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Lec 14 Missing Observations in RCBD.ppt

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					Missing Observations in RCBD




             Tariq Mahmood Bajwa
                    Missing Observations in RCBD

  During the conduct of experiment, it is possible that one
  or more observations are missing or unusable as when

 An animal become sick or dies but not as a result of the
      treatment.
 A flask breaks in the laboratory during an experiment.
 There has been an obvious recording error.
 Occurrence of missing data results in two major
      difficulties
Loss of information
Non-applicability of the standard analysis of
      variance technique as treatments are no longer
      orthogonal to blocks as a result each block is
      not a complete block
                   Missing Observations in RCBD




 F-Yates developed a method for        estimating such
     missing observations.
 The missing value is estimated by minimizing the
     error sum of squares.
 An estimate of a missing values does not supply
     additional information to the experimenter, it only
     facilitates the analysis of the remaining data.
                  Missing Observations in RCBD


Steps for estimating missing observation. Step-1

If there is only one missing observation then estimate
the missing observation by using the formula
                         rB  tT  G *
                  Xm 
                          (r  1)(t  1)
 Xm = Estimate of missing observation.
 B,T = Sum of observed values of block and treatment
       having a missing observation
 r,t = Number of blocks and treatments
 G* = Sum of observed values, i.e., sum of all the
       values except missing value
                Missing Observations in RCBD


Step-1

The estimated value is substituted for that missing
observation and analysis is completed.
Step – 2
Subtract one from both the total and error degree of
freedom
Step – 3: Calculate the amount of bias as:
                       B  (t  1) X 
                                       2

             Bias =
                           t (t  1)
and then subtract this amount of bias from both
Treatment SS and Total SS.
           Missing Observations in RCBD
Seed            Grain Yield (Kg/ha)
Kg/ha                                       T=
 Treat   Rep.I Rep.II Rep.III Rep.IV
  25     5113     5398    5307    4678
  50     5346     5952     X      4264   15562
  75     5272     5713    5483    4749
  100    5164     4831    4986    4410     G=
  125    4804     4848    4432    4748
  150    5254     4542    4919    4098
         B=              25127           114311
                Missing Observations in RCBD

 Formula                   rB  tT  G *
                    Xm 
                            (r  1)(t  1)




           (4)(25127)  (6)(15562)  (114311)
     Xm 
                      (4  1)(6  1)
     X m = 5304


The estimated value is substituted for that missing
observation and the remaining analysis is.
             Missing Observations in RCBD

Seed             Grain Yield (Kg/ha)      Treat.
Kg/ha                                     Total
  Treat   Rep.I Rep.II Rep.III Rep.IV
   25     5113     5398    5307    4678   20496
   50     5346     5952    5304    4264   20866
   75     5272     5713    5483    4749   21217
  100     5164     4831    4986    4410   19391
  125     4804     4848    4432    4748   18832
  150     5254     4542    4919    4098   18813
Rep.Total 30953 31284 30431        26947 119615
                      Missing Observations in RCBD

   Calculation of various Sum of Squares


      G 119615
        2                 2

C.F.=    =       = 596156176
      rt    24
             t   t
Total S.S. =  X ij -C.F.
                      2

            i=1 j=1


Total S.S.=  51132 +  53982 +……+  40982  -596156176
                                              
Total S.S.= 4847551
                                    Missing Observations in RCBD

      Calculation of various Sum of Squares
                    t

                   T
                   i=1
                            i
                                2


Treatment S.S. =                    - C.F.
                        r
                  20496  2 +  20281 2 +……+ 18813  2   
Treatment S.S.=                                              -596156176
                
                                      4                     
                                                             
Treatment S.S.= 1399108
                                      r

                                     R
                                     j=1
                                              2
                                              j

Block/Replication S.S. =                          - C.F.
                                          t
                    30953  2 +  31284  2 +……+  26947  2   
Replication S.S.=                                                -596156176
                  
                                         6                      
                                                                 
Replication S.S.= 2004396
Error S.S. = Total S.S. - Treatment S.S. - Replication S.S.
Error S.S. = 4847551 - 1399108 - 2004396
Error S.S. = 1444047
                 Missing Observations in RCBD
  Adjusted ANOVA Table

    SOV        SS           DF           MSS     Fcal
   Block   2004396      (r-1)  = 3 688132 6.67**
 Treatment 1399108      (t-1)  = 5 279822 2.71NS
                               = 14
   Error    1444047 (r-1)(t-1)      103146
  TOTAL                          = 22
            4847551     (rt-1)
                                           1%    5%
F (Tabulated) for Blocks     = F(3,14)    5.56   3.34
F (Tabulated) for Treatments = F(5,14)    4.69   2.96
                 Missing Observations in RCBD
 Statistical Report



Since the F- ratio for treatments is Non Significant so
we conclude that the experiment failed to show any
significance difference among six treatments. On the
other hand the F-ratio for blocks is highly significant
so we say that there is difference among four blocks
and blocks are effective in reducing the size of
experimental error.
                           Missing Observations in RCBD

                                                                         B  (t  1) X 
                                                                                                  2
Calculation of amount of bias
                                                    Bias =
                                                                              t (t  1)



                       Bias         
                                      25127  553042
                                             65
                       Bias  64681
 Standard Errors:

                                                                     MSE 103146
        Standard Error of a treatment mean                                     160.58
                                                                      r     4
                                                                        2MSE 2 103146
        Standard Error of the differencebetween two treatment means                   227.09
                                                                          r      4

				
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Description: Lec 14 Missing Observations in RCBD.ppt