A Field Guide to Experimental 
Designs

The Completely Randomized Design (CRD)

The CRD is the simplest of all designs. It is equivalent to a t-test when only two treatments are examined.

Field marks:

  • Replications of treatments are assigned completely at random to independent experimental subjects.
  • Adjacent subjects could potentially have the same treatment.

Sample layout:
Different colors represent different treatments. There are 4 (A-D) treatments with 4 replications (1-4) each.
CRD sample layout

     A1  B1  C1  A2
     D1  A3  D2  C2
     B2  D3  C3  B3
     C4  A4  B4  D4

 

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/MSE
Error (E) t*(r-1) SSQE SSQE/(t*(r-1))  
Total (Tot) t*r-1 SSQTot    
awhere t=number of treatments and r=number of replications per treatment.

Sample ANOVA table:

Source of
variation
Degrees of
freedom
Sums of
squares (SSQ)
Mean
square (MS)
F
Treatments 3 80.92 26.97 9.68a
Error 12 33.43 2.79  
Total 15 114.35    
aF test with 3,12 degrees of freedom at P=0.05 is 3.49

Sample SAS GLM statements:

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

Compare with:

 

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Friday, August 25, 2000