Randomized designs are a type of experimental design where randomization process is used to assign the units (like people or objects) to different treatment groups. The randomization process helps to control for bias and ensures that any observed differences between the groups are likely due to the treatment itself, rather than some other factors.

**Randomized Designs**

In randomized designs, the treatments are applied randomly, therefore the conclusions drawn are supported by statistical tests. The classification of randomized designs for single-factor are:

- Completely Randomized Design (CRD)
- Randomized Complete Block Design (RCBD)
- Latin Square Design (LSD)

**Example:** A market gardener wants to test three types of peas, $A$, $B$, and $C$, on his land. He divides a square plot into nine equal squares, three to be planted with each type of pea. The problem he then faces is which square to plant with which type.

One method is a Completely Randomized Design (CRD) which might,

1 | 2 | 3 |
---|---|---|

C | A | C |

B | A | A |

B | B | C |

This would be all right if all the plots were equally desirable. If however, there were prevailing north wind so that the northernmost plots were exposed, he might decide to use, a Randomize Complete Block Design (RCBD).

Randomized Complete Block Design, where each of the types $A$, $B$, and $C$ is planted once in each west-east block.

1 | 2 | 3 |
---|---|---|

A | B | C |

A | C | B |

C | B | A |

If the gardener also felt that the soil to the east was rather better than that to the west, he would use, a Latin Square Design (LSD).

A Latin Square design, where each type of pea is planted once in each row (west-east), and once in each column (north-south).

Block 1 | Block 2 | Block 3 |
---|---|---|

A | B | C |

B | C | A |

C | A | B |

For Randomized Designs, Note that

- Completely Randomized Design (CRD) is a statistical experimental design where the treatments are assigned completely at random so that each treatment unit has the same chance (equal chance) of receiving any one treatment.
- In CRD any difference among experimental units receiving the same treatment is considered as an experimental error.
- CRD is applicable only when the experimental material is homogeneous (eg., homogeneous soil conditions in the field).
- Since soil is heterogeneous in the field, the CRD is not a preferable method in field experiments. Therefore, CRD generally applies to the lab experimental conditions, as in labs, the environmental conditions can be easily controlled.
- The concept of “local control” is not used in CRD.
- CRD is best suited for experiments with a small number of treatments.

The best design for a study will depend on the specific research question and the factors that one needs to control for. By incorporating randomization, you can control for extraneous variables that might influence the outcome and improve the validity of the findings.

However, the choice of the randomized design depends on the specific research question(s) being asked. It is important to consider the strengths and weaknesses of each design before making a decision.

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