RCB repeated at more than one location
Field marks:
 Blocks are laid out at more than one location. Treatments
are assigned at random to those blocks as below.
 Treatments are assigned at random within blocks of adjacent subjects, each treatment once per
block.
 The number of blocks is the number of replications.
 Any treatment can be adjacent to any other treatment, but not to the same treatment within the block.
Sample layout:
Different colors represent different treatments or locations. Blocks are delineated. There are 3 treatments, 3 locations and 3 blocks per location in this example.
Location 1 Location 2
Block I II III Block I II III
A B C B C B
B A B A B C
C C A C A A
Location 3
Block I II III
A C A
C B C
B A B
ANOVA table format:
Source of variation 
Degrees of freedom^{a} 
Sums of squares (SSQ) 
Mean square (MS) 
F 
Locations (L) 
l1 
SSQ_{L} 
SSQ_{L}/(l1) 
MS_{L}/MS_{El} 
Error for Locations (El) 
l*(b1) 
SSQ_{El} 
SSQ_{El}/(l*(b1)) 

Treatments (Tr) 
t1 
SSQ_{Tr} 
SSQ_{Tr}/(t1) 
MS_{Tr}/MS_{E} 
Treatments X Locations (TxL) 
(t1)*(l1) 
SSQ_{TxL} 
SSQ_{TxL}/((t1)*(l1)) 
MS_{TxL}/MS_{E} 
Error (E) 
l*(t1)*(b1) 
SSQ_{E} 
SSQ_{E}/(l*(t1)*(b1)) 

Total (Tot) 
l*t*b1 
SSQ_{Tot} 


^{a}where l=number of locations, t=number of treatments and b=number of blocks or replications. 
Sample ANOVA table:
Source of variation 
Degrees of freedom^{a} 
Sums of squares (SSQ) 
Mean square (MS) 
F 
Locations 
2 
33.63 
16.82 
1.17^{a} 
Error for Locations 
6 
86.05 
14.34 

Treatments 
2 
186.76 
93.38 
11.47^{a} 
Treatments X Locations 
4 
16.84 
4.21 
0.52^{a} 
Error 
12 
97.72 
8.14 

Total 
26 
421.01 


^{a}F test with 2,6 degrees of freedom at P=0.05 is 5.14; 2,12 is 3.89; 4,12 is 3.26 
Sample SAS GLM statements:
PROC GLM;
CLASS LOCS BLOCKS TREATS;
MODEL WHATEVER = LOCS BLOCKS(LOCS) TREATS
TREATS*LOCS ;
TEST H = LOCS E = BLOCKS(LOCS);
RUN;
Compare with:
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fax: 5096628714
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July 7, 2000
