6 pts
8 pts
6 pts
4 pts
CROP 590 Experimental Design in Agriculture
Second Midterm Exam
Winter, 2015
Name____ ______________
1) An animal scientist would like to determine if three different species of pasture grass affect milk yield of Jersey cows in Australia. She would like to use the individual cows as blocks to control variation among animals. She also knows that milk yield varies throughout the year, so she decides to use time of year as an additional blocking factor.
She intends to use a Latin Square Design. Each cow is individually fed equal quantities of pasture grass. a) Show one possible randomization for a Latin Square Design by assigning the pasture grasses (A,B, and C) to the experimental units below.
Sept-Oct
Period 1
1
Cow
2 3
Nov-Dec 2
Jan-Feb 3
b) Provide a skeleton ANOVA for this experiment, showing sources of variation and degrees of freedom.
c) Assume that the means for the pastures are A=16, B=30, and C=26 liters of milk per cow per day. Calculate the Sums of Squares for Pastures from these means.
d) Do you think there will be adequate power in this experiment to detect differences among the pasture grasses? Can you suggest a way to increase power without including additional treatments in a Latin Square Design?
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8 pts
2) The residual plot below was obtained from a yield trial of 112 barley varieties. Data recorded were number of days to heading (flowering). The experimental design was an
RBD with 2 blocks.
Heading Date in Barley
8
6
4
2
0
-2
-4
-6
-8
156 158 160 162 164
Predicted
166 168 170 172
How would you interpret this graph? If this were your own trial, what steps would you take to address any concerns you have about the data?
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6 pts
4 pts
3) A researcher wished to know how soil type and a seed treatment (fungicide) influenced the emergence of red clover seedlings. Factorial combinations of three soil types (Sand,
Silt Loam, and Clay) and two levels of the fungicide (None and Treated) were utilized as treatments. Three pots of each treatment combination were grown in the greenhouse using a Completely Randomized Design. The number of emerged seedlings in each pot was recorded. Results from the ANOVA using SAS PROC GLM are shown below:
Dependent Variable: germ
Source
Model
DF Sum of Squares Mean Square F Value Pr > F
5 6630.277778 1326.055556 17.00 <.0001
Error 12 936.000000 78.000000
Corrected Total 17 7566.277778
R-Square Coeff Var Root MSE germ Mean
0.876293 10.82176 8.831761 81.61111
Source fungicide
DF Type III SS Mean Square F Value Pr > F
1 1300.500000 1300.500000 16.67 0.0015 soil 2 4588.777778 2294.388889 29.42 <.0001 fungicide*soil 2 741.000000 370.500000 4.75 0.0302
Table of means for all treatment combinations:
Fungicide
None
Sand
94.667
Mean
Treated 100.667
97.667
Soil Type
Silt Loam
82.333
92.333
87.333
Clay
42.333
77.333
59.833
Mean
73.111
90.111
81.611
a) Briefly interpret the results of the F tests for all of the treatment effects in the model.
b) On the basis of these results, which means should be reported? Why? Calculate the standard error for the means that you have chosen.
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12 pts
4) You wish to evaluate the effect of three methods for pruning grapes (no pruning, standard method, new method) and two fertilizer levels (low and high) on fruit yield.
Your experiment consists of all possible combinations of these two treatment factors in a Randomized Complete Block Design. Write orthogonal contrast coefficients that would address the following questions:
1. Does fertilizer level affect fruit yield?
2. Does pruning affect fruit yield?
3. Are yields with the New pruning method the same as with the Standard method?
4. Is the difference between the New and Standard methods the same at both levels of fertilizer?
Fill in the appropriate coefficients below the corresponding treatment combinations:
Fertilizer: Low Low Low High High High
Pruning None Standard New None Standard New
Contrast #
1
2
3
4
5 pts a) Describe how you would verify that these contrasts are orthogonal to each other
(give one numerical example).
