Experimental Design Summary

1
Experimental DesignSummary
2
Completely Randomized Block
Yij ? gi eij
Average over the whole experiment
Effect of ith genotype



Error
jth replicate of the ith genotype
3
Completely Randomized Block

• Can be used with unbalanced replication of
  entries.
• Genetic studies (i.e. F1, F2, BC1)
• Simple to analyze.
• Completely random.
• Can fit into any area.
• Unlikely to manage fertility gradients.

4
Randomized Complete Block
Yijk ? ri gj eijk
Average over the whole experiment
Effect of jth genotype
Effect of ith replicate



Error

ith genotype in the jth replicate block
5
Randomized Complete Block

• Layout is simple and can be adjusted to fit
  almost any shapes experimental area.
• Simple and relatively robust to errors (say in
  planting).
• Analyses is simple to carry out.
• Block effects are often significant.
• No restraints on entry numbers.

6
Latin Square
Yijk ? gi rj ck eijk
Where Yijk is the performance of the ith genotype
in the jth row and kth column ? in the overall
mean gi is the effect of the ith genotype rj
is the effect of the jth row ck is the effect of
the kth column and eijk is the error term.
7
Latin Square

• Advantage of latin square designs is their
  accuracy and ability to remove gradients in two
  directions.
• Disadvantage is that they require large levels of
  replication. A 10 entry experiment would require
  100 experimental units.
• Latin square analyses are intolerant to missing
  values.

8
Lattice Square
Yijk ? gai bak rj eijk
Where Yijk is the performance of the ith genotype
in the jth replicate and kth sub-block ? in the
overall mean gai is the effect of the ith
genotype adjusted according to sub-blocks bak is
the effect of the kth sub-block adjusted
according to the entries in that block rj is the
effect of the jth replicate and eijk is the
error term.
9
Lattice Square

• Lattice squares are usually more effective than
  RCBs.
• Have restraints on the number of entries and
  replicates.
• Are not truly randomized.
• Errors in plot arrangement (i.e. planting)
  renders them useless.
• Lattice squares are resolvable.

10
Rectangular Lattice
Yijk ? gai bak rj eijk
Where Yijk is the performance of the ith genotype
in the jth replicate and kth sub-block ? in the
overall mean gai is the effect of the ith
genotype adjusted according to sub-blocks bak is
the effect of the kth sub-block adjusted
according to the entries in that block rj is the
effect of the jth replicate and eijk is the
error term.
11
Rectangular Lattice

• More flexible in entry and replicate number than
  square lattices.
• Designs are resolvable.
• Designed for statutory cultivar field testing.

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Interactions
Genotype Nitrogen 1 Nitrogen 2
A 3,468 4,088
B 2,504 4,791
A
B
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Factorial Experimental Design
Irrigation Days between defoliation Days between defoliation Days between defoliation Days between defoliation
Irrigation 0 4 8 12
1 day I1.D0 I1.D4 I1.D8 I1.D12
2 day I2.D0 I2 D4 I2D8 I2D12
3 day I3.D0 I3.D4 I3D8 I3D12
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Factorial Experimental Design
3 t3 1 t2 2 t2 1 t3 3 t4 3 t1
2 t3 3 t2 1 t1 2 t4 4 t1 1 t4
I
3 t2 1 t1 3 t3 2 t4 1 t3 3 t4
3 t1 2 t2 1 t4 2 t1 1 t2 2 t3
II
1 t2 3 t1 2 t1 1 t1 2 t4 3 t2
1 t3 3 t3 2 t2 3 t4 1 t4 2 t3
III
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Two-Factor Factorial Model
Yijk ? ri dj wk dwjk eijk
Where Yijk is the performance of the the ith
replicate, and the jth d factor and kth w factor
? in the overall mean rj is the effect of the
jth replicate di is the effect of the ith
d-factor wk is the effect of the kth w-factor
dwjk is the interaction effect between dj and wk
and eijk is the error term.
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Factorial Experimental Designs

• Can be used with any number of factors and factor
  levels.
• Gives equal precision to estimating all factors
  and levels.
• Greatest mistake by researchers is to include too
  many factors where interpretation of three-way
  interactions can be difficult.

