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Split-Plot Design - Lecture Notes | ANSC I, Study notes of Animal Biology

University of Maryland Animal Biology

Split-Unit Design Material Type: Notes; Subject: Animal Science; University: University of Maryland; Term: Unknown 1989;

Typology: Study notes

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4/5/04 1Split Plot

SPLIT-UNIT (split-plot) DESIGN

1DESCRIPTION

An experiment in which an extra factor (second) is introduced

into a study by dividing the large experimental units(whole unit)

for the first factor into smaller experimental units(sub-units) on

which the different levels of the second factor will be applied.

Each whole unit is a complete replicate of all the levels of the

second factor (RBD). The whole unit design may be CRD,

RCBD or LS design.

Randomization - The first factor levels are randomly assigned to

the whole units according to the rules for the whole unit design

(i.e., CRD, RCBD or LS design). While the second factor levels

are randomly assigned sub-units within each whole unit

according to the rules of a RCBD. The name of the split-plot

design is prefixed with the design name associated with the

whole plot design, i.e., Randomized Complete Block Split-Plot

Design. The design for the sub-plot is never given, but is

assumed since it must by definition be RBD.

Discover Study notes of Animal Biology University of Maryland

Partial preview of the text

Download Split-Plot Design - Lecture Notes | ANSC I and more Study notes Animal Biology in PDF only on Docsity!

SPLIT-UNIT (split-plot) DESIGN

1 DESCRIPTION

An experiment in which an extra factor (second) is introduced

into a study by dividing the large experimental units(whole unit)

for the first factor into smaller experimental units(sub-units) on

which the different levels of the second factor will be applied.

Each whole unit is a complete replicate of all the levels of the

second factor (RBD). The whole unit design may be CRD,

RCBD or LS design.

Randomization - The first factor levels are randomly assigned to

the whole units according to the rules for the whole unit design

(i.e., CRD, RCBD or LS design). While the second factor levels

are randomly assigned sub-units within each whole unit

according to the rules of a RCBD. The name of the split-plot

design is prefixed with the design name associated with the

whole plot design, i.e., Randomized Complete Block Split-Plot

Design. The design for the sub-plot is never given, but is

assumed since it must by definition be RBD.

2 ADVANTAGES

2.1 Since sub-unit variance is generally less than whole unit

variance, the sub-unit treatment factor and the interaction

are generally tested with greater sensitivity.

2.2 Allows for experiments with a factor requiring relatively

large amounts of experimental material (whole units) along

with a factor requiring relatively little experimental

material (sub -unit) in the same experiment.

2.3 If an experiment is designed to study one factor, a second

factor may be included at very little cost.

2.4 It is the design (univariate) for experiments involving

repeated measures on the same experimental unit (whole

unit), while the repeated measures in time are the sub-unit.

5 Example: RCB split plot, with a 3x2 factorial arrangement of

treatments.

Rep I Rep II ____________________a^2 a^1 a^3 ____________________a^3 a^1 a^2 || || || || || || || || || b2 || b2 || b1 || || b2 || b1 || b2 || |------|------|------|| | | | |------|------|------|| | | | ||______|______|______| b1 | b1 | b2 | ||______|______|______| b1 | b2 | b1 |

Other reps the same except a new randomization for each rep.

6 The Model RCB Split Plot

6.1 Linear additive model

Yijk = : + Dk + "i + *ik + $j + ("$)ij + ,ijk

where: Yijk is the observed value for the kth^ replicate of the ith

level of factor A and the jth^ level of factor B

(where i = 1 to a, j = 1 to b and k = 1 to r).

: is the general mean.

Dk is the block effect for the kth^ block; the block effect

may be either fixed or random.

"i is the effect of the ith^ level of factor A; the effect

may be either fixed or random.

*ik is the whole plot random error effect, for the ith^ , kth

combination of block and factor A.

$j is the effect for the jth^ level of factor B; the effect

may be either fixed or random.

"$ij is the interaction effect of the ith^ level of factor A

with the jth^ level of factor B; the interaction effect

may be either fixed or random

,ijk is the subplot random error effect associated with

the Yijk subplot unit.

7.2 Standard error of the means for an A main effect mean

for a B main effect mean

for an AB mean

7.3 Standard errors of the differences between means

at the same level of A, different levels of B

at the same level of B, different or same levels of A

7.5 Split-plot designs for three factor factorials.

Split-Split-Plot Split-Plot

1 factor for each split A & B on whole units, C on sub-units

Sources df Sources df

Blocks r-1 Blocks r-

A a-1 A a-

Error a (a-1)(r-1) B b-

TotalW ar-1 AB (a-1)(b-1)

Error a (ab-1)(r-1)

B b-1 TotalW abr-

AB (a-1)(b-1)

Error b a(r-1)(b-1) C c-

TotalS ar(b-1) AC (a-1)(c-1)

BC (b-1)(c-1)

C c-1 ABC (a-1)(b-1)(c-1)

