experimental design summary. completely randomized block y ij = + g i + e ij average over the whole...
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![Page 1: Experimental Design Summary. Completely Randomized Block Y ij = + g i + e ij Average over the whole experiment = Effect of i th genotype ++ Error j](https://reader035.vdocuments.net/reader035/viewer/2022062409/56649f125503460f94c25888/html5/thumbnails/1.jpg)
Experimental DesignExperimental DesignSummarySummary
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Completely Randomized BlockCompletely Randomized Block
YYijij = = + g + gii + e + eijij
Average over Average over the whole the whole
experimentexperiment== Effect of iEffect of ith th
genotypegenotype++ ++ ErrorError
jjthth replicate of the i replicate of the ithth genotype genotype
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Completely Randomized BlockCompletely 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.
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Randomized Complete BlockRandomized Complete Block
YYijkijk = = + r + rii +g +gjj + e + eijkijk
Average over Average over the whole the whole
experimentexperiment== Effect of jEffect of jth th
genotypegenotype++ ++ ErrorError
iithth genotype in the j genotype in the jthth replicate block replicate block
Effect of iEffect of ith th
replicatereplicate ++
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Randomized Complete BlockRandomized 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.
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Latin SquareLatin Square
YYijkijk = = +g +gii + r + rj j + c+ ck k + e+ eijkijk
Where YWhere Yijkijk is the performance of the i is the performance of the ithth genotype genotype
in the jin the jthth row and k row and kthth column; column; in the overall in the overall mean; gmean; gii is the effect of the i is the effect of the ithth genotype; r genotype; rj j is the is the
effect of the jeffect of the jthth row; c row; ck k is the effect of the kis the effect of the kthth
column; and ecolumn; and eijk ijk is the error term.is the error term.
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Latin SquareLatin SquareAdvantage 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.
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Lattice SquareLattice Square
YYijkijk = = +g +gaaii + b + baa
k k + r+ rj j + e+ eijkijk
Where YWhere Yijkijk is the performance of the i is the performance of the ithth genotype genotype
in the jin the jthth replicate and k replicate and kthth sub-block; sub-block; in the in the overall mean; goverall mean; gaa
ii is the effect of the i is the effect of the ithth genotype genotype
adjusted according to sub-blocks; badjusted according to sub-blocks; baak k is the effect is the effect
of the kof the kthth sub-block adjusted according to the sub-block adjusted according to the entries in that block; rentries in that block; rj j is the effect of the jis the effect of the jthth
replicate; and ereplicate; and eijk ijk is the error term.is the error term.
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Lattice SquareLattice SquareLattice squares are usually more effective
than RCB’s.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.
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Rectangular LatticeRectangular Lattice
YYijkijk = = +g +gaaii + b + baa
k k + r+ rj j + e+ eijkijk
Where YWhere Yijkijk is the performance of the i is the performance of the ithth genotype genotype
in the jin the jthth replicate and k replicate and kthth sub-block; sub-block; in the in the overall mean; goverall mean; gaa
ii is the effect of the i is the effect of the ithth genotype genotype
adjusted according to sub-blocks; badjusted according to sub-blocks; baak k is the effect is the effect
of the kof the kthth sub-block adjusted according to the sub-block adjusted according to the entries in that block; rentries in that block; rj j is the effect of the jis the effect of the jthth
replicate; and ereplicate; and eijk ijk is the error term.is the error term.
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Rectangular LatticeRectangular Lattice
More flexible in entry and replicate number than square lattices.
Designs are resolvable.Designed for statutory cultivar field
testing.
