A Field Guide to Experimental 
Designs

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.
RCB repeated at several locations sample layout

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
freedoma
Sums of
squares (SSQ)
Mean
square (MS)
F
Locations (L) l-1 SSQL SSQL/(l-1) MSL/MSEl
Error for Locations (El) l*(b-1) SSQEl SSQEl/(l*(b-1))  
Treatments (Tr) t-1 SSQTr SSQTr/(t-1) MSTr/MSE
Treatments X Locations (TxL) (t-1)*(l-1) SSQTxL SSQTxL/((t-1)*(l-1)) MSTxL/MSE
Error (E) l*(t-1)*(b-1) SSQE SSQE/(l*(t-1)*(b-1))  
Total (Tot) l*t*b-1 SSQTot    
awhere l=number of locations, t=number of treatments and b=number of blocks or replications.

Sample ANOVA table:

Source of
variation
Degrees of
freedoma
Sums of
squares (SSQ)
Mean
square (MS)
F
Locations 2 33.63 16.82 1.17a
Error for Locations 6 86.05 14.34  
Treatments 2 186.76 93.38 11.47a
Treatments X Locations 4 16.84 4.21 0.52a
Error 12 97.72 8.14  
Total 26 421.01    
aF 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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July 7, 2000