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Split-Plot Design
I II
III IV




3 2 1 4 3 1 4 2
3 1 2 4 2 4 1 3
A A B A
B B A B
A B B A
B A A B
B B A A
A A B B
B A B B
A B A A
3 2 1 4 3 1 4 2
3 1 2 4 2 4 1 3
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Split-Plot Design Model
Yijk ? ri gj e(1)ij tk gtjk e(2)ijk
Where Yijk is the performance of the the ith
replicate, and the jth main-plot and kth
sub-plot ? in the overall mean rj is the effect
of the jth replicate gi is the effect of the ith
main-plot e(1)ij is the main-plot error tk is
the effect of the kth sub-plot gtjk is the
interaction effect between gj and tk and
e(2)ijk is the sub-plot error term.
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Strip-Plot Design
B A C
A C B
1
1








2
2
I
IV
4
4
3
3
B A C
A C B
3
3








1
1
III
II
2
2
4
4
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Strip-Plot Design Model
Yijk ?rigje(g)ijtke(t)ijgtjke(gt)ijk
Where Yijk is the performance of the the ith
replicate, and the jth strip and kth strip ? in
the overall mean rj is the effect of the jth
replicate gi is the effect of the ith
strip-plot e(g)ij is the g-factor error tk is
the effect of the kth strip-plot e(t)ij is the
t-factor error dwjk is the interaction effect
between gj and tk and e(gt)ijk is the sub-plot
error term.
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Restraints
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Genotypes/Species
23
Facilities

• Glasshouse, Laboritory, Field, Growth rooms.
• Types of data.
• Time availability
• Funding.

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Restraints Facilities, Data types, Timing, and
Funding Factors, levels Replicates, Plot size
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Examples
Scottish Summers Day
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Jeannies Oriental Mustard

• Oriental mustard (Brassica juncea L.) is a new
  crop to the PNW
• Growers have little experience growing the crop.
• Design an experiment to determine the optimum
  growing conditions to maximize productivity.

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Jeannies Oriental Mustard
Factors ?
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Jeannies Oriental Mustard

• Four cultivars.
• 2 oilseed and 2 condiment.
• 2 planting dates.
• 3 seeding rates.
• 5 nitrogen levels.
• 3 Replicates.

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Jeannies Oriental Mustard





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Jeannies Oriental Mustard
I II
III
910
78
56
34
1-2
Late Planting
Early Planting
Late Planting
Late Planting
Early Planting
Early Planting
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Jeannies Oriental Mustard
910
78
56
34
1-2
Late Planting
Early Planting
32
Jeannies Oriental Mustard
I II III
I II III
910
78
56
34
1-2
Late Planting
Early Planting
33
Jeannies Oriental Mustard
I II III
I II III
910 75lb 25lb 75lb 50lb 0lb 25lb
78 0lb 0lb 25lb 70lb 50lb 100lb
56 25lb 50lb 100lb 25lb 75lb 75lb
34 50lb 75lb 50lb 0lb 100lb 0lb
1-2 100lb 100lb 0lb 100lb 25lb 50lb
Late Planting
Early Planting
34
Jeannies Oriental Mustard
I II III
I II III
910 75lb 25lb 75lb 50lb 0lb 25lb
78 0lb 0lb 25lb 70lb 50lb 100lb
56 25lb 50lb 100lb 25lb 75lb 75lb
34 50lb 75lb 50lb 0lb 100lb 0lb
1-2 100lb 100lb 0lb 100lb 25lb 50lb
Late Planting
Early Planting
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Jeannies Oriental Mustard


2
Arid 3 g
Arid 5 g
1
Arid 4 g
36
Jeannies Oriental Mustard


2
Amulat 5 g
P. Gold 3 g
Kodiak 5 g
Kodiak 3 g
Arid 3 g
Arid 5 g
1
Kodiak 4 g
Arid 4 g
Amulat 4 g
Amulat 3 g
P. Gold 5 g
P. Gold 4 g
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Jeannies Oriental Mustard


2
Arid 3 g
Arid 5 g
Arid 4 g
1
38
Jeannies Oriental Mustard


2
Arid 3 g
Arid 5 g
Arid 4 g
Kodiak 5 g
Kodiak 3 g
Kodiak 4 g
1
Amulat 4 g
P. Gold 5 g
P. Gold 4 g
P. Gold 3 g
Amulat 5 g
Amulat 3 g
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Example 1 4 p79

• Soil erosion in PNW.
• Normal barley/wheat rotation.
• New crops canola and AWP.
• Test erosion of new crops in no tillage, minimum
  tillage and conventional tillage.

