A Randomized Complete Block Design (RCBD) is defined by an experiment whose treatment combinations are assigned randomly to the experimental units within a block. Generally, blocks cannot be randomized as the blocks represent factors with restrictions in randomizations such as location, place, time, gender, ethnicity, breeds, etc. It is not simply possible to randomly assign a particular gender to a person. It is not possible to pick a country and call X country. However, the presence of these factors (also known as nuisance factors) will introduce systematic variation in the study. For example, the crops produced in the northern vs the southern part will get exposed to different climate conditions. Therefore, they should be controlled whenever possible. Controlling these nuisance factors by blocking will reduce the experimental error, thereby increasing the precision of the experiment and many other benefits. In the completely randomized design (CRD), the experiments can only control the random unknown and uncontrolled factors (also known as lucking nuisance factors). However, the RCBD is used to control/handle some systematic and known sources (nuisance factors) of variations if they exist.

Randomized Complete Block Design (RCBD) is arguably the most common design of experiments in many disciplines, including agriculture, engineering, medical, etc. In addition to the experimental error reducing ability, the design widens the generalization of the study findings. For example, if the study contains the place as a blocking factor, the results could be generalized for the places. A fertilizer producer can only claim that it is effective regardless of the climate conditions when it is tested in various climate conditions.

The “complete block” part of the name indicates that each treatment combination is applied in all blocks. If a block misses one or more treatment combinations, the experiment would be called Randomized Incomplete Block Design. The design would still be called randomized because the treatment combinations are randomly assigned to the experimental units within the blocks. If a block is only missing data points from a couple of observation units, the experiment will still be called randomized complete block design (RCBD) with missing data, but not “incomplete block design.”

Randomized Complete Block Design Analysis Model

The effects model for the RCBD is provided in Equation 1.

Equation 1

The primary interest is the treatment effect in any RCBD, therefore the hypothesis for the design is statistically written as.