A Field Guide to Experimental 
Designs

The Randomized Complete Block design (RCB)

The RCB is the standard design for agricultural experiments. The field or orchard is divided into units to account for any variation in the field. Treatments are then assigned at random to the subjects in the blocks-once in each block.

Field marks:

  • 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.
  • Used to control variation in an experiment by accounting for spatial effects.

Sample layout:
Different colors represent different treatments; each horizontal row represents a block. There are 4 blocks (I-IV) and 4 treatments (A-D) in this example.
RCB sample layout


Block I     A   B   C   D
Block II    D   A   B   C
Block III   B   D   C   A
Block IV    C   A   B   D

ANOVA table format:

Source of
variation
Degrees of
freedoma
Sums of
squares (SSQ)
Mean
square (MS)
F
Blocks (B) b-1 SSQB SSQB/(b-1) MSB/MSE
Treatments (Tr) t-1 SSQTr SSQTr/(t-1) MSTr/MSE
Error (E) (t-1)*(b-1) SSQE SSQE/((t-1)*(b-1))  
Total (Tot) t*b-1 SSQTot    
awhere t=number of treatments and b=number of blocks or replications.

Sample ANOVA table:

Source of
variation
Degrees of
freedom
Sums of
squares (SSQ)
Mean
square (MS)
F
Blocks 3 26.36 8.79 1.36a
Treatments 3 216.23 72.08 11.19a
Error 9 57.95 6.44  
Total 15 300.54    
aF test with 3,9 degrees of freedom at P=0.05 is 3.86

Sample SAS GLM statements:

PROC GLM;
  CLASS BLOCKS TREATS;
  MODEL WHATEVER = BLOCKS TREATS;
RUN;

Compare with:

 

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Friday, August 25, 2000