# 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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