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Unformatted text preview: Statistical Techniques II
Design Layouts Appendix 13 Supplement
Page 252 Schematic layouts of some CRD experiments.
1) CRD: Treatment levels are t=5 where each
treatment occurs in 3 cells (experimental units :
n=3) and each cell is sampled once. CRD with
experimental error. Model
Source
Treatments
Error Yij = iij
Expected Mean Squares
2 n 2 2) CRD: Treatment levels are t=5 where each A
B
D
E
B
Yijk = iijijk
Expected Mean Squares
2 nnd
2 n
2 treatment occurs in 3 cells (experimental units
: d=3) and each cell is sampled twice
(sampling units : n=2). CRD with both
experimental error and sampling error. Model
Source
Treatment
Experimental Error
Sampling Error A
B
D
E
B A
B
D
E
B A
C
A
D
E A
C
A
D
E 3) CRD?: Treatment levels=5; each treatment occurs in one
cell (experimental unit) and each cell is
sampled three times. CRD with no
experimental error, this experiment has
sampling error only (Pseudoreplication).
Model
Source
Treatments
Sampling Error A
C
A
D
E C
A
D
E
B D
B
E
C
C D
B
E
C
C C
A
D
E
B D
B
E
C
C C
A
D
E
B Yijk = iijk
Expected Mean Squares
2 nn
2 James P. Geaghan  Copyright 2011 Statistical Techniques II
Design Layouts Appendix 13 Supplement
Page 253 Schematic layouts of some RBD experiments.
4) RBD: Three blocks (b=3) and five treatment
levels (t=5) where each block has 5 cells
(experimental units) and each treatment occurs once
in each block and each is sampled once. RBD with
experimental error only Block 1
C
A
D
E
B Block 2
B
C
A
D
E Block 3
D
B
E
A
C Block 1
C
C
A
A
D
D
E
E
B
B
Yijk = ijijijk
Expected Mean Squares
2 nnb
2 nnt
2 n
2 Block 2
B
B
C
C
A
A
D
D
E
E Block 3
D
D
B
B
E
E
A
A
C
C Model
Yij = ijij
Source
Expected Mean Squares
Treatment 2b
2
Block t
2
Error 5) RBD: Three blocks (b=3) and five treatment
levels (t=5) where each block has 5 cells, and each
treatment occurs once in each block and each cell is
sampled twice (n=2). In this case the residual error
term measures only within cell variation. Model
Source
Treatment
Block
Block*Treatment
Error 6) RBD: Blocks=3, Treatment levels=5; each
block has 10 cells and each treatment occurs
twice in each block. Each cell (treatment by
block and within block replicate combination)
is sampled once. In this case the residual error
term measures between cell variation. Model
Source
Treatment
Block
Block*Treatment
Error Block 1
D
C
A
E
A
E
B
C
D
B
Yijk = ijijijk
Expected Mean Squares
2 nnb
2 nnt
2 n
2 Block 2
A
E
B
A
E
C
C
D
B
D Block 3
C
A
D
B
A
E
D
B
E
C James P. Geaghan  Copyright 2011 Statistical Techniques II
Design Layouts Appendix 13 Supplement
Page 254 Layouts of some other experiments. E2  E1
7) CRD Splitplot : Main plot treatment levels are
A2  A1
t1=5, subplot treatment levels t2=2 where each
D1  D2
main plot treatment occurs in d=3 cells
E2  E1
(experimental units) and each cell is subdivided into
A1  A2
two parts (d=2) for one application of each level of
the subplot treatment.
Model
Yijk = + 1i ij2k12ikijk
Source
Expected Mean Squares
2
2
2
2
Treatment nd n ndt2 2 B2
C1
B1
D2
E2 



 B1
C2
B2
D1
E1 D1
B1
C2
A1
C1 



 D2
B2
C1
A2
C2 2 Error a t2 SubPlot Treatment
Interaction n nt1
2
2 n Error b 2 2 2 2 8) RBD: Blocks=3, Treatment Levels=5;
each block has 10 cells and each treatment
occurs twice in each block. Each cell
(treatment by block combination) is sampled
twice. Block
D D
A A
A A
B B
D D C
E
E
C
B C
E
E
C
B Block
A A
B B
E E
C C
B B E
A
C
D
D E
A
C
D
D Block
C C
D D
A A
D D
E E A
B
E
B
C A
B
E
B
C Yijk = ijijijijl
Expected Mean Squares
2
2
2
2 n ns nsb
2
2
2
2 n ns nst Model
Source
Treatment
Block
Treatment*Block
Rep(Treatment*Block)
Error 2 2 2 n ns 2
2 n 2 9) Latin Square Design (LSD): Three rows (r=3)
C
B
A
and three columns (c=3) for three treatment levels
B
A
C
(t=3) where each treatment occurs in each row and
B
A
C
column. Experimental units are row by column
combination cells. There could also be several separate squares (blocks) and several sampling units
within cells for Latin Square Designs.
Model Yijk = ijkijk Source
Row Expected Mean Squares Column
Treatment
Error 2 r
2 r
2 r
2 James P. Geaghan  Copyright 2011 ...
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This note was uploaded on 12/29/2011 for the course EXST 7015 taught by Professor Wang,j during the Fall '08 term at LSU.
 Fall '08
 Wang,J

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