STAM101 :: Lecture 22 :: Strip plot design – layout – ANOVA Table
Strip Plot Design
This design is also known as split block design. When there are two factors in an experiment and both the factors require large plot sizes it is difficult to carryout the experiment in split plot design. Also the precision for measuring the interaction effect between the two factors is higher than that for measuring the main effect of either one of the two factors. Strip plot design is suitable for such experiments.
In strip plot design each block or replication is divided into number of vertical and horizontal strips depending on the levels of the respective factors.
Replication 1 Replication 2
a0 a2 a3 a1 a3 a0 a2 a1
b1 




b0 




b2 




b1 




b2 




b0 




In this design there are plot sizes.
 Vertical strip plot for the first factor – vertical factor
 Horizontal strip plot for the second factor – horizontal factor
 Interaction plot for the interaction between 2 factors
The vertical strip and the horizontal strip are always perpendicular to each other. The interaction plot is the smallest and provides information on the interaction of the 2 factors. Thus we say that interaction is tested with more precision in strip plot design.
Analysis
The analysis is carried out in 3 parts.
 Vertical strip analysis
 Horizontal strip analysis
 Interaction analysis
Suppose that A and B are the vertical and horizontal strips respectively. The following two way tables, viz., A X Rep table, B X Rep table and A X B table are formed. From A X Rep table, SS for Rep, A and Error (a) are computed. From B X Rep table, SS for B and Error (b) are computed. From A X B table, A X B SS is calculated.
When there are r replications, a levels for factor A and b levels for factor B, then the ANOVA table is
X 
d.f. 
SS 
MS 
F 
Replication 
(r1) 
RSS 
RMS 
RMS/EMS (a) 
A 
(a1) 
ASS 
AMS 
AMS/EMS (a) 
Error (a) 
(r1) (a1) 
ESS (a) 
EMS (a) 

B 
(b1) 
BSS 
BMS 
BMS/EMS (b) 
Error (b) 
(r1) (b1) 
ESS (b) 
EMS (b) 

AB 
(a1) (b1) 
ABSS 
ABMS 
ABMS/EMS (c) 
Error (c) 
(r1) (a1) (b1) 
E SS (c) 
EMS (c) 

Total (rab – 1) TSS 
Analysis
Arrange the results as follows:
Treatment Combination 
Replication 
Total 

R1 
R2 
R3 
… 

A0B0 
a0b0 
a0b0 
a0b0 
… 
T00 
A0B1 
a0b1 
a0b1 
a0b1 
… 
T01 
A0B2 
a0b2 
a0b2 
a0b2 
… 
T02 
Sub Total 
A01 
A02 
A03 
… 
T0 
A1B0 
a1b0 
a1b0 
a1b0 
… 
T10 
A1B1 
a1b1 
a1b1 
a1b1 
… 
T11 
A1B2 
a1b2 
a1b2 
a1b2 
… 
T12 
Sub Total 
A11 
A12 
A13 
… 
T1 
. 
. 
. 
. 
. 
. 
Total 
R1 
R2 
R3 
… 
G.T 
TSS = [ (a0b0)2 + (a0b1)2+(a0b2)2+…]CF
 Vertical Strip Analysis
Form A x R Table and calculate RSS, ASS and Error(a) SS
Treatment 
Replication 
Total 

R1 
R2 
R3 
… 

A0 
A01 
A02 
A03 
… 
T0 
A1 
A11 
A12 
A13 
… 
T1 
A2 
A21 
A22 
A23 
… 
T2 
. 
. 
. 
. 
. 
. 
Total 
R1 
R2 
R3 
… 
GT 
Error (a) SS= A x R TSSRASSASS.
 Horizontal Strip Analysis
Form B x R Table and calculate RSS, BSS and Error(b) SS
Treatment 
Replication 
Total 

R1 
R2 
R3 
… 

B0 
B01 
B02 
B03 
… 
T0 
B1 
B11 
B12 
B13 
… 
T1 
B2 
B21 
B22 
B23 
… 
T2 
. 
. 
. 
. 
. 
. 
Total 
R1 
R2 
R3 
… 
GT 
 Error (b) SS= B x R TSSRSSBSS
3) Interaction Analysis
Form A xB Table and calculate BSS, Ax B SSS and Error (b) SS
Treatment 
Replication 
Total 

B0 
B1 
B2 
… 

A0 
T00 
T01 
T02 
… 
T0 
A1 
T10 
T11 
T12 
… 
T1 
A2 
T20 
T21 
T22 
… 
T2 
. 
. 
. 
. 
. 
. 
Total 
C0 
C1 
C2 
… 
GT 
ABSS= A x B Table SS – ASS ABSS
Error (c) SS= TSSASSBSSABSS –Error (a) SS. –Error (a) SS
Then complete the ANOVA table.
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