รูปแบบต่างๆ
ของ Balanced
repeated measures (Kleinbaum,
1998)
3. A balanced repeated measures design with one nest factor.(Treatments)
Table
6 Data layout for balanced repeated measures design with one
nest factor.
|
|
|
Repeats |
|||
|
Treatment |
Subject
Number |
1 |
2 |
|
r |
|
1 |
(1,1) (2,1) : (s,1) |
Y111 Y211 : Ys11 |
Y112 Y212 : Ys12 |
|
Y11r Y21r : YS1r |
|
2 |
(1,2) (2,2) : (s,2) |
Y121 Y221 : Ys21 |
Y122 Y222 : Ys22 |
|
Y12r Y22r : YS2r |
|
|
: |
: |
: |
|
: |
|
t |
(1,t) (2,t) : (s,t) |
Y1t1 Y2t1 : Yst1 |
Y1t2 Y2t2 : Yst2 |
|
Y1tr Y2tr : Ystr |
Anova
model with treatments a fixed factor :
Yijk
= m
+ Si(j) + tj
+ Ek(ij)
(3)
Where
i = 1,
,s
(s = number of subject given each treatment)
j
= 1,
,t
(t = Number of treatment)
k = 1,
,r
(r = Number of repeats measured on the ith subject for a
given treatment)
m
= Overall mean
tj
= Fixed effect of treatment j (and åtj
=0)
Si(j) = Random effect of subject i within
subject j
Ek(ij)
= Random error for repeat k on subject i at treatment j
And we assume that
{ Si(j) } and { Eijk
} are mutually independent.
Si(j) is distributed as N(0,sS2)
Ek(ij)
is distributed as N(0,s2)
Figure
3 Partitioning the total sums of squares for balanced repeated
measures design with one nest factor.
คลิกขยายภาพ
Table
7 ANOVA table for balanced repeated measure design with one
nest factor.(Treatments)
|
Source |
d.f. |
MS |
F
( Fixed or Random Treatment Factor ) |
|
Between
Subjects |
ts-1 |
MSS |
|
|
Treatments |
t-1 |
MST |
MST
/MSS(T) |
|
Subjects
within Treatments |
t(s-1) |
MSS(T) |
|
|
Within
Subjects (i.e.Error) |
ts(r-1) |
MSW |
|
|
Total
(corrected) |
str
- 1 |
|
|