CRD

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 freedom^a	Sums of squares (SSQ)	Mean square (MS)	F
Treatments (Tr)	t-1	SSQ_Tr	SSQ_Tr/(t-1)	MS_Tr/MS_E
Error (E)	t*(r-1)	SSQ_E	SSQ_E/(t*(r-1))
Total (Tot)	t*r-1	SSQ_Tot
^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	9.68^a
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:

CRD with subsampling: measurements are made on experimental sub-units.
Randomized Complete Block (RCB): treatments are assigned at random within blocks of adjacent subjects, each treatment once per block.
Two-way Factorial arrangement on a CRD: the treatments are combinations of two sets of treatments.
Experiment with pseudo-replication: multiple measurements made on sub-units, but no replication on independent experimental units.
Regression--treatments from a continuous range: treatments come from a single quantitative range.

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Friday, August 25, 2000