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The Split Plot on a CRD
Field marks:
- Main experimental subjects of a CRD are divided further into
additional independent units (subplots) to which another set of treatments are randomly assigned.
- Replications of treatments are assigned completely at random to main independent experimental subjects, not to the subplots.
- Adjacent main independent subjects could potentially have the same treatment.
Sample layout:
Different colors represent different treatments. Top colors represent
assignment of main effects or treatments; bottom colors subplot treatments. There are 4 replications (1-4) each of 3 main treatments (A-C) divided into 3 further treatments (a-c).
A1a A1b A1c B1c B1b B1a A2b A2c A2a C1a C1c C1b
C2c C2a C2b A3b A3c A3a B2c B2a B2b C3b C3a C3c
B3b B3c B3a A4a A4c A4b C4c C4a C4b B4a B4b B4c
ANOVA table format:
Source of
variation |
Degrees of
freedoma |
Sums of
squares (SSQ) |
Mean
square (MS) |
F |
| Treatments (Tr) |
t-1 |
SSQTr |
SSQTr/(t-1) |
MSTr/MSEm |
| Error-main plots (Em) |
t*(r-1) |
SSQEm |
SSQEm/(t*(r-1)) |
|
| Subplots (S) |
s-1 |
SSQS |
SSQS/(s-1) |
MSS/MSEs |
| Subplots X Treatments (SxT) |
(t-1)*(s-1) |
SSQSxT |
SSQSxT/(t-1)*(s-1) |
MSSxT/MSEs |
| Error-subplots (Es) |
t*(r-1)*(s-1) |
SSQEs |
SSQEs/(t*(r-1)*(s-1)) |
|
| Total (Tot) |
t*r*s-1 |
SSQTot |
|
|
| awhere t=number of main treatments, r=number of replications per treatment and s=number of subplots. |
Sample ANOVA table:
Source of
variation |
Degrees of
freedom |
Sums of
squares (SSQ) |
Mean
square (MS) |
F |
| Treatments |
2 |
199.08 |
99.54 |
10.20a |
| Error-main plots |
9 |
87.80 |
9.76 |
|
| Subplots |
2 |
193.46 |
96.73 |
15.00b |
| Subplots X Treatments |
4 |
25.38 |
6.35 |
0.98c |
| Error-subplots |
18 |
116.08 |
6.45 |
|
| Total |
35 |
621.81 |
|
|
aF test with 2,9 degrees of freedom at P=0.05 is 4.26
bF test with 2,18 degrees of freedom at P=0.05 is 3.55
cF test with 4,18 degrees of freedom at P=0.05is 2.93. |
Sample SAS GLM statements:
PROC GLM;
CLASS TREATS REPS SUBPLOTS;
MODEL WHATEVER = TREATS TREATS(REPS) SUBPLOTS
SUBPLOTS*TREATS;
TEST H = TREATS E = TREATS(REPS);
RUN;
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Thursday, August 17, 2000
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