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(Rancangan Petak Terbagi)

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1 (Rancangan Petak Terbagi)
Split Plot Design (Rancangan Petak Terbagi) Kuswanto, 2006

2 Split Plot Design: In RCB designs or Latin Squares, the experiment is broken up into homogenous blocks – every block gets every treatment combination The idea is to have the variation within each block as small as possible (reduces experimental error)

3 The greater the number of treatment combinations, the bigger each block must be - therefore the variation within each block increases To overcome this increased variation within large blocks, we may use the split plot design – but we pay a price We sacrifice precision in estimating the effects of one of the variables, but often gain precision in estimating effects of the second factor.

4 Each of these is referred to as a main plot
The split plot design examining irrigation (4 levels and variety (4 levels): We begin by assigning levels of one factor randomly to blocks as in a RCB design: eg irrigation levels H L M Block 1 L H M Block 2 M L H Block 3 Each of these is referred to as a main plot

5 Next, we assign treatment levels of the second factor randomly to sub-plots within each main plot. eg variety H L M a c d b Block 1 L H M b d c a Block 2 M L H Block 3 d c a b

6 main-plot sub-plots H L M Block 1 L H M Block 2 M L H Block 3 a c d b
a c d b Block 1 L H M b d c a Block 2 M L H Block 3 d c a b

7 In a split plot design, we sacrifice precision for the factor assigned to main plots, but we gain precision for factor assigned to subplots (compared to RCB design) main-plot sub-plots H L M a c d b Block 1

8 error between main plots should be larger than error for sub-plots
a c d b Block 1

9 We may use a split plot when we are interested in testing the effect of one factor over a wider variety of conditions (in our example, test variety over a range of water conditions) Here we are more interested in the effect of variety than water.

10 We might also use a split plot design when we are interested in adding a factor to an existing experiment – ie blocks already set up, then add sub-plots. requires enough size in main-plots to be split into sub-plots

11 Another use of a split plot design is for treatments which require a certain area to be applied (eg types of harvesting equipment, pesticide applications etc.) These factors can be assigned to main plots, with a second factor assigned to sub-plots

12 Remember the idea is that variation between main plots is greater than within sub-plots.
Other possible situations include parts of plants – variation between plants may be greater than within leaves of the same plant so plants could be main plots with leaves as sub-plots Age of animals may add variation to response to a treatment – litters of animals could form main-plots, while individuals within a litter could form sub-plots

13 H L M L H M M L H Analysis of a split plot design:
In a split plot design, we first look at the effect of main plot treatment, then sub-plot treatment H L M Block 1 L H M Block 2 M L H Block 3 so in our main plot, we have effect of water and block

14 H L M L H M M L H Block 1 Block 2 Block 3
Block 1 L H M Block 2 M L H Block 3 so in our main plot, we have effect of water and block GLM model for this is just like a RCB design: block irrigation block*irrigation (remainder)

15 But we must still deal with sub-plots:
Block 1 Block 2 Block 3 c a d b H L M But we must still deal with sub-plots: GLM for sub plots looks like: variety variety*irrigation error (really block*irrigation*variety)

16 So the whole model looks like:
block irrigation block*irrigation (remainder a) variety variety*irrigation error (remainder b) main plot effects sub plot effects remainder a is error term used to test main plot effects remainder b is error term to test sub plot effects

17 a generalized model looks like:
block main-plot treatment mp treat * block (remainder a) sub-plot treatment sp treat*mp treat error (remainder b)

18 Example: A field trial is set up as a split plot with 5 blocks
Example: A field trial is set up as a split plot with 5 blocks. Variety is assigned to the main plot (4 levels) with nitrogen treatment (2 levels) assigned to the sub plot. data file splitplot 1.xls A field trial is set up with three blocks with two nitrogen treatments assigned to the main plots. Four manure treatments are then assigned to the subplots Data are in splitplot 2.xls

19 Split Plot Design main-plot sub-plots H L M Block 1 L H M Block 2 M L
a c d b Block 1 L H M b d c a Block 2 M L H Block 3 d c a b

20 .... split-split plot design ....
.. to be continue .. .... split-split plot design ....

21 THE SPLIT-SPLIT PLOT DESIGN (Rancangan petak-petak terbagi)
Useful for a three factor design to facilitate field operations or whenever it is desirable to keep treatment combinations together. Like the split plot design, we loose precision in estimating effects of main plot and in sub-plot

22 The design looks like the split plot design, with the sub-plots further divided into sub-subplots:
M a c d b Block 1 L H M b d c a Block 2 M L H Block 3 d c a b

23 The design looks like the split plot design, with the sub-plots further divided into sub-subplots:
M a1 c2 d1 c1 b2 a2 d2 b1 The third treatment factor is then randomly assigned to the sub-sub-plots

24 The analysis of a split-split plot is similar to a split plot, with the addition of the sub-subplot factor to the model Remember a model for split plot looks like: block main-plot treatment mp treat * block (remainder a) sub-plot treatment sp treat*mp treat error (which is block*mp*sp) (remainder b)

25 The model for a split-split plot looks like:
block main-plot treatment mp treat * block (remainder a) sub-plot treatment sp treat*mp treat block*mp*sp (remainder b) sub-subplot treatment ssp*mp ssp*sp ssp*mp*sp sub-subsplot error (remainder c) 4way interaction

26 Example: In a viral control experiment, researchers were interested in the effects of planting date (3 levels), harvest date (3 levels) and viral suppression spray on sugar beet yields. Harvest date was feasible to vary over small plots, and required the most precision in the experiment. The spray had to be applied to larger areas, while the planting date required larger areas and did not require much precision (factor of least interest)

27 A split-split plot design was chosen, with 4 blocks
planting date was then assigned to main plots: Block 1 Block 2 P1 P3 P2 Block 3 Block 4

28 Spray treatment was assigned to sub-plots

29 Harvest date is then randomly assigned to sub-subplots within each subplot:

30 main-plot sub-plots sub-sub plots Block 1 H2 H3 H1

31 data file: split split plot.xls
In a table grape experiment, the effects of 3 fertilizer types, 2 variety types and 3 pruning techniques were evaluated with respect to yield. A split split plot was used with 4, blocks. Fertilizer was assigned to the main plot, variety to the sub plot, and pruning technique to the sub-sub plot data file: split split plot1.xls

32 ... to be continue ...

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