10.6Two-Way Analysis of Variance with Interaction 469

TABLE 10.4

Two-way ANOVA with l Observations per Cell: N

=

nm

(l

−

1)

Source of Degrees ofVariation Freedom Sum of Squares

F-Statistic

Level

α

Test

p-Value if

F

=

v

Row

m

−

1

SS

=r

ln

∑

m i=

( 1

Xi

−..

X...

(^2) )
Fr

SS
/(r
m
−

1. SS
   /e
   N
   Reject
   H
   r 0
   P{
   Fm
   −1,
   N

   
   

   v}
   if
   Fr

   
   

   Fm
   −1,
   N
   ,α
   Column
   n
   −
   1
   SS
   =e
   lm
   ∑
   n j=
   ( 1
   X.
   j.
   −
   X...
   (^2) )
   Fc

   
   

   SS
   /(c
   n
   −

   
   

   
   


2. 
   

   SS
   /Ne
   Reject
   H
   c 0
   P{
   Fn
   −1,
   N

   
   

   
   

   v}
   if
   Fc

   
   

   Fn
   −1,
   N
   ,α
   Interaction (
   n−
   1)(
   m
   −

   
   

   
   


3. 
   

   SS
   int

   
   

   ∑l
   n j=
   1
   Fint

   
   

   SS
   int
   /(n
   −
   1)(
   m
   −

   
   


4. 
   

   SS
   /e
   N
   Reject
   H
   int 0
   P{
   F(
   n−
   1)(
   m−
   1),
   N

   
   

   
   

   v}
   ×
   ∑
   m i=
   ( 1
   Xij
   −.
   Xi
   −..
   X.
   j.

   
   

   
   

• X...
  (^2) )
  if
  Fint

  
  

  F(
  n−
  1)(
  m−
  1),
  N
  ,α
  Error
  NSS
  =e
  ∑
  l k=
  ∑ 1
  n j=
  1
  ×
  ∑
  m i=
  ( 1
  Xijk
  −
  Xij
  (^2) ).