Randomized block design

Randomized block design
A randomized block design (RBD) is a design in which the whole set of experimental units arranged in several blocks which are internally homogeneous and extremely heterogeneous and then the selected treatments are randomly allocated to the experimental units within each block such that each treatment occurs one or same number of times in each block.

Advantages of RBD
i)      RBD is more efficient than CRD and thus provides more accurate and precise results than CRD.
ii)     Any number of blocks and any number of treatments can be used in RBD except the restriction that at least two replicates are needed to a carry out the test of significance.
iii)    Analysis of data is simple and straight forward in RBD.
iv)    RBD provides a method of eliminating or reducing the effects of trends.
v)     It is flexible readily adoptable and easy to analyze.

Disadvantage of RBD
i)      RBD is not suitable for large number of treatments as large error variation may arise in such case and when the blocks are within heterogeneous.
ii)     Property of orthogonality is lost by missing values in a RBD leading to complicated analysis of data.
iii)    RBD has less error  than comparable to CRD.
iv)    Since RBD controls variability due to one extraneous factor it is unsatisfactory when several extraneous factor exists among the experimental unit.
v)     The efficiency of RBD decreases as the block size increases.

Reasons of blocking
i)      One major reason for use of blocks is to make inferences over a large number of environmental conditions.
ii)     Another major reason is to reduce error variation by removing an unwanted source of variation from error variation.

Uses of RBD
i)      RBD removes one extraneous source of variation from experimental error and so increases precision. Thus RBD is used to increase precision.
ii)     Its use is found to be satisfactory in many experimental situations and thus it avoids the necessity of using more complex designs.
iii)    RBD provides unbiased estimates of block means in addition to that of treatment means and thus furnishes additional information from the experiment. It is not necessary that all blocks be conducted at the same location or at same time.

In what situation we have to apply RBD?
CRD is appropriate only for experiments having homogeneous experimental units and a small number of treatments. In experiments having heterogeneous experimental units and large number of treatments randomized block design is appropriate. It specially is used to control the heterogeneity and variability among the experimental units involving blocks as local control measure. If CRD is used in situations having heterogeneous experimental units, then the variation in yields form different experimental units can no longer be appropriate.
Why we use one tail  test in analysis of variance.
Suppose we want to test the following hypothesis
To test the hypothesis we use the following statistic
which follows  distribution under  with  and  

Relatively large values of Treatment  reflecting real differences among the treatments produce large values of  statistic and so lead to the rejection of null hypothesis. Thus upper tail of  distribution serves as critical region for the null hypothesis of no differences among the treatments and hence one tail  test is used in analysis of variance. In fact, the greater the differences between the and , the greater is the evidence that corresponding treatment means are different. So relatively large values of  provides greater evidence favoring rejection of the hypothesis of no treatment differences.

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