🙇‍♂️ Randomized Block Design (RBD)

• We have seen that in a completely randomized design no local control measure was adopted excepting that the experimental units should be homogeneous.
• Usually, when experiments require a large number of experimental units, completely randomized designs cannot ensure precision of the estimates of treatment effects.
• In agricultural field experiments, usually the experimental materials are not homogeneous. In such situations the principle of local control is adopted and the experimental material is grouped into homogeneous sub groups. The subgroup is commonly termed as block. Since each block will consist the entire set of treatments a block is equivalent to a replication. The blocks are formed with units having common characteristics which may influence the response under study.
• In agricultural field experiments the soil fertility is an important character that influences the crop responses. The uniformity trial is used to identify the soil fertility of a field. If the fertility gradient is found to run in one direction (say from north to south) then the blocks are formed in the opposite direction (from east to west).
• If the number of experimental units within each group is same as the number of treatments and if every treatment appears precisely once in each group, then such an arrangement is called a randomized block design.

Layout

• Let us consider 5 treatments A, B, C, D and E each replicated 4 times. We divide the whole experimental area into 4 relatively homogeneous blocks and each block into 5 plots. Treatments are then allocated at random to the plots of a block, fresh randomization being done for each block.
• A particular layout as follows:

  

Statistical Analysis

• The results from RBD can be arranged in two way table according to the replications (blocks) and treatments, there will be ‘rk’ observations in total. The data can be arranged in the following table.

Mathematical Model

y_ij = μ + α_i + β_j + ξ_ij

• i = 1, 2,… k
• j = 1, 2,… r
• Where,
  • y_ij is the j^th replication of the i^th treatment
  • μ = general mean effect
  • α_i = the effect due to i^th treatment
  • β_i = the effect due to j^th block
  • ξ_ij = error effect
• Source of Variability:
  • Due to treatment
  • Block
  • Error

Null hypothesis:

• H₀₁: There is no significant difference between the treatment effects.

  i.e. α₁ = α₂ = ……… = α_k

• H₀₂: There is no significant difference between the block effects

  i.e. β₁ = β₂= ……… = β_r

• The null hypothesis can be verified by applying the ANOVA procedure. The different steps are in the analysis of data are:

  

  

  

  

Advantages and disadvantages of RBD

• Two-way classification (treatment wise and replication/block wise) and one-way control (local control).
• The principle advantage of RBD is that it increases the precision of the experiment. This is due to the reduction of experimental error by adoption of local control.
• The amount of information obtained in RBD is more as compared to CRD. Hence, RBD is more efficient than CRD.
• Flexibility is another advantage of RBD. Any number of replications can be included in RBD. If large number of homogeneous units are available, large number of treatments can be included in this design.
• Since the layout of RBD involves equal replication of treatments, statistical analysis is simple. Even when some observations are missing of certain treatments, the data can be analysed by the use of missing plot technique.
• When the number of treatments is increased, the block size will increase. If the block size is large it may be difficult to maintain homogeneity within blocks. Consequently, the experimental error will be increased. Hence, RBD may not be suitable for large number of treatments. But for this disadvantage, the RBD is a versatile design. It is the most frequently used design in agricultural experiments.
• The optimum blocks size in field experiments is 21 plots. i.e. we cannot compare treatments which are > 21 in RBD to preserve homogeneity of plots, within a block. It is used up to 20 treatments without appreciable loss of efficiency.
• This design appropriate when the fertility gradient in the field is in one direction only.
• In RBD the most number of blocks must be equal to the number of replications fixed for coach treatment.
• The number of plots in each block should be equal to the number of treatments.
• It provides more accurate results than CRD due to formation of homogenous blocks.
• This design utilizes all the three basic principles of field experimentation.
• Error degree of freedom in RBD: (r-1) x (k-1).