Name:
CROP 590 – Experimental Design in Agriculture
First Midterm
Winter 2013
Please remember to show your calculations.
12 pts
8 pts
1) You have just been hired by grass seed company to conduct field trials to evaluate the seed
yield of orchardgrass. Last year, your predecessor compared a new variety with several
varieties already on the market. Although average seed yields were higher with the new
variety, the results were not statistically significant. List at least four changes in the
experimental design and protocol you might consider to improve the likelihood of obtaining
significant results in the coming season.
2) You are conducting an experiment with 6 treatments and 3 replications using a Randomized
Complete Block Design. One of your plots is lost before you collect harvest data. Fill in the
appropriate degrees of freedom in the skeleton ANOVA for the analysis of harvest yield,
making appropriate adjustments for the missing plot.
Source
DF
Total
Blocks
Treatments
Error
1
3) You have conducted an experiment to compare the tillering capacity of three varieties of
wheat in a Completely Randomized Design with four replicates of each variety. The table
below shows the means for tillers/plant for each variety, as well as the grand mean for the
entire experiment.
Varieties
Means
Custer
Ike
Karl
Grand Mean
3.78
4.31
5.23
4.44
a) Use the means to compute the Sums of Squares for Varieties (show your work).
8 pts
8 pts
b) The Mean Square Error (MSE) from the ANOVA in this experiment was 0.15. What is
the LSD value? (You will need to use the table at the end of this exam)
8 pts
c) Is there a significant difference between the varieties Karl and Ike? (you can use the
result from part b to help you answer this question)
2
4) A research scientist would like to determine the effect of daylength on flowering date in
cowpeas. Three growth chambers are available for the experiment, and these are set at 8,
12, and 16 hours of daylight. Ten plants are placed in each chamber, and flowering dates
are recorded on each plant.
6 pts
8 pts
4 pts
a) What are the treatments in this experiment?
b) Having taken CROP 590, you have some concerns about the design of this experiment.
How would you explain those concerns to the scientist and how will they affect the
interpretation of results?
c) How could the design be modified to overcome your concerns?
3
5) An experiment was conducted to determine the effect of four feed supplements on weight
gain of lambs. Five ranches were used in the study. On each ranch, four lambs were
included in the study and each of the lambs received a different feed supplement. Data
recorded were pounds gained in 100 days.
6 pts
a) Are there any blocks in this experiment? If so, what are they?
b) Fill in the shaded cells to complete the ANOVA.
16 pts
Source
DF
Total
SS
MS
998.00
4
576.20
3
Error
F
19.47
111.00
88.80
8 pts
c) Do the results indicate that there were differences among the treatments? Support your
statement with a significance test using the tables provided at the end of this exam.
8 pts
d) Calculate the standard error of a treatment mean. Show your work.
4
F Distribution 5% Points
Denominator
df
1
1 161.45
2 18.51
3 10.13
4
7.71
5
6.61
6
5.99
7
5.59
8
5.32
9
5.12
10
4.96
11
4.84
12
4.75
13
4.67
14
4.60
15
4.54
16
4.49
17
4.45
18
4.41
19
4.38
20
4.35
21
4.32
22
4.30
23
4.28
24
4.26
25
4.24
26
27
28
29
30
Student's t Distribution
Numerator
(2-tailed probability)
2
3
4
5
6
199.5 215.71 224.58 230.16 233.99
19 19.16 19.25 19.30 19.33
9.55
9.28
9.12
9.01
8.94
6.94
6.59
6.39
6.26
6.16
5.79
5.41
5.19
5.05
4.95
5.14
4.76
4.53
4.39
4.28
4.74
4.35
4.12
3.97
3.87
4.46
4.07
3.84
3.69
3.58
4.26
3.86
3.63
3.48
3.37
4.1
3.71
3.48
3.32
3.22
3.98
3.59
3.36
3.20
3.09
3.88
3.49
3.26
3.10
3.00
3.8
3.41
3.18
3.02
2.92
3.74
3.34
3.11
2.96
2.85
3.68
3.29
3.06
2.90
2.79
3.63
3.24
3.01
2.85
2.74
3.59
3.20
2.96
2.81
2.70
3.55
3.16
2.93
2.77
2.66
3.52
3.13
2.90
2.74
2.63
3.49
3.10
2.87
2.71
2.60
3.47
3.07
2.84
2.68
2.57
3.44
3.05
2.82
2.66
2.55
3.42
3.03
2.80
2.64
2.53
3.40
3.00
2.78
2.62
2.51
3.38
2.99
2.76
2.60
2.49
5
df
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
0.4
1.376
1.061
0.978
0.941
0.920
0.906
0.896
0.889
0.883
0.879
0.876
0.873
0.870
0.868
0.866
0.865
0.863
0.862
0.861
0.860
0.859
0.858
0.858
0.857
0.856
0.856
0.855
0.855
0.854
0.854
0.5
0.05
0.01
1.000 12.706 63.667
0.816 4.303 9.925
0.765 3.182 5.841
0.741 2.776 4.604
0.727 2.571 4.032
0.718 2.447 3.707
0.711 2.365 3.499
0.706 2.306 3.355
0.703 2.262 3.250
0.700 2.228 3.169
0.697 2.201 3.106
0.695 2.179 3.055
0.694 2.160 3.012
0.692 2.145 2.977
0.691 2.131 2.947
0.690 2.120 2.921
0.689 2.110 2.898
0.688 2.101 2.878
0.688 2.093 2.861
0.687 2.086 2.845
0.686 2.080 2.831
0.686 2.074 2.819
0.685 2.069 2.807
0.685 2.064 2.797
0.684 2.060 2.787
0.684 2.056 2.779
0.684 2.052 2.771
0.683 2.048 2.763
0.683 2.045 2.756
0.683 2.042 2.750