5 pts
b) Is this a complete set of orthogonal contrasts? If not, how many additional contrasts would be required to make a complete set?
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12 pts
4 pts
6 pts
6) A study was conducted to determine the relationship between nitrogen fertilizer applied and yield of barley. Nitrogen treatments were 0, 25, 50, 75, and 100 lbs/acre. The experiment was conducted in a Randomized Block Design with four blocks. The mean yield in bu/acre for each treatment level is shown in the table below. The MSE from the
ANOVA was 42.5.
a) Complete the table of orthogonal polynomial contrasts by filling in the shaded cells.
N level lbs/acre
Mean
0 25 50 75 100
28.4 66.8 87.0 92.0 85.7  k i
2 L i
SSL Fcalc
Linear
Quadratic
Cubic
Quartic
-2 -1
2
-1
1
-1
2
-4
0
-2
0
6
1
-1
-2
-4
2
2
1
1
10 139.8 7817.62 183.94
10
70
6.9
0.9
19.04 0.4481
0.05 0.0011
b) What is the critical F value for determining if any one of these contrasts is significant?
c) What do the results tell you about the relationship between Nitrogen and yield of barley?
5

8 pts
4 pts
7) Match the mean comparison tests with the descriptions below.
Dunnett Dunnett test
SNK
HSD
BLSD
Student-Newman-Keuls test
Tukey's honestly significant difference
Waller and Duncan's Bayes LSD
A widely used multiple comparison procedure that provides good control of Experimentwise Type I error rate.
Criterion for significance depends on magnitude of the F ratio
Criterion for significance depends on relative ranking of means that are being compared
Compares all treatments to a control
8) To test the assumption that the errors (residuals) have a common variance, one could use: (circle the best answer). a) Tukey’s test b) Shapiro Wilk’s test c) LSD test d) Levene’s test
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F Distribution 5% Points
Denominator Numerator
Student's t Distribution
(2-tailed probability) df 1 2 3 4 5 6 7 df 0.40 0.05 0.01
1 161.45 199.5 215.71 224.58 230.16 233.99 236.77 1 1.376 12.706 63.667
2 18.51 19.00 19.16 19.25 19.30 19.33 19.36 2 1.061 4.303 9.925
3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 3 0.978 3.182 5.841
4 7.71 6.94 6.59 6.39 6.26 6.16 6.08 4 0.941 2.776 4.604
5 6.61 5.79 5.41 5.19 5.05 4.95 5.88 5 0.920 2.571 4.032
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 6 0.906 2.447 3.707
7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 7 0.896 2.365 3.499
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 8 0.889 2.306 3.355
9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 9 0.883 2.262 3.250
10 4.96 4.10 3.71 3.48 3.32 3.22 3.13 10 0.879 2.228 3.169
11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 11 0.876 2.201 3.106
12 4.75 3.88 3.49 3.26 3.10 3.00 2.91 12 0.873 2.179 3.055
13 4.67 3.80 3.41 3.18 3.02 2.92 2.83 13 0.870 2.160 3.012
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 14 0.868 2.145 2.977
15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 15 0.866 2.131 2.947
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 16 0.865 2.120 2.921
17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 17 0.863 2.110 2.898
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 18 0.862 2.101 2.878
19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 19 0.861 2.093 2.861
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 20 0.860 2.086 2.845
21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 21 0.859 2.080 2.831
22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 22 0.858 2.074 2.819
23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 23 0.858 2.069 2.807
24 4.26 3.40 3.00 2.78 2.62 2.51 2.42 24 0.857 2.064 2.797
25 4.24 3.38 2.99 2.76 2.60 2.49 2.40 25 0.856 2.060 2.787
26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 26 0.856 2.056 2.779
27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 27 0.855 2.052 2.771
28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 28 0.855 2.048 2.763
29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 29 0.854 2.045 2.756
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 30 0.854 2.042 2.750
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