COMPONENTS
IN
REPEATED MEASURES DESIGNS
Hans-Magne Eikeland
UNIVERSITY OF OSLO
1973
REPEATED MEASURES DESI
1
1965 1966
1969 )
s d bl
no
By
Mo t
(S 1954
Moore 1963
on i mo to
occur
"It
not
c c
onnec
c 1941 )
k
c
on
of
c c t
(
to one can
c e on
t i
t i
d
em
1970)
e
A
c
measures 5s de TABI1E 1
T1 T2
ss
5 1 6 4 0 4 0
b 4 2 6
c
0 1 0:3
'7 .) 6 04 6 R 4· 5
d 1 5 6
3 3 6 0 To 20 9
vc
(row) 0 = 5 -I 2( '5) 2 5
) 0 == 5 +· 5 ( 1 '0) 1 '0
) 5 = 5 5,0
0 zero c
1 1 ,j un-
t
d 1
rows i sum score e
p ec d
c sum
p It is more t
t score tion p
On some
p c c c
t
It is to ze rows
c ons of e
i of
c
5 e
e-c s
v
= 4 ov 1v 2,5
The e rows is c be
c i
0 rrhe re row c
anc p ons 5 ( 5)=
5 0 or 4 0 ( 1 ) 5
ze score e
e 0
e ore 0
V( )
It s
It
p TABLE 1
One
score
k
uncommon
no dou
s i c
d
is on
to ve en
AN OVA
i
t c
'FADLE 1
TABJ~E
The more c c
more
s The
e
It c
more c order
on
same
rows
c
t to cone more
score
sum
on en
it ore
e score
t 1 It
2
49 50
GURJ~ 1
onunon
0
k'
AJ\TOVA me fo
( 1 960)
p
lVfo
GURE
(1 0)
ourc
t
do A B
c
It t
46 223 11.
0
sum
lu p
d 1
'l'
( 19 )
4 49 49 49
t
+ + 4
ved
1 J
c
on
vc
1 'Z _) 4 55
3 1 1 39
0 49
5 46
p
.
'
3 MS'
t
e sum 4
ANOVA en
ons
is sum
ons Source C
look TABLE 3
c
It
rst the es of c ons of ed. ~Phe sum score
is o on ore
( 1 1 + 2 + 1 + 2 ) ( 1 )
(1),16 s c e 0
es one 1 c
c 3
c ( ) co-
The bo
He e
sponse
c e c
T11 rp12 T21 T2
T11 v T12
1 v
~p 2 v
:
re ,but not e of c
( 4
1
t
TABJ~E 4
t
0
The
+
v + As
one
on
The e
v v
b N- ---
v
dBy
e
sum score so t is 1/k
v
or 1/ksum ore ro
c
e p
sj on
ons
c on
se 1 c
.L (
1 + 12 1 2
2: (
1 12 + 1( 1 1 2 1 +
( 5 ) ( 6) ( 7)'
e was the
to
)2 )2 )2
by sum ons
i e
i e be
AN OVA
sum score
e
(2)
( 3)
(4)
i
( 5) (6) (7)
st
( r7) one
~f
v (4) (8) (9)
e
s of
e
(10) one
ourc
s
TABIJ~i 5
c e
e 4
e
es c
ons (5),(6)
0
MS'
on
c ons
( 8) (9) ( 10) 3
TABI,E 5 t t
c tions of
e =
s i v
cruci e
as e
c
A B
c
(P,PS PR)v ) c )
v +
t
s c
c A or
PS t i not so
d it i
c p
d
A d
o sources
( 1969 )
It PH
the
to e c
as so on l ons e
A c
d
c tions
,on
e some
PH
one d s
e i i
row
He
11 1 21 22
1 1 1 556 3 161 7 044 4 55 12 3 161 11,556 4 552 7 044
1 7 044 4 55 11,556 3 161
2 1 1 556
c
e e
TABLE 6
ance-c c
be een
c
TABLI~~ 7
1 1
1
1
4 55
2
e
c
e be
sum
TABLE '7
1 '391 4 552 492 1 391
,903 4 552
s 0 e
ec on
s
1 d
e
e i cons
1 391
i
a sum
By c
It i
sa;ne
v
pc s 4 5 903 + 8
en -11 rp
1 391 + t3
sum
5 903 + 2 1 ~391 + 2 2 4
to no
ore mo
e
by
1
ean
TABLE 7
4 + 16 4 55 - 105 25 +
4 4
552 6 313t Al\fOVA
0
to
The on o:f
5 903 I 4
0 2 + 0 189
e tt
cl sum. score
on
2 + 18' 208
0 106 + 0 692
t
on c
26 313 1 000
s c
sum ore scores
c
t sum
c
should c
ore
t ve
ore
d SUJTI to st
c-:> + 2 1 391 + 4,55 -- 11,556
0 511 + 0 216 0' 120 + 0 394 1 000 t e
on 0 394)
c PS c
,o
394 0 120o,
74'monos
c - 0 + PR
c 0 394 + 0 0 610,i
e st c -- 0 603)
t
reason
It
po
i
AtTOVA
The
e e
s
t do c
c
compared s
of
t 0 connec
on
0 394
s are not
i same
on
be
p
p d
e
0
PS,
,i
e
c on
t
maJ{e it
7,
0
PR TABLE 5
0,297
At some 1 com-
c
1 t
on
Osnes (1971) ons
c
re Osne
are
no c
( )
no cone
to s
on errors on
no on
e
c
k'
OS
e
i
t
on
ons
1
on )
s j_s 24 2
on de
d measures de ,as can en TABLE 8
s d
A1 X X X X X X X X X X X X
A2 _{\ v X X X X X X X X X X X
.,.11'1
3 X X X X X X X X X X X
X
X
A
no of
s here is
the s
c
t
Bock s
c e
c
the sent Thi erence be en
no c e on of the
c to be c d the s
can be seen TABLE 9, s
s are
~~ABJ~E 9
I ('1971 ) MJOVA
Source
ss
A 4081 1 23
B 76 1 1
c
224 0 1AB 524 1 3
AC 231 9 23
BC 1 1 1
ABC 693 0 23
D(ABC) 2730,0 192
To 8561,3 287
e
c sources of
s
) )
( ) + +
I
( ) T ( )
to cone
c ch was
the sarne s ones,
177 439 76 100 2
,ooo
22 787 10 084
1 100 30 130 14 219
+ 6
cone
scus
ANOVA resul c
vc
14,558
1,224 341 5 304 14 219
(AB) (AC)
mo
c on
of ,one
0
t
of th e
(
c
or
c
d
cons
c
c
c
0
e
s
c
s to
c by c
0 or
t
on
t
es
,or
lower
found
on on
,067
,206 14
on
c
ar1ce c seem
a i
to c s be
c ANOVA least e
d measures de"')~F-,L!.>J i t can be{shown
c e c
e A
sources
d terms
measure s
to ace
i even e mean
c
c
t de
c ance c
s ble to
c t
e o:f de t some o:f
c
on
,bo i t
ch
eem c
d
ear
e
om-
0 t
ci c
er,G C , ore
1965,
,H E.
of
H
1959
re
ec c
e c
70 ..
,N source of
Holt
01Tl
)
Conce 1 t
es 1963,_2_,441 10
ected ANOVA ,204 13
1970
e
ton 196
or by
'311
8c
e
c e