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InteractionsInteractionsGenotype Nitrogen 1 Nitrogen 2
A 3,468 4,088
B 2,504 4,791
2300
2800
3300
3800
4300
4800
5300
N-1 N-2
AA
BB
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Factorial Experimental DesignFactorial Experimental Design
IrrigationDays between defoliation
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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3 t2 1 t1 3 t3 2 t4 1 t3 3 t4
3 t1 2 t2 1 t4 2 t1 1 t2 2 t3
3 t3 1 t2 2 t2 1 t3 3 t4 3 t1
2 t3 3 t2 1 t1 2 t4 4 t1 1 t4
1 t2 3 t1 2 t1 1 t1 2 t4 3 t2
1 t3 3 t3 2 t2 3 t4 1 t4 2 t3
I
II
III
Factorial Experimental DesignFactorial Experimental Design
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Two-Factor Factorial ModelTwo-Factor Factorial Model
YYijkijk = = + r + ri i + d+ djj + w + wk k + dw+ dwjk jk + e+ eijkijk
Where YWhere Yijkijk is the performance of the the i is the performance of the the i thth
replicate, and the jreplicate, and the jthth d factor and k d factor and kthth w factor; w factor; in the overall mean; rin the overall mean; rj j is the effect of the jis the effect of the jthth
replicate; dreplicate; dii is the effect of the i is the effect of the ithth d-factor; w d-factor; wk k is is
the effect of the kthe effect of the kthth w-factor; dw w-factor; dwjkjk is the is the
interaction effect between dinteraction effect between d jj and w and wkk; and e; and eijk ijk is is
the error term.the error term.
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Factorial Experimental DesignsFactorial Experimental Designs
Can be used with any number of Can be used with any number of factors and factor levels.factors and factor levels.
Gives equal precision to estimating Gives equal precision to estimating all factors and levels.all factors and levels.
Greatest mistake by researchers is to Greatest mistake by researchers is to include too many factors where include too many factors where interpretation of three-way interpretation of three-way interactions can be difficult.interactions can be difficult.
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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
I II III IV
Split-Plot DesignSplit-Plot Design
3 2 1 4 3 1 4 2 3 1 2 4 2 4 1 3
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Split-Plot Design ModelSplit-Plot Design Model
YYijkijk = = + r + ri i + g+ gjj + e(1) + e(1)ijij + t + tk k + gt+ gtjk jk + e(2)+ e(2)ijkijk
Where YWhere Yijkijk is the performance of the the i is the performance of the the i thth
replicate, and the jreplicate, and the jthth main-plot and k main-plot and kthth sub-plot; sub-plot; in the overall mean; rin the overall mean; rj j is the effect of the jis the effect of the jthth
replicate; greplicate; gii is the effect of the i is the effect of the ithth main-plot; main-plot;
e(1)e(1)ijij is the main-plot error; t is the main-plot error; tk k is the effect of the is the effect of the
kkthth sub-plot; gt sub-plot; gtjkjk is the interaction effect between is the interaction effect between
ggjj and t and tkk; and e(2); and e(2)ijk ijk is the sub-plot error term.is the sub-plot error term.
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1243
1243
B A C 3
24
A C B 3124
IVIV
IIIIII
II
IIII
B A C A C B
Strip-Plot DesignStrip-Plot Design
1
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Strip-Plot Design ModelStrip-Plot Design Model
YYijkijk = = +r+rii+g+gjj+e(g)+e(g)ijij+t+tkk+e(t)+e(t)ijij+gt+gtjkjk+e(gt)+e(gt)ijkijk
Where YWhere Yijkijk is the performance of the the i is the performance of the the i thth
replicate, and the jreplicate, and the jthth strip and k strip and kthth strip; strip; in the in the overall mean; roverall mean; rj j is the effect of the jis the effect of the jthth replicate; g replicate; gii
is the effect of the iis the effect of the ithth strip-plot; e(g) strip-plot; e(g)ijij is the g- is the g-
factor error; tfactor error; tk k is the effect of the kis the effect of the kthth strip-plot; strip-plot;
e(t)e(t)ijij is the t-factor error; dw is the t-factor error; dwjkjk is the interaction is the interaction
effect between geffect between gjj and t and tkk; and e(gt); and e(gt)ijk ijk is the sub-is the sub-
plot error term.plot error term.
