# Completely Randomized Design (CRD)

### Introduction to Completely Randomized Design (CRD)

The simplest and non-restricted experimental design, in which the occurrence of each treatment has an equal number of chances, each treatment can be accommodated in the plan, and the replication of each treatment is unequal is known to be a completely randomized design (CRD). In this regard, this design is known as an unrestricted (a design without any condition) design that has one primary factor. In general form, it is also known as a one-way analysis of variance.

### Example of CRD

There are three treatments named $A, B$, and $C$ placed randomly in different experimental units.

We can see that from the table above:

• There may or may not be a repetition of the treatment
• The only source of variation is the treatment
• Specific treatment doesn’t need to come in a specific unit.
• There are three treatments such that each treatment appears three times having P(A)=P(B)=P(C)=3/9.
• Each treatment appears an equal number of times (it may be unequal i.e. unbalanced)
• The total number of experimental units is 9.

### Some Advantages of Completely Randomized Design (CRD)

1. The main advantage of this design is that the analysis of data is simplest even if some unit does not respond due to any reason.
2. Another advantage of this design is that it provides a maximum degree of freedom for error.
3. This design is mostly used in laboratory experiments where all the other factors are under the control of the researcher. For example, in a tube experiment, CRD is best because all the factors are under control.

An assumption regarding completely randomized design (CRD) is that the observation in each level of a factor will be independent of each other.

### Statistical Model of CRD

The general model with one factor can be defined as

$Y_{ij}=\mu + \eta_i +e_{ij}$

where$i=1,2,\cdots,t$ and $j=1,2,\cdots, r_i$ with $t$ treatments and $r$ replication. $\mu$ is the overall mean based on all observations. $eta_i$ is the effect of ith treatment response. $e_{ij}$ is the corresponding error term which is assumed to be independent and normally distributed with mean zero and constant variance for each.

### Importance of CRD

• Simplicity: CRD is the easiest design to implement, in which treatments are assigned randomly to eliminate complex layouts and make them manageable for beginners.
• Fairness: Randomization ensures each experimental unit has an equal chance of receiving any treatment. The randomization reduces the bias and strengthens the validity of the comparisons between treatments.
• Flexibility: CRD can accommodate a wide range of experiments with different numbers of treatments and replicates. One can also adjust the design to fit the specific needs.
• Data Analysis: CRD boasts the simplest form of statistical analysis compared to other designs. This makes it easier to interpret the results and conclude the experiment.
• Efficiency: CRD allows for utilizing the entire experimental material, maximizing the data collected.

### When CRD is a Good Choice

• Laboratory experiments: Due to the controlled environment, CRD works well for isolating the effects of a single factor in lab settings.
• Limited treatments: If there are a small number of treatment groups, CRD is a manageable and efficient option.
• Initial investigations: CRD can be a good starting point for initial explorations of a factor’s effect before moving on to more complex designs.

### Summary

The advantages and importance of CRD make it a valuable starting point for many experiments, particularly in controlled laboratory settings. However, it is important to consider limitations like the assumption of homogeneous experimental units, which might not always be realistic in field experiments.

Read from Wikipedia: Completely Randomized Design (CRD)