Randomized Complete Block Design

Definition

Randomized complete Block design, commonly referred to as RCBD, is an experimental design in which the subjects are divided into blocks or homogeneous unit. Eeach block/unit contains a complete set of treatments which are assigned randomly to the units. A randomized complete block design is said to complete mainly because experimental units and the number of treatments are equal. The main assumption of the RCBD is that there is no interaction between the treatments and the block effects hence controlling variation. RCBD is often preferred over all other designs because it governs the effects of the treatments on the response variables.

Randomized Complete Block Design Example

Suppose that there are 4 treatments and 3 blocks in a randomized complete block design. The experimental layout would be as shown below;

Block 1 Block 2 Block 3
A B C
B C D
C D A
D A B

The general model of a RCBD is defined as;

Randomized Complete Block Design model design

Where µ is the overall mean, i is the number of treatments, j is the number of blocksi is the effectif the ith treatment, xi is the effect of the jthblock on treatment i and eij is the error term.

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