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RestraintsRestraints
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Genotypes/SpeciesGenotypes/Species
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Glasshouse, Laboritory, Glasshouse, Laboritory, Field, Growth rooms.Field, Growth rooms.
Types of data.Types of data.Time availabilityTime availabilityFunding.Funding.
FacilitiesFacilities
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RestraintsRestraints
Facilities, Data types, Facilities, Data types, Timing, and FundingTiming, and Funding
Factors, levelsFactors, levels
Replicates, Plot sizeReplicates, Plot size
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ExamplesExamples
Scottish Summers DayScottish Summers Day
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Jeannie’s Oriental MustardJeannie’s 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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Jeannie’s Oriental MustardJeannie’s Oriental Mustard
Factors ?Factors ?
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Jeannie’s Oriental MustardJeannie’s Oriental Mustard
Four cultivars.2 oilseed and 2 condiment.
2 planting dates.3 seeding rates.5 nitrogen levels.3 Replicates.
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Jeannie’s Oriental MustardJeannie’s Oriental Mustard
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9&10
7&8
5&6
3&4
1-2
Lat
e P
lant
ing
Ear
ly P
lant
ing
Jeannie’s Oriental MustardJeannie’s Oriental MustardI II IIII II III
Lat
e P
lant
ing
Lat
e P
lant
ing
Ear
ly P
lant
ing
Ear
ly P
lant
ing
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9&10
7&8
5&6
3&4
1-2
Late Planting Early Planting
Jeannie’s Oriental MustardJeannie’s Oriental Mustard
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9&10
7&8
5&6
3&4
1-2
Late Planting Early Planting
Jeannie’s Oriental MustardJeannie’s Oriental MustardI II IIII II III I II IIII II III
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9&10 75lb 25lb 75lb 50lb 0lb 25lb
7&8 0lb 0lb 25lb 70lb 50lb 100lb
5&6 25lb 50lb 100lb 25lb 75lb 75lb
3&4 50lb 75lb 50lb 0lb 100lb 0lb
1-2 100lb 100lb 0lb 100lb 25lb 50lb
Late Planting Early Planting
Jeannie’s Oriental MustardJeannie’s Oriental MustardI II IIII II III I II IIII II III
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9&10 75lb 25lb 75lb 50lb 0lb 25lb
7&8 0lb 0lb 25lb 70lb 50lb 100lb
5&6 25lb 50lb 100lb 25lb 75lb 75lb
3&4 50lb 75lb 50lb 0lb 100lb 0lb
1-2 100lb 100lb 0lb 100lb 25lb 50lb
Late Planting Early Planting
Jeannie’s Oriental MustardJeannie’s Oriental MustardI II IIII II III I II IIII II III
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Jeannie’s Oriental MustardJeannie’s Oriental Mustard
11
22
Ari
d 3
gA
rid
3 g
Ari
d 4
gA
rid
4 g
Ari
d 5
gA
rid
5 g
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Jeannie’s Oriental MustardJeannie’s Oriental Mustard
11
22
Ari
d 3
gA
rid
3 g
Ari
d 4
gA
rid
4 g
Ari
d 5
gA
rid
5 g
Am
ulat
4 g
Am
ulat
4 g
Am
ulat
5 g
Am
ulat
5 g
Am
ulat
3 g
Am
ulat
3 g
P. G
old
5 g
P. G
old
5 g
P. G
old
3 g
P. G
old
3 g
P. G
old
4 g
P. G
old
4 g
Kod
iak
5 g
Kod
iak
5 g
Kod
iak
3 g
Kod
iak
3 g
Kod
iak
4 g
Kod
iak
4 g
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Jeannie’s Oriental MustardJeannie’s Oriental Mustard
11
22
Ari
d 3
gA
rid
3 g
Ari
d 5
gA
rid
5 g
Ari
d 4
gA
rid
4 g
