A completely randomized design (CRD) is one where the treatments are assigned completely at random so that each experimental unit has the same chance of receiving any one treatment. CRD is only appropriate for experiments with homogeneous experimental units. CRD is rarely used in field experiments because of large variations among experimental plots. Randomization and Layout Consider an experiment to test the larval population on six wheat varieties. The step by step procedure for randomization and layout of a field experiment with six treatments each replicated three times is Step-1 : How many Experimental plots Treatments = t = 6 ( V1, V2, V3, V4, V5, V6) Replications= r = 3 Total Plots = n = 18 (n=t*r) Randomization and Layout Step-2: Assign a plot 1 2 3 number to each experimental plot in 4 5 6 any convenient manner: for example, 7 8 9 consecutively from 1to n. For our 10 11 12 example, the plot numbers 1,……….,18 13 14 15 are assigned to the 18 experimental plots. 16 17 18 Randomization and Layout STEP 3: Assign the treatments to the experimental plots by any of the following randomization schemes: A. Lottery Method B. Random number table method Lottery Method Make 18 slips of paper. Write V1 on 3 slips, V2 on 3 slips and so on. Place them in a bowl and mix them thoroughly. Draw the slips one at a time without replacement . Assign the treatment on the first slip drawn to the first experimental unit ,treatment on the second slip on the second experimental unit,…..treatment on the 18th slip to the 18th experimental unit. 1. Select a starting point somewhere in the random no. table and take 18 random numbers. 2. Choose the 18 distinct three digit random numbers. 3. Rank the n = 18 random numbers obtained in the step 2 in ascending or descending order. 4. Divide the rank columns derived in step-3 into t groups. E.g. 18 ranks into six groups each consisting of 3 numbers as follows S. no. Random no`s Ranks Treatment 1 785 14 V1 2 749 13 V1 G-1 3 858 17 V1 4 222 6 V2 5 159 4 V2 6 185 5 V2 7 825 16 V3 8 038 1 V3 9 481 8 V3 S. no. Random no`s Ranks Treatment 10 969 18 V4 11 120 3 V4 12 569 10 V4 13 240 7 V5 14 496 9 V5 15 585 11 V5 16 721 12 V6 17 786 15 V6 18 92 2 V6 Now, the layout is as follows: 1 2 3 4 5 6 V3 V6 V4 V2 V2 V2 7 8 9 10 11 12 V5 V3 V5 V4 V5 V6 13 14 15 16 17 18 V1 V1 V 6 V 3 V1 V4 OUTLINE OF ANALYSIS OF VARIENCE IS AS FELLOWS SOURCE OF DEGREE OF SUM OF MEAN COMPUTED TABULAR F VARIATION FREEDOM SQUARES SQUARE F 5% 1% TREATMENT t-1 EXPERIMENTAL t(r-1) ERROR TOTAL (r)(t)-1 The design is completely flexible, any number of treatments and of replications may be used. Moreover, the number of replications for any treatment needs not to be equal. It gives maximum degrees of freedom for error sum of squares as compared with the other designs for the same situation. The design is very simple and is easily laid out. The statistical analysis is very simple both for equal and unequal number of replications. If the data from some experimental units is missing, it does not complicate the analysis. The missing observations can be discarded without affecting the results of the experiment and efficiency of this design is not severely affected. The design is applicable only to a small number of treatments. The design is applicable only to homogeneous experimental material. If the experimental units are not homogeneous, then the use of this design gives the large experimental error as compared to some other designs, which use the homogeneous experimental units as blocks and ultimately reduce the experimental error. There is possibility of entering the whole of the variation among the experimental units into the experimental error, as the randomization is not restricted in any direction.