Completely Randomized Design in Experiments

Completely Randomized Design (CRD)

• Each treatment represents a population.
• In CRD, treatments are assigned completely at random to experimental units, so each unit has an equal chance of receiving any treatment.
• Experimental units used are relatively homogeneous to minimize differences among units receiving the same treatment, which is considered experimental error.

Experimental Error

• Refers to the differences among experimental units subjected to the same treatment.

When to Use CRD

• CRD is used when experimental units are relatively homogeneous.
• It is suitable for laboratory or greenhouse experiments where the researcher has more control over the environment.

Advantages of CRD

• Easy to layout.
• Has the simplest statistical analysis among all experimental designs.
• Allows for unequal number of replications without complicating statistical analysis.

Disadvantages of CRD

• Often difficult to obtain sufficiently homogeneous experimental units.
• Limited to a small number of treatments.
• Usually used for laboratory experiments, as it is hard to control environmental factors affecting homogeneity outside the laboratory.

Data Presentation and Notations for CRD

• Data is presented in a table with treatments as rows and observations as columns.

Sources of Variation in CRD

• There are two sources of variation among the observations: treatment variation and experimental error.
• The relative size of these two variations is used to determine if the observed difference among treatments is real or due to chance.

ANOVA for CRD

• The sources of variation are partitioned into treatments and experimental error.
• The degrees of freedom, sum of squares, mean square, F-computed, and P-value are calculated to determine if the treatment difference is real.

Decision Rule

• Reject the null hypothesis if F-computed is greater than the tabular F-value or if the P-value is less than α.