STAT-C 3213 (EXPERIMENTAL DESIGN)

Introduction

The Randomized Complete Block (RCB) Design is one of the most widely used experimental designs in agricultural research. The Design is especially suited for field experiments where the number of treatments is not large and experimental area has a predictable productivity gradient. The primary distinguishing feature of the RCB design is the presence of blocks of equal size each of which contains all treatments. 

The primary purpose of blocking is to reduce experimental error by eliminating the contribution of known sources of variation among experimental units. This is done by grouping the experimental units into blocks such that variability within each block is minimized and variability among blocks is maximized. Because only the variation within a block becomes part of the experimental error. Blocking is most effective when the experimental area has a predictable pattern, plot shape and block orientation can be chosen so that much of the variation is accounted for by the difference among blocks, and experimental plots within the same block are kept as uniform as possible. 

There are two important decisions that have to made in arriving at an appropriate and effective blocking technique. These are: 

• The selection of the source of variability to be used as the basis for blocking 

• The selection of the block shape and orientation 

An ideal source of variation to use as the basis for blocking is one that is large and highly predictable. 

Examples are: 

• Soil Heterogeneity, in a fertilizer or variety of trial where yield data is the primary character of interest 

• Direction of insect migration, in an insecticides trial where insect infestation is the primary character of interest 

• Slope of the field, in a study of plant reaction to water stress.

After identifying the specific source of variability to be used as the basis for blocking, the size and shape of the blocks must be selected to maximize variability among blocks. The guidelines for this decision are: 

1. When the gradient is unidirectional (i.e., there is only one gradient), use long and narrow blocks. Furthermore, orient these blocks so their length is perpendicular to the direction of the gradient. 

2. When the fertility gradient occurs in two directions with one gradient much stronger than the other, ignore the weaker gradient and follow the preceding guideline for the case of the unidirectional gradient 

3. When the fertility gradient occurs in two directions with both gradients equally strong and perpendicular to each other, choose one of these alternatives: 

a. Use blocks that are as square as possible 

b. Use long and narrow blocks with their length perpendicular to the direction of one gradient and use covariance technique to take care of the other gradient. 

c. Use the Latin Square Design with two-way blockings, one for each gradient. 

4. When the pattern of variability is not predictable, blocks should be as square as possible. 

Whenever blocking is used, the identity of the blocks and the purpose for their use must be consistent throughout the experiment. That is, whenever a source of variation exists that is beyond the control of the researcher, he should assure that such variation occurs among blocks rather than within blocks. 

For example, if certain operations such as application of insecticides or data collection cannot be completed for the whole experiment in one day, the task should be completed for all plots of the same block in the same day. In this way, variation among days (which may be enhanced by weather factors) becomes part of block variation and is, thus, excluded from the experimental error. If more than one observer is to make measurements for all plots of the same block. In this way, the variation among observers, if any, would constitute a part of block variation instead of the experimental error. 

The Randomization process for a RCB Design is applied separately and independently to each of the blocks. We use a field experiment with six (6) treatments A, B, C, D, E, F and four replications to illustrate the procedure. 

It is worthwhile, at this point, to emphasize the major difference between CRD and a RCB Design. Randomization in the CRD is done without any restrictions, but for a RCB design, all treatments must appear in each block. This difference can be illustrated by comparing the RCB design layout with the hypothetical layout of the same trial based on a CRD. Note that each treatment in a CRD layout can appear anywhere among nth plots in the field. For example, in the CRD layout, treatment A appears in three adjacent plots (plot 5,8, and 11). This is not possible in a RCBD layout.