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CRD.ppt

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					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.

				
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