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Example 1 4 p79

• As much land as needed.
• Cultivators set to 20 feet.
• Tradition drill at 10 feet and no tillage drill
  at 15 feet.
• Design a suitable experiment.

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Example 1a 4 p79
100
30
42
Example 1a 4 p79
43
Example 1a 4 p79
Ba
AP
AP
Ba
Ca
Ca
Ba
Ba
Ca
Ca
AP
AP
Ba
Ca
Ca
AP
Ba
AP
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Example 1a 4 p79
45
Example 1b 4 p79
46
Example 1b 4 p79
Ba
AP
AP
Ba
Ca
Ca
Ba
Ba
Ca
Ca
AP
AP
Ba
Ca
AP
Ca
Ba
AP
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Example 1a 4 p79
Ba
Ba
Ca
Ca
AP
AP
Ba
Ba
Ca
Ca
AP
AP
Ba
Ba
Ca
Ca
AP
AP
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Example 1a 4 p79
Ba
Ba
Ca
Ca
AP
AP
Ba
Ba
Ca
Ca
AP
AP
Irrigate
Ba
Ba
Ca
Ca
AP
AP
Buffer
Ba
Ba
Ca
Ca
AP
AP
Not Irrigate
Ba
Ba
Ca
Ca
AP
AP
Ba
Ba
Ca
Ca
AP
AP
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Example 1b 4 p79
Buffer
Buffer
Buffer
Irrigate
Irrigate
No Irrigate
No Irrigate
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Example 3 6 p.80

• Restrictions on insecticides on beans stop BMV.
• Aphids max out at 5 weeks before harvest.
• Apply 6 of water, one inch/4 weeks.
• Reduced irrigation early maturity, less cost.

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Example 3 6 p.80

• Reduced N accelerated maturity and reduces cost.
• Early maturity is important to avoid aphids and
  hence BMV.

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Example 3 6 p.80

• Triangular field, 300 x 400 x 500 feet.
• Solid set irrigation every 30 from the 400
  edge.
• Experiment to optimize irrigation and N
  application.

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Example 3 6 p.80
I
II
III
54
Example 3 6 p.80

• 6 cultivars
• 4 irrigations, 4, 5, 6, 7.
• 6 N levels 120, 140, 160, 180, 200, 210 units
  N/acre.
• Three replicates.

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Example 3 6 p.80
N1N2N3N4N5N6
I
II
III
W1 W2 W3 W4 W2 W3 W4 W1
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Example 4 2 p.57

• Wild oat infestation reduces yield and quality in
  spring barley.
• Increased N on barley increase crop
  competitiveness against oat.
• Traditionally apply 110 units of N.
• 4 wild oat plants/square foot.

57
Example 4 2 p.57

• Barley predominated by Golden Sunrise and
  Malter.
• 5 wide seed planter (10 to 30 length plots).
• 20 continious planter.
• 5 plot combine
• 200 x 200 of land, 2 locations.

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Example 4 2 p.57
200
160
160
200
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Example 4 2 p.57
20
20
20
20
20
20
20
40
2wo
4wo
6wo
8wo
20
60
Example 4 2 p.57
20
30
30
20
20
20
G. Sunrise
Malster
2wo
4wo
G. Sunrise
Malster
Malster
G. Sunrise
6wo
8wo
Malster
G. Sunrise
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Example 4 2 p.57
20
30
30
20
20
20
G. Sunrise
Malster
2wo
4wo
G. Sunrise
Malster
Malster
G. Sunrise
6wo
8wo
Malster
G. Sunrise
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Examples
Scottish Winters Day
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New High protein live stock feed
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Eight Maids a Milking

• Traditional dairy feed is grass or alfalfa hay.
• Potential new feed Raphanobrassica.
• Design one or more experiment to determine.
• Raphanobrassica digestability.
• Optimum feed mix ratios for most milk.

