Experimental Design in Agriculture
Name:
KEY
CROP 590
First Midterm
Winter 2014
1) You are an agronomist investigating the effects of nitrogen fertility on yield of canola. You
intend to apply five rates of nitrogen fertilizer in a replicated field experiment. Describe at
least four potential natural sources of experimental error in your field and steps you could
take to control them.
16 pts
Border effects – make sure that the plot area is surrounded by border rows to maintain
uniform competition
Stand losses – overplant and thin the seedlings back to a uniform plant density; fence the
experimental area to keep out rodents and other animals.
Seasonal variation – conduct the experiment over several years to ensure that results are
consistent from one year to the next.
Field gradients (moisture, fertility, etc.) – for known patterns of variation, blocking can be
used to get more precise comparisons among treatments.
Soil heterogeneity – increase plot size (up to a point) or number of replicates or measure a
concomitant variable to use as a covariate.
Other answers are possible…
2) You are conducting an experiment on wheat with 8 treatments and 3 replications using a
Randomized Complete Block Design (RBD).
8 pts
a) Fill in the appropriate degrees of
freedom in the skeleton ANOVA
below for the analysis of harvest
yield.
Source
DF
Total
23
b) Assume that one of the harvest bags was
damaged by mice in storage and all of the
contents were lost. Show how the degrees of
freedom would need to be adjusted for
postharvest analysis of grain protein (with
one missing plot).
Lost a plot
Source
DF
Total
22
Blocks
2
Blocks
2
Treatments
7
Treatments
7
Error
14
Error
13
1
3) The response of soybeans to three seed treatments was measured in a Completely
Randomized Design (CRD). Each treatment was replicated an equal number of times.
Fill in the shaded cells to complete the ANOVA below.
14 pts
Source
DF
SS
MS
F
Total
26
6754
Treatments
2
4030
2015
17.75
Error
24
2724
113.5
a) 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.
F calculated = 17.75
6 pts
F critical (α = 0.05, 2, 24 df) = 3.40
17.75 > 3.40, so we reject the null hypothesis and conclude that there are differences
among the seed treatments.
b) Suppose that the data for this experiment had been analyzed with statistical software
such as SAS or with the Excel Analysis Toolpak. Circle the actual probability value (Pr>F
or P-value) that would most likely be associated with the observed value of F that you
calculated in the ANOVA.
6 pts
8 pts
i.
< 0.0001
ii.
0.05
iii.
0.10
iv.
0.50
c) The mean for treatment A is 20 units greater than for treatment B. Is this difference
significant? Show your work.
One can do either an LSD test or a t test. There are 27 experimental units and 3
treatments, so we can deduce that there were 9 replications.
Y1  Y 2  20
LSD  t  0.05,df 24 2MSE r
LSD=2.064*sqrt(2*113.5/9)=10.365
20>10.365, so the difference is significant

t  Y1 Y 2
2MSE r
tcalc=20/sqrt(2*113.5/9)=3.982
3.982>2.064, so reject the null and conclude
that the means are different.
2
4) You wish to compare eight varieties of dry beans. The last time you conducted a trial in this
field you obtained a mean yield of 2000 kg/ha and a standard deviation of 260 kg/ha using a
standard plot size and four replications in a randomized block design. In your new trial, you
would like to have an 80% probability of detecting differences that are 15% of the mean,
using a significance level of 5%.
8 pts
a) What was the CV of your previous experiment in this field?
CV 
s
260
* 100 
* 100  13%
Y
2000
b) If you use 4 replications again in an RBD, can you expect to have the desired level of
power in your experiment, using a significance level of 5%? Use the tables at the end
of this exam. Show your work and interpret your answer.
Hints: There are several ways to solve this problem – look for the easiest way!
12 pts
You won’t be able to calculate power (1-) directly, but you should be able to
answer the question.
(4-1)(8-1) = 21
dfe = (r-1)(t-1)
2
2
2
2

0.05
 = 1-0.80
0.20
t1(0.05, 21 df)
2.08
t2(0.40, 21 df)
0.859
CV
r
Goal d%
2  t1  t 2  CV
2  2.080  0.859  13

r
4
2 *0.73788*169

 729.89
4
d  27%
d2 
13
4
15
No, the desired power is not attained. With the stated conditions you will only have an
80% chance of detecting a difference that is 27% of the mean. Therefore you will have
less than an 80% chance of detecting a 15% difference.
You could also show that the CV would have to be 7.2% to meet the specified goal, so
the level of precision with 4 reps and a CV of 13% is not sufficient.
You could also show that 13 replications would be needed to have the desired level of
power, but that would take a little more calculation (and the table provided does not
include t values for 84 df).
If you try to solve for t2 you will get a negative value for the specified conditions, so that
will not easily provide an estimate of power.
5) An experiment is conducted as a Randomized Complete Block Design (RBD). After the
experiment is completed it is determined that the relative efficiency compared to a CRD is
2.25. Circle the answer below that provides the best interpretation of this result.
6 pts
a. A CRD would have been 125% more efficient than the RBD
b. The RBD was 125% more efficient than a CRD
c. The RBD was 2.25% more efficient than the CRD
d. You would need to have 23 replications to attain the same efficiency using a CRD
3
6) You have been hired as a consultant to critique a small grains research program. On a trip
to the field station you observe an experiment designed to investigate the effect of three
planting densities (D1=100, D2=200, and D3=300 plants/m2) on grain yield of oats. You
know from a soil map that the clay content of the soil is higher on the west side and lower on
the east side of the field. The experiment has been divided into three blocks as shown
below.
16 pts
What is your assessment of the layout of this experiment? What would you do differently?
What features of the design do you like? How would you explain your answers to the
scientist who is conducting the experiment?
Problems:
1) Plots are not randomized in each block which could bias results.
2) Plots within each block should be oriented west to east so that all
plots within a block are exposed to similar soil conditions.
Good points:
1) Blocks arranged along the gradient so that differences among blocks
are maximized.
2) Border areas around the plots
3) Long, narrow plot shape and square blocks
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