cultivars?
4 pts
b) Are Replications and Locations nested or cross-classified? Explain your answer.
4 pts
4 pts
c) The seven oat cultivars include the most promising new cultivars from your breeding
program, and you are considering them for commercial release. Do you think that
cultivars should be designated as fixed or random effects in this experiment? Defend
your choice.
d) Using Cultivars as an example, explain what the Expected Mean Square in the
ANOVA represents and define each of its components.
1
2) A researcher wished to study the relationships between irrigation and nitrogen
response in corn. Because irrigation could only be applied to large plots, she decided
to use a split plot design with the irrigation treatments (irrigated and nonirrigated)
as main plots and nitrogen fertility (60, 90, 120, 150 and 180 lbs/acre) as the
subplots. The trial was planted in four complete blocks. Yield was recorded in
bu/acre.
10 pts
Complete the ANOVA (fill in shaded areas):
Source
Total
Block
Irrigation
df
39
3
1
SS
12879
1911
MS
F
637
128
Nitrogen
Error b
5 pts
4
24
1834
585
720
15.28
146.25
30
a) Using the F table in the back of this exam, what are your conclusions regarding
the effects of irrigation and nitrogen on corn yield?
b) Calculate the standard error for an irrigation treatment mean.
5 pts
3) 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?
8 pts
2
4) An experiment was conducted to determine the effect of storage temperature on
the potency of an antibiotic. Fifteen samples of the antibiotic were obtained and
three samples, selected at random from the fifteen, were stored at each of five
temperatures: 10, 30, 50, 70, 90. At the end of a thirty day storage period the
samples were tested for potency with the following results:
Temperature
Mean
10
58
30
31
50
18
70
13
Source
df
SS
Total
14
4680.4
4
4520.4
1130.1
10
160.0
16.0
Temperature
Error
90
11
MS
F
70.63**
Orthogonal Polynomial Coefficients are used to obtain the following contrasts:
Temperature
10
30
50
70
90
Linear
-2
-1
0
1
2
2
-1
-2
-1
2
-1
2
0
-2
1
-4
6
-4
Quadratic
Cubic
Quartic
8 pts
6 pts
k2
L
SS(L)
-112
10
3763.20
235.2
1
-11
10
36.30
2.27
1
1
70
0.04
0
a) Fill in the shaded areas to complete the analysis of contrasts. Show your
calculations below.
b) What do these results tell you about the relationship between storage
temperature and antibiotic potency? Use the F table at the end of this exam to
support your conclusions.
3
F
5) Eight meadowfoam families were evaluated for seed oil content in a field study. The
experiment was blocked to account for soil heterogeneity and for ease of field
operations. Each of the 8 families was randomly assigned to two complete blocks. A
3' x 20' area of each plot was harvested and threshed and the seeds were cleaned
and weighed. A representative sample of seed was taken from each plot and sent to
the OSU seed lab for determination of oil content (%). The researcher requested that
duplicate NMR analyses be conducted on each sample. All of the data was analyzed
in PROC GLM in SAS.
The GLM Procedure
Dependent Variable: Oil
Source
DF Sum of Squares Mean Square F Value Pr > F
Model
15
50.75397187
3.38359812
Error
16
8.41925000
0.52620313
Corrected Total 31
59.17322187
6.43 <.0001
R-Square Coeff Var Root MSE Oil Mean
0.857719 2.831204
Source
DF
0.725399 25.62156
Type III SS Mean Square F Value Pr > F
Block
1
2.32740312
2.32740312
4.42 0.0516
Family
7 45.33204687
6.47600670
12.31 <.0001
Block*Family
7
0.44207455
0.84 0.5706
3.09452187
a) Is the F Value and Pr>F for Families in this output correct? Explain your answer.
4 pts
b) Calculate the correct F statistic for families and determine if there are significant
differences among families using the F table at the back of this exam.
6 pts
4
6 pts
6) An experiment has been conducted to determine the effects of Nitrogen and
Phosphorus fertilizer on the growth of spinach. Because the fertilizer treatments
were applied with a farm-scale fertilizer spreader, a strip-plot design was used with
three complete blocks. In the diagram below, shade or circle examples of the
designated experimental units:
a) Block I – an experimental unit for a Nitrogen treatment
b) Block II – an experimental unit for a Phosphorus treatment
c) Block III – the experimental unit for a specific combination of Nitrogen and
Phosphorus that would be used to evaluate the importance of Nitrogen x
Phosphorus interactions
Block I
N2
N3
Block II
N1
N2
N1
Block III
N3
N1
P3
P1
P3
P1
P3
P2
P2
P2
P1
N3
N2
Part II. Experimental Design (Answer Questions A through E)
As an agronomist, you are interested in studying the effect of phosphate fertilizer and
potash fertilizer on the yield of a perennial forage crop. Optimum rates have been
established for each of the fertilizers individually, but you would like to find out if the
application of one fertilizer affects the response to the other fertilizer. Other studies
have indicated that the timing of application has an effect on the crop’s ability to use
the fertilizer. To test this, you decide to use three different application dates: November
1, January 1, and March 1. The fertilizer application does not require large machinery. A
local farmer has a large field that has been uniformly planted to the forage crop. There
is also greenhouse space available, and flats in which you could plant the crop.
A) Which site will you use for the experiment? Justify your choice.
3 pts
4 pts
B) List the treatments of the experiment. Be sure to include any necessary controls.
Explain why you have chosen this particular set of treatments.
5
6 pts
6 pts
C) What type of experimental design will you use? Justify your choice. Indicate any
basic assumptions that you have made.
D) Draw a diagram to indicate the experimental layout. For one replication, show how
the treatments will be randomized and assigned to experimental units.
6
8 pts
E) Break out the ANOVA in terms of Sources of Variation and degrees of freedom.
Indicate the appropriate error terms for the F tests for the effects of interest.
7
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
8
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