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Table 14.2. Computational formulas for the complex mixed design of two between-subjects factors and one within-subjects factor
Source
df
SS
MS
F
Between subjects
A 2
( b )( c )( n )
T 2
( a )( b )( c )( n )
SS A
df A
MS A
MS S / AB
A
a
1
B 2
( a )( c )( n )
T 2
( a )( b )( c )( n )
SS B
df B
MS B
MS S / AB
B
b 1
AB 2
( c )( n )
A 2
( b )( c )( n )
B 2
( a )( c )( n ) +
T 2
( a )( b )( c )( n )
SS A × B
df A × B
MS A × B
MS S / AB
A × B
( a 1)( b 1)
S 2
c
AB 2
( c )( n )
SS S / AB
df S / AB
S / AB
( a )( b )( n 1)
Within subjects
C 2
( a )( b )( n )
T 2
( a )( b )( c )( n )
SS C
df C
MS C
MS C × S / AB
C
c 1
AC 2
( b )( n )
A 2
( b )( c )( n )
C 2
( a )( b )( n ) +
T 2
( a )( b )( c )( n )
SS A × C
df A × C
MS A × C
MS C × S / AB
A
×
C
( a
1)( c
1)
BC 2
( a )( n )
B 2
( a )( c )( n )
C 2
( a )( b )( n ) +
T 2
( a )( b )( c )( n )
SS B × C
df B × C
MS B × C
MS C × S / AB
B × C
( b 1)( c 1)
ABC 2
n
( b )( n )
AC 2
( a )( n )
BC 2
AB 2
( c )( n ) +
A 2
( b )( c )( n )
SS A × B × C
df A × B × C
MS A × B × C
MS C × S / AB
A
×
B
×
C
( a
1)( b
1)( c
1)
B 2
( a )( c )( n ) +
C 2
( a )( b )( n )
T 2
( a )( b )( c )( n )
+
AB 2
S 2
c
+
( c )( n )
ABC
n
SS C × S / AB
df C × S / AB
Y 2
C × S / AB
( a )( b )( n 1)( c 1)
T 2
( a )( b )( c )( n )
Total
( a )( b )( c )( n )
1
Y 2
 
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