65
Eight Maids a Milking

• Three feed treatments.
• Grass hay.
• Alfalfa hay .
• Raphanobrassica.
• 9 cows (nested design).
• Psudo Latin Square.

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Eight Maids a Milking
Grass hay Alfalfa hay Raphano-brassica Meal
Cow 1-3
Cow 4-6
Cow 7-9
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Eight Maids a Milking

• SilageRaphanobrassica mix.
• 101, 51, 11, 15, 110 ratios.
• 20 Cows
• 4 Cows/mix treatment.
• RCB
• Assess milk quantity and quality.

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Example 2 5 p.79

• Kentucky blue grass burning is banned as of now.
• Seed Production is related to temperature, length
  of vernalization and day-length.
• Design an experiment to examine production
  systems without burning.

70
Example 2 5 p.79

• 12 cultivars.
• 3 vernalization chambers, each with six shelves.
• 4 glasshouse bays with day-length control.
• 4 benches/bay (15 feet x 3 feet).
• Pot size is 4, 6, or 12.

71
Example 2 6 p.80
45 x 9 405 - 4 Pots
15 x 3 45 - 12 Pots
30 x 6 180 - 6 Pots
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Example 2 6 p.80
45 x 9 405 4
15 x 3 45 - 12 Pots
30 x 6 180 6
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Example 2 6 p.80

• 5 cultivars.
• 3 vernalization times, one from each chamber.
• 12 pots 45/bench
• 3 Replicates/bench (blocked)
• 4 benches (12 reps/treatment).
• 4 day-lengths, one/bay.

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Example 2 6 p.80
15 pots
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Question 5

• These have been some suggestion that TRV and PCN
  interact to cause severe yield loss and more
  importantly a quality problem (internal necrosis)
  in potato tubers.
• You have been assigned to address this
  question and design a suitable experiment to
  examine this interaction between virus and
  nematode.

76
Question 5

• You are to conduct your research in a greenhouse
  bay containing four benches each 10 feet x 5 feed
  in dimension. Design a suitable experiment
  (explain all the details) and outline any
  difficulties that may arise in carrying out this
  experiment 50 points.

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Question 5a





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Question 5a





79
Question 5a



80
Question 5a

• Have 8 plots per bench.
• Four benches (obvious replicate blocks).
• 8 Treatments
• TRV infected mother tubers.
• PCN-None Low, Intermediate High cysts.
• TRV not infected mother tubers.
• PCN-None, Low, Intermediate High cysts.

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Question 5

• Split-split-plot design
• Main plot TRV infected or healthy
• Split plot PCN treatment (x4).
• Four replicates.
• 3 plants per plot.
• Each plant in a 12 pot.

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Question 5a

TRV infected TRV Healthy

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Question 5a
I I I I I I I I I I
TRV PCN 4 TRV PCN 2 TRV PCN 1 TRV PCN 3 TRV - PCN 3 TRV - PCN 4 TRV - PCN 2 TRV - PCN 1

84
Question 5a OR

• Factorial design.
• TRV infected or healthy
• PCN treatment (x4).
• Four replicates.
• 3 plants per plot.
• Each plant in a 12 pot.

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Question 5a
I I I I I I I I I I
TRV PCN 2 TRV - PCN 1 TRV - PCN 4 TRV PCN 3 TRV - PCN 3 TRV PCN 4 TRV - PCN 2 TRV PCN 1

86
Question 5 OR!



87
Question 5b

• Have 8 plots per bench.
• Four benches (2 replicates/bench).
• 4 Treatments
• TRV infected mother tubers.
• PCN-None and field rate.
• TRV not infected mother tubers.
• PCN-None and field rate.
• Two harvest times (2 benches each).

88
Question 5b
I II I II I II I II I II I II I II I II I II I II
TRV PCN TRV - PCN - TRV - PCN TRV PCN - TRV - PCN TRV PCN - TRV - PCN TRV PCN

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Experimental DesignTest 2Due Wednesday
February 28, 2007