Transcript V. RCBD MISSING DATA atau DATA RUSAK

MISSING DATA ATAU DATA
RUSAK
Missing data occurs whenever a valid
observation is not available for any one of the
experimental unit
Loss information
Nonapplicability of standard
analysis of variance
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Common causes of missing data
 Improper treatment (nonapplication,
incorrect dose, wrong timing)
 Destruction of experimental plant (physical
damage, pest damage, poor germination)
 Lost of harvested samples
 Illogical data (recognized after recorded and
transcribed)
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The new data do not increasing the
experiment error.
 Experiment error =  (ij)2
data ij=0
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Missing data in RCBD
Xij     i   j   ij
0
Xij    ( X i .  X ..)  ( X . j  X ..)
If missing data = a
X ' ..  a  X 'i .  a X ' ..  a   X ' j .  a X ' ..  a 
a





t.r
t.r   t
t.r 
 r
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'
'
'
'



X ..  a
X i .  a X ..  a
X j .  a X ..  a 
a





t.r
t.r   t
t.r 
 r
'
X 'i .  a X ' j .  a X ' ..  a
a


r
t
t.r
t.r.a  t ( X 'i .  a)  r ( X ' j .  a)  X ' ..  a
a(t.r  t  r  1)  t ( X 'i .)  r ( X ' j .)  X ' ..
t ( X 'i .)  r ( X ' j .)  X ' .. t ( X 'i .)  r ( X ' j .)  X ' ..
a

(t.r  t  r  1)
(t  1)( r  1)

X
Bias 
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j
.  (t  1) a
t (t  1)

2
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Anova
 df total = (t.r-1)-m
 df error = [(t-1)(r-1)]-m
 m = numbers of missing data
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Example 1
A
B
I
61
49
II
55
50
III
54
a
IV
54
46
Yi.
224
145+a
C
D
49
49
48
47
49
46
149+a
46
50
192
192
753+a
753  a 145  a 753  a  149  a 753  a 
a





16
16   4
16 
 4
16a-8a+a=423
a=47 or
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rB  tT  G 4 x149  4 x145  753
a

 47
(t  1)( r  1)
3x3
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(149  3x 47) 2
Bias 
 5,33
4.3
2242  1922  1922  1922 8002
SStreat 

 5,33  186,67
4
16
SV
Block
df
3
Treatment
3
Error
(9-1)-1
Total
(15-1)-1
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186,67
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Example 2
A
B
I
61
49
II
55
50
III
54
a
IV
54
46
Yi.
224
145+a
C
D
49
49
b
47
152+b
49
46
149+a
46
50
144+b
192
705+a+b
i) 16a=4(145+149+2a)-(705+a+b)
9a+b=471
ii) 16b=4(152+144+2b)-(705+a+b)
a+9b=479
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Elimination/substitution
9a+b=471
9a+81b=4311
-80b=-3840
b=48
9a+b=471
9a+48=471
a=47
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Konsekuensi adanya missing data untuk uji
lanjut dg LSD
a. Jika tidak ada missing data
LSD %  t( %; dbsesatan)
2KTsesa tan
r
b. Mengandung satu missing data
LSD %  t( %; dbsesatan)
t
KTsesa tan
(2 
)
(r  1)(t  2)
r
c. Mengandung dua missing data
LSD %  t( %; dbsesatan)
1 1
(  ) KTsesa tan
r1 r2
r1 dan r2 : angka ulangan efektif
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Cara mencari ulangan efektif r1
dan r2
 Perhatikan treatment tersebut pada tiap blok
dalam hubungannya dengan treatment yang
lain yang sama-sama mengalami missing
data:
 Bila treatment I tidak ada nilainya 0
 Bila treatment I ada, treatment II tidak ada
nilainya ½
 Bila treatment I dan treatment II sama-sama
adanya nilainya 1
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Contoh
1
2
3
4
5
A
Ө
B
C
Ө
D
B
D
1
1
1
2
1/2
0
3
1
1
4
0
1/2
5
1
1
3½
3½
r1 = 3 ½
r2 = 3 ½
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