AC (a-1)(c-1) Error c ab(r-1)(c-1)

BC (b-1)(c-1) TotalS abr(c-1)

ABC (a-1)(b-1)(c-1)

Error c ab(r-1)(c-1) TOTAL abcr-

TotalSS abr(c-1)

TOTAL abcr-

8 AN EXAMPLE OF A SPLIT PLOT

8.1 Consider the following split plot experiment:

, 16 subjects, 8 males and 8 females

, Every subject received each of two exercise treatments (A,B) three

days apart

, Within males and females four subjects were randomly assigned to

treatment A first followed by B, while the remaining subject

received treatment B followed by A

, The response variable was the unresisted ankle simple reaction

time

, Name the experimental and treatment design(?).

8.4 The results Sources ofVariation Fixed/Random 1 Ankle Reaction Timedf F/VC prob )))))))))))))))))))))))))))))))))))))))))))))))))))) Gender Fixed 1 0.6 <. Subject/Gender Random 14 236.0 <. Day Random 1 2.0 <. Treatment Fixed 1 10.7 <. Gender*Treatment Fixed 1 0.8 <. Residual )))))))))))))))))))))))))))))))))))))))))))))))))))) Random 13 119. (^1) F ratios are reported for tests of fixed effects and variance components for random effects with the probability for the log likelihood chi square test.

Split-Plot Design - Lecture Notes | ANSC I, Study notes of Animal Biology

Related documents

Partial preview of the text

Download Split-Plot Design - Lecture Notes | ANSC I and more Study notes Animal Biology in PDF only on Docsity!

SPLIT-UNIT (split-plot) DESIGN

1 DESCRIPTION

An experiment in which an extra factor (second) is introduced

into a study by dividing the large experimental units(whole unit)

for the first factor into smaller experimental units(sub-units) on

which the different levels of the second factor will be applied.

Each whole unit is a complete replicate of all the levels of the

second factor (RBD). The whole unit design may be CRD,

RCBD or LS design.

Randomization - The first factor levels are randomly assigned to

the whole units according to the rules for the whole unit design

(i.e., CRD, RCBD or LS design). While the second factor levels

are randomly assigned sub-units within each whole unit

according to the rules of a RCBD. The name of the split-plot

design is prefixed with the design name associated with the

whole plot design, i.e., Randomized Complete Block Split-Plot

Design. The design for the sub-plot is never given, but is

assumed since it must by definition be RBD.

2 ADVANTAGES

2.1 Since sub-unit variance is generally less than whole unit

variance, the sub-unit treatment factor and the interaction

are generally tested with greater sensitivity.

2.2 Allows for experiments with a factor requiring relatively

large amounts of experimental material (whole units) along

with a factor requiring relatively little experimental

material (sub -unit) in the same experiment.

2.3 If an experiment is designed to study one factor, a second

factor may be included at very little cost.

2.4 It is the design (univariate) for experiments involving

repeated measures on the same experimental unit (whole

unit), while the repeated measures in time are the sub-unit.

5 Example: RCB split plot, with a 3x2 factorial arrangement of

treatments.

Other reps the same except a new randomization for each rep.

6 The Model RCB Split Plot

6.1 Linear additive model

Yijk = : + Dk + "i + *ik + $j + ("$)ij + ,ijk

where: Yijk is the observed value for the kth^ replicate of the ith

level of factor A and the jth^ level of factor B

(where i = 1 to a, j = 1 to b and k = 1 to r).

: is the general mean.

Dk is the block effect for the kth^ block; the block effect

may be either fixed or random.

"i is the effect of the ith^ level of factor A; the effect

may be either fixed or random.

*ik is the whole plot random error effect, for the ith^ , kth

combination of block and factor A.

$j is the effect for the jth^ level of factor B; the effect

may be either fixed or random.

"$ij is the interaction effect of the ith^ level of factor A

with the jth^ level of factor B; the interaction effect

may be either fixed or random

,ijk is the subplot random error effect associated with

the Yijk subplot unit.

7.2 Standard error of the means for an A main effect mean

for a B main effect mean

for an AB mean

7.3 Standard errors of the differences between means

at the same level of A, different levels of B

at the same level of B, different or same levels of A

7.5 Split-plot designs for three factor factorials.

Split-Split-Plot Split-Plot

1 factor for each split A & B on whole units, C on sub-units

Sources df Sources df

Blocks r-1 Blocks r-

A a-1 A a-

Error a (a-1)(r-1) B b-

TotalW ar-1 AB (a-1)(b-1)

Error a (ab-1)(r-1)

B b-1 TotalW abr-

AB (a-1)(b-1)

Error b a(r-1)(b-1) C c-

TotalS ar(b-1) AC (a-1)(c-1)

BC (b-1)(c-1)

C c-1 ABC (a-1)(b-1)(c-1)

AC (a-1)(c-1) Error c ab(r-1)(c-1)