Transcript Fixed

Fixed Model
1. Partitioni ng X irc into independen t components
X irc    t r  t c  t rc   irc
t r  ( r   )
tc  ( c   )
t rc  (  rc   )  (  r   )  (  c   )
 i rc  ( X irc   rc )
2.  t r  0   (  r  )  0
t
t
c
rc
0
0
3. irc are randomly sampled from a normal population ( ,  )
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All  irc are independen t.
Homogeneit y of variance ; all  rc    .
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2
X 11    t1.  t .1  t11   11
X 12    t1.  t .2  t12   12
X 1.    t1.  0  0   1.
X 21    t 2.  t.1  t 21   21
X 22    t 2.  t .2  t 22   22
X 2.   t 2.  0  0   2.
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X .1    0  t .1  0   . 1
E ( MS R )  cn R
E ( MSc ) 
E ( MS RC ) 
E ( MS wcells ) 
X . 2    0  t . 2  0   .2
2
rn c
2
n RC
2

2
 
2

2
2
C  Fixed Variable
R  Random Variable
X irc     r .  t.c   RC   irc
t
.c
0
t
r.
0
c

rc
0

rc
0
r
X 11     1.  t.1   11   11
X 12     1.  t .2   12   12
X .1     1.  0  0   1.
X 21     2.  t .1   12   21
X 22     2.  t.2   22   22
X 2.     2.  0  0   1.
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X .1      t.1   1.   .1
E ( MS R )  cn R
X .2      t.2   .2   .2
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E ( MS C ) 
E ( MS RC ) 
E ( MS wcells ) 
FR  MS R / MS wcells
Fc  MS c / MS RC
FRC  MS RC / MS wcells

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rn c  n RC
2

2
 n RC
2

2
2
2