STAM101 :: Lecture 21 :: Split plot design – layout – ANOVA Table
Splitplot Design
In field experiments certain factors may require larger plots than for others. For example, experiments on irrigation, tillage, etc requires larger areas. On the other hand experiments on fertilizers, etc may not require larger areas. To accommodate factors which require different sizes of experimental plots in the same experiment, split plot design has been evolved.
In this design, larger plots are taken for the factor which requires larger plots. Next each of the larger plots is split into smaller plots to accommodate the other factor. The different treatments are allotted at random to their respective plots. Such arrangement is called split plot design.
In split plot design the larger plots are called main plots and smaller plots within the larger plots are called as sub plots. The factor levels allotted to the main plots are main plot treatments and the factor levels allotted to sub plots are called as sub plot treatments.
Layout and analysis of variance table
First the main plot treatment and sub plot treatment are usually decided based on the needed precision. The factor for which greater precision is required is assigned to the sub plots.
The replication is then divided into number of main plots equivalent to main plot treatments. Each main plot is divided into subplots depending on the number of sub plot treatments. The main plot treatments are allocated at random to the main plots as in the case of RBD. Within each main plot the sub plot treatments are allocated at random as in the case of RBD. Thus randomization is done in two stages. The same procedure is followed for all the replications independently.
The analysis of variance will have two parts, which correspond to the main plots and subplots. For the main plot analysis, replication X main plot treatments table is formed. From this twoway table sum of squares for replication, main plot treatments and error (a) are computed. For the analysis of subplot treatments, main plot X subplot treatments table is formed. From this table the sums of squares for subplot treatments and interaction between main plot and subplot treatments are computed. Error (b) sum of squares is found out by residual method. The analysis of variance table for a split plot design with m main plot treatments and s subplot treatments is given below.
Analysis of variance for split plot with factor A with m levels in main plots and factor B with s levels in subplots will be as follows:
Sources of 
d.f. 
SS 
MS 
F 
Replication 
r1 
RSS 
RMS 
RMS/EMS (a) 
A 
m1 
ASS 
AMS 
AMS/EMS (a) 
Error (a) 
(r1) (m1) 
ESS (a) 
EMS (a) 

B 
s1 
BSS 
BMS 
BMS/EMS (b) 
AB 
(m1) (s1) 
ABSS 
ABMS 
ABMS/EMS (b) 
Error (b) 
m(r1) (s1) 
ESS (b) 
EMS (b) 

Total rms – 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
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.
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 (b) SS= Table SSASSBSSABSS –Error (a) SS.
Then complete the ANOVA table.
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