**Types of Experimental Designs in Statistics**

*Completely Randomized Design (CRD), Randomized Block Design (RBD), Latin Square Design (LSD) – Advantages and Disadvantages*

In the previous post, we have discussed the **Principles of Experimental Designs.** There we discussed the concept of Experimental design in statistics and their applications. In the present post, we will discuss different types of statistical experimental designs, its applications, advantages and limitations.

**Learn more:** Principles of Experimental Designs

**Different types of Experimental Designs**

**Different types of Experimental Designs**

Ø **Experimental designs** are broadly classified into TWO categories:

**(A). Single-Factor Experiments**

**(B). Multi-factor Experiments**

**(A). Single-Factor Experiments:**

Ø Single factor experiments are those experiments in which only a single factor varies while all others are kept constant.

Ø Here the treatments consist exclusively of the different levels of the single variable factor.

Ø All other factors are applied uniformly to all plots.

Ø Examples of Single-Factor Experimental Designs:

**(1). Completely Randomized Design (CRD)**

**(2). Randomized Block Design (RBD)**

**(3). Latin-Square Design (LSD)**

**(1). Completely Randomized Design**

Ø It is commonly called as CRD.

Ø CRD is a statistical experimental design where the treatments are assigned completely at random so that each treatment unit has the same chance of receiving any one treatment.

Ø In CRD, any difference among experimental units receiving the same treatment is considered as an experimental error.

Ø CRD is applicable only when the experimental material is homogenous (Example: Homogenous soil condition in the field).

Ø Usually in the field, the soil will be HETEROGENOUS.

Ø Thus, CRD is not a preferable method in field experiments.

Ø CRD is generally applicable to the lab experimental conditions.

Ø In labs, the environmental conditions can be easily controlled.

Ø The concept of ‘Local-control’ is not used in CRD.

**Advantages of CRD**

Ø CRD is easy to understand and calculate the variance.

Ø The number of replications can vary from treatment to treatment.

Ø CRD has high flexibility and thus any number of treatments can be used.

Ø Simple statistical analysis is required in the analysis of CRD.

Ø CRD provides maximum number of degree of freedom.

**Disadvantages of CRD**

Ø CRD can be applied only to homogenous experiments.

Ø The principle of ‘Local-control’ is not used in CRD.

**(2). Randomized Block Design**

Ø It is also called RBD.

Ø RBD is the most commonly used experimental design in agriculture.

Ø Here the ‘local-control’ is adopted and the experimental material is grouped into homogenous subgroups.

Ø Each such sub-group is called blocks.

Ø A block contains the entire set of treatments and thus a block is equivalent to a replication.

Ø Characteristic of RBD:

$ Presence of blocks of equal sizes, each of which contains all the treatments.

$ In RBD, we have to use all the three principles of design of experiments (replication, randomization and local-control).

**Advantages of RBD**

Ø RBD is more efficient and accurate when compared to CRD.

Ø Chance of error in RBD is comparatively less.

Ø Flexibility is also very high in RBD and thus any number of treatments and any number of replications can be used.

Ø Statistical analysis is relatively simple and easy.

Ø Statistical analysis simple when one value is missing.

Ø Errors of any treatment can be isolated.

**Disadvantages of RBD**

Ø RBD is not advised for very large number of treatments.

Ø If the heterogeneity of the plot is very high, RBD cannot be applied. When the number of treatments is very large then the size of each block will be increased so that there may be heterogeneous blocks within.

Ø With large number of treatments, the possibility of experimental errors will be high.

**(3). Latin Square Design**

Ø Commonly called as LSD.

Ø LSD is a design where the experimental material is divided into ‘m’ rows, ‘m’ columns and ‘m’ treatments – assigned by randomization method to rows and columns.

Ø The randomization is in such a way that each treatment occurs only once in each row and in each column.

**Advantages of LSD**

Ø Statistical analysis is relatively simple (complicated than CRD and RBD).

Ø Statistical analysis is simple if one value is missing.

Ø Most efficient design when compared to CRD and RBD.

**Disadvantages of LSD**

Ø LSD is not suitable for agricultural experiments.

Ø Statistical analysis is complicated when two or more values are missing.

Ø Difficult when treatments are more than ten.

**(2). Multi-Factor Designs**

Ø Multi-factor experimental designs are also called as factorial experiments.

Ø They are used in the experiments where the effects of more than one factor are to be determined.

Ø It is used to study a problem that is affected by a large number of factors.

Ø In factorial experiments, the factors are denoted by capital letters (Example: N, P)

Ø The level of each factor are denoted by small letters (Example: n, p)

Ø The combination of levels can be written as n_{0}p_{0}, n_{0}p_{1}, n_{1}p_{o}, n_{1}p_{1} etc.

Ø If there are ‘f’ factors each at ‘l’ levels, then we have** l ^{f} **factorial design.

Ø Example: 22 Factorial design (Two factors and Two levels)

**References**

**Balaji, K. et al**. (2012). Biostatistics. I.K. International Publishing House Pvt. Ltd., New Delhi

**Kothari, C. R.** (2004). Research Methodology: Methods and Techniques. New Age International.

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