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Jeannie’s Oriental MustardJeannie’s Oriental Mustard
11
22
Ari
d 3
gA
rid
3 g
Am
ulat
4 g
Am
ulat
4 g
P. G
old
5 g
P. G
old
5 g
Kod
iak
5 g
Kod
iak
5 g
Kod
iak
3 g
Kod
iak
3 g
Kod
iak
4 g
Kod
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4 g
P. G
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4 g
P. G
old
4 g
P. G
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3 g
P. G
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3 g
Am
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5 g
Am
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5 g
Am
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3 g
Am
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3 g
Ari
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5 g
Ari
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Example 1 ~ #4 p79Example 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 p79Example 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 p79Example 1a ~ #4 p79
30’30’
100’100’
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Example 1a ~ #4 p79Example 1a ~ #4 p79
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Example 1a ~ #4 p79Example 1a ~ #4 p79
BaBa
BaBa
BaBa
BaBa
BaBa
BaBa CaCa CaCa
CaCa
CaCaCaCa
CaCa
APAP
APAP
APAP
APAP
APAP
APAP
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Example 1a ~ #4 p79Example 1a ~ #4 p79
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Example 1b ~ #4 p79Example 1b ~ #4 p79
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Example 1b ~ #4 p79Example 1b ~ #4 p79
BaBa
BaBa
BaBa
BaBa
BaBa
BaBa CaCa CaCa
CaCa
CaCaCaCa
CaCa
APAP
APAP
APAP
APAP
APAP
APAP
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Example 1a ~ #4 p79Example 1a ~ #4 p79
BaBa
BaBa
BaBa
BaBa
BaBa
BaBa CaCa CaCa
CaCa
CaCaCaCa
CaCa
APAP
APAP
APAP
APAP
APAP
APAP
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Example 1a ~ #4 p79Example 1a ~ #4 p79
BaBa
BaBa
BaBa
BaBa
BaBa
BaBa CaCa CaCa
CaCa
CaCaCaCa
CaCa
APAP
APAP
APAP
APAP
APAP
APAP
BaBa
BaBa
BaBa
BaBa
BaBa
BaBa CaCa CaCa
CaCa
CaCaCaCa
CaCa
APAP
APAP
APAP
APAP
APAP
APAP
BufferBuffer
IrrigateIrrigate
Not Not IrrigateIrrigate
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Example 1b ~ #4 p79Example 1b ~ #4 p79
IrrigateIrrigate IrrigateIrrigate No IrrigateNo IrrigateNo IrrigateNo Irrigate
Buf
fer
Buf
fer
Buf
fer
Buf
fer
Buf
fer
Buf
fer
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Example 3 ~ #6 p.80Example 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.80Example 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.80Example 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.80Example 3 ~ #6 p.80
II
IIII IIIIII
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Example 3 ~ #6 p.80Example 3 ~ #6 p.80
6 cultivars4 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.80Example 3 ~ #6 p.80
II
IIII
N1N1N2N2N3N3N4N4N5N5N6N6
IIIIII
W1 W2 W3 W4 W2 W3 W4 W1W1 W2 W3 W4 W2 W3 W4 W1
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Example 4 ~ #2 p.57Example 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.
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Example 4 ~ #2 p.57Example 4 ~ #2 p.57Barley predominated by ‘Golden
Sunrise’ and ‘Malter’.5’ wide seed planter (10’ to 30’
length plots).20’ continious planter.5’ plot combine200’ x 200’ of land, 2 locations.
