Randomized Block Design

Applications

Randomized block design is most useful in situations in which the experimental material is heterogeneous and it is possible to divide the experimental material into homogeneous groups of units or plots, called blocks or replications.

It is mostly used in agricultural field experiments, where soil heterogeneity may be present due to soil fertility gradient, and in clinical trials on animals, where the animals (experimental units) vary in age, breed, initial body weight, and so on. A randomized block design can eliminate effects of heterogeneity in one direction only.

Advantages and Disadvantages

The design is very flexible as no restrictions are placed on the number of treatments or replications. The statistical analysis is simple, and if some observations are missing or lost accidentally, one has recourse to the missing plot technique. The design is more efficient than completely randomized design as error variance is reduced as a result of blocking (assigning to blocks or replications), which increases the precision of the experiment. The design is not suitable if a large number of treatments are used or the experimental material is reasonably homogeneous.

Layout of the Design

The plan of allocation of the treatments to the experimental material is called layout of the design. Let the ith (i = 1,2,…, v) treatment be replicated r times. Therefore N = vr is the total number of required experimental units. Blocks or replications are formed perpendicular to the soil [Page 1208]fertility gradient in field experiments, or age, breed, initial body weight, and so on, in the clinical trials on animals, or education, age, religion, and so on, in social science experiments. Then, the treatments are allocated to the experimental units or plots in a random manner within each replication (or block). Each treatment has equal probability of allocation to an experimental unit within a replication or block.

Given in Table 1 is the layout plan of RBD in a field experiment with five treatments denoted by T1, T2, T3, T4, and T5, each replicated three times and allocated to 15 experimental units (rows are replications). The shaded areas are guard areas, nonexperimental areas, or areas under use as irrigation channels.

Randomization

Some common methods of random allocation of treatments to the experimental units are illustrated in the following examples:

• For an experiment that has no more than 10 treatments, each treatment is allotted a number, using a 1-digit random number table. The researcher picks random numbers without replacement (i.e., a random number may not be repeated) from the random number table until the number of replications of that treatment is exhausted.
• For more than 10 treatments, researchers may use a 2-digit random number table or combine two rows or columns of 1-digit random numbers. Here each 2-digit random number is divided by the number of treatments, and the residual number is selected. The digit 00 is discarded.
• On small pieces of paper identical in shape and size the numbers 1, 2, …, N are marked. These are thoroughly mixed in a box, and the papers are drawn one by one. The numbers on selected papers are random numbers.
• The random numbers may also be generated by computational algorithms.

Statistical Analysis

The data from RBD are treated by the method of analysis of variance for two-way classification. The analysis of data from RBD is performed using the linear fixed-effects model given

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