split plot design

1. Split Plot Design
In factorial experiments certain factors may require larger plots
than for others. For e.g., experiments on irrigation, tillage etc
require larger areas.
On the other hand experiments on fertilizers, weedicides etc., may
not require larger area.
To accommodate factors which require different sizes of
experimental plots in the same experiment split-plot design has
been evolved.

2. In this design larger plots are taken for the factor which requires
larger plots.
Each of the larger plots is split into smaller plots. To
accommodate the other factors. The different treatments
are allotted at random to their respective plots. Such
arrangement is called split-plot design.
Factor – A – larger area – 3 levels
Factor – B – smaller area – 3 levels

3. Example 1:
a1 a0 a2
a1b1 a0b0 a2b1
a1b2 a0b1 a2b0
a1b0 a0b2 a2b2
a1b1 a2b0 a0b0
a1b0 a2b1 a0b1

4. In split plot design the larger plots are called Main plots. Smaller
plots with in each of this larger plot are called as sub plots.
The factor levels allotted to the Main plots or main plot
treatments and the factor levels allotted to the subplots are
called as sub plot treatments.
Advantages:
This design provides increased precision in the estimates of
subplot treatments and interaction effect compared to FRBD
with 2 factors.
This design helps in saving in experimental material. In many
cases it would be enough to have wider borders between main
plots only. This results in the saving of experimental area and
resources devoted to the provision of border rows.

5. Disadvantages
The major disadvantage of split plot design is that the effects
of main plot treatments are estimated with less precision than
they are in factorial RBD.
The analysis becomes more complex when missing data
occurs.
The difference in the precision of the estimates of main plot
treatment & subplot treatment is due to the sizes of main plots
& subplots. Since the main plots are larger in size than the
subplot, the heterogeneity will be more within main plot than
within subplot.

6. Hence the experimental error for main plot will be more than that
for subplot treatments. Split plot should therefore we used only
after careful consideration of the relative importance of the
factors to be examine. It should not be used when all the
factors are to be compared with equal precision.
Layout and analysis:
First, the main plot treatment and subplot treatment are
decided based on the required precision.
The factor for which greater precision is required is assigned
to subplots. The replication is then divided into number of
main plots equal to main plot treatments.

7. Each main plot is divided into subplot depending on the number
of subplot treatments. The main plot treatments are allotted at
random to the main plots as in the case of RBD.
Within each main plot the subplot treatments are allocated at random as
in the case of RBD. The same procedure is followed for all the
replications.
Rep I Rep II Rep III
a3 a1 a2
b2 b3 b1
b3 b2 b1
b1 b2 b3

8. ANOVA Model:
Yij = µ +ri + tj +eij ----------RBD
Yijk = µ +ri + Aj + bk + ABjk + eijk ---------FRBD (two factors)
Split plot design
Yijk = µ +ri + Mj + e(a) ij + Sk + MSjk + e(b)ijk

9. Sources df SS Mss F
Rep r-1 Rss Rms Rms/ E(a)ms
Main plot m-1 Mss Mms Mms/ E(a) ms
Error (a) (r-1) (m-1) E(a)ss E(a)ms
Subplot s-1 Sss Sms Sms/ E(b)ms
Main X Sub (m-1) (s-1) M x Sss M x Sms M x Sms/ E (b) ms
Error (b) m(r-1) (s-1) E(b)ss E(b)ms
Total rms-1 Tss
Note: Error (b) df = Total df - all df