# Lec 14 Missing Observations in RCBD.ppt

Document Sample

```					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

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

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 6 posted: 1/9/2013 language: English pages: 13
Description: Lec 14 Missing Observations in RCBD.ppt