The Split-split Plot on a RCB
Sometimes in experiments, subjects are assigned at random to a set of treatments. Then those are subdivided into sub-units to which another set of treatments are applied. And then, those in turn are subdivided again and a third set of treatments are applied. This is the split-split plot, not be confused with a 3-way factorial.
A split-split plot can also be imposed on a CRD, but is not included at this time in the field guide.
- Main experimental subjects of a RCB are divided further into
additional independent units (subplots) to which another set of treatments are randomly assigned. These subplots are additionally
split into subunits assigned randomly to yet another set of
- Main treatments are assigned at random within blocks of adjacent subjects, each treatment once per
- The number of blocks is the number of replications.
- Any main treatment can be adjacent to any other treatment, but not to the same treatment within the block.
Different colors represent different treatments; each horizontal row represents a block. Plot colors represent
assignment of main effects or treatments; top plant colors split plots; bottom colors split-split treatments. There are 3 blocks (I-III) each of 2 main treatments (A & B) split into 2 treatments (1 & 2) and further split into 3 treatments (a-c) in split-split plots.
Block I Treatment A + Treatment B
1a 1b 1c 2c 2b 2a + 2b 2c 2a 1a 1c 1b
Block II Treatment B + Treatment A
1c 1a 1b 2b 2c 2a + 2c 2a 2b 1b 1a 1c
Block III Treatment A + Treatment B
2b 2c 2a 1a 1c 1b + 1c 1a 1b 2a 2b 2c
ANOVA table format:
|Error-main plots (Em)
|Subplots X Treatments (SxT)
|Split-subplots X Treatments (UxT)
|Split-subplots X Subplots (UxS)
|Split-subplots X Subplots X Treatments (UxSxT)
|awhere t=number of main treatments, b=number of blocks and s=number of subplots.|
Sample ANOVA table:
|S X T
|T X U
|S X U
|T X S X U
aF test with 2,2 degrees of freedom at P=0.05 is 19.00|
bF test with 1,2 degrees of freedom at P=0.05 is 18.51
cF test with 1,4 degrees of freedom at P=0.05 is 7.71
dF test with 2,16 degrees of freedom at P=0.05 is 3.63.
Sample SAS GLM statements:
CLASS Blk Trt Sub U;
MODEL WHATEVER = Blk Trt Trt*Blk
Sub Sub*Trt Blk*Sub(Trt)
U U*Trt U*Sub U*Trt*Sub;
TEST H = Blk Trt E = Trt*Blk;
TEST H = Sub Sub*Trt E = Blk*Sub(Trt);
Note: a Split-block-split-plot design is possible, but is not illustrated in the field guide.
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Thursday, August 17, 2000