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Example 4 ~ #2 p.57Example 4 ~ #2 p.57
200’200’
200’200’
160’160’
160’160’
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Example 4 ~ #2 p.57Example 4 ~ #2 p.57
20’20’
20’20’
20’20’
20’20’
2wo’2wo’
4wo’4wo’
6wo’6wo’
8wo’8wo’
20’20’20’20’ 40’40’
20’20’
20’20’
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Example 4 ~ #2 p.57Example 4 ~ #2 p.57
20’20’
20’20’
20’20’
20’20’
30’30’ 30’30’
G. SunriseG. Sunrise MalsterMalster
MalsterMalster
MalsterMalster
MalsterMalsterG. SunriseG. Sunrise
G. SunriseG. Sunrise
G. SunriseG. Sunrise
2wo’2wo’
4wo’4wo’
6wo’6wo’
8wo’8wo’
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Example 4 ~ #2 p.57Example 4 ~ #2 p.57
20’20’
20’20’
20’20’
20’20’
30’30’ 30’30’
G. SunriseG. Sunrise MalsterMalster
MalsterMalster
MalsterMalster
MalsterMalsterG. SunriseG. Sunrise
G. SunriseG. Sunrise
G. SunriseG. Sunrise
2wo’2wo’
4wo’4wo’
6wo’6wo’
8wo’8wo’
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ExamplesExamples
Scottish Winters DayScottish Winters Day
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New High protein New High protein live stock feed live stock feed
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Eight Maids a MilkingEight 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.
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Eight Maids a MilkingEight Maids a Milking
Three feed treatments.Grass hay.Alfalfa hay .Raphanobrassica.
9 cows (nested design).Psudo Latin Square.
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Grass hay
Alfalfa hay
Raphano-brassica
Meal
Cow 1-3
Cow 4-6
Cow 7-9
Eight Maids a MilkingEight Maids a Milking
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Eight Maids a MilkingEight Maids a Milking
Silage:Raphanobrassica mix.10:1, 5:1, 1:1, 1:5, 1:10 ratios.
20 Cows4 Cows/mix treatment.RCBAssess milk quantity and quality.
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Example 2 ~ #5 p.79Example 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.
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Example 2 ~ #5 p.79Example 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”.
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Example 2 ~ #6 p.80Example 2 ~ #6 p.80
45 x 9 = 45 x 9 = 405 - 4” Pots405 - 4” Pots
30 x 6 = 30 x 6 = 180 - 6” Pots180 - 6” Pots
15 x 3 = 15 x 3 = 45 - 12” Pots45 - 12” Pots
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Example 2 ~ #6 p.80Example 2 ~ #6 p.80
45 x 9 45 x 9 = 405 4”= 405 4”
30 x 6 30 x 6 = 180 6”= 180 6”
15 x 3 = 15 x 3 = 45 - 12” Pots45 - 12” Pots
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Example 2 ~ #6 p.80Example 2 ~ #6 p.80
5 cultivars.3 vernalization times, one from
each chamber.12” pots = 45/bench3 Replicates/bench (blocked)4 benches (~12 reps/treatment).4 day-lengths, one/bay.
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Example 2 ~ #6 p.80Example 2 ~ #6 p.80
15 15 potspots
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Question #5Question #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.
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Question #5Question #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 5aQuestion 5a
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Question 5aQuestion 5a
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Question 5aQuestion 5a
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Question 5aQuestion 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 5Question 5
Split-split-plot designMain plot = TRV infected or healthySplit plot = PCN treatment (x4).Four replicates.3 plants per plot.Each plant in a 12’ pot.
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Question 5aQuestion 5a
TRV infected TRV Healthy
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Question 5aQuestion 5a
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
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Question 5a ~ ORQuestion 5a ~ OR
Factorial design.TRV infected or healthyPCN treatment (x4).Four replicates.3 plants per plot.Each plant in a 12’ pot.
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Question 5aQuestion 5a
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
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Question 5 ~ OR!Question 5 ~ OR!
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Question 5bQuestion 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).
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Question 5bQuestion 5b
I II
TRV
+
PCN +
TRV
-
PCN -
TRV
-
PCN +
TRV
+
PCN -
TRV
-
PCN +
TRV
+
PCN -
TRV
-
PCN +
TRV
+
PCN +
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Experimental DesignExperimental DesignTest #2Test #2
Due Wednesday Due Wednesday February 28, 2007February 28, 2007