Repeated Measures:
2 x 2 within Ss
TREATMENT
(1) a b ab
1 12 20 12 30
2 13 21 13 31
3 14 22 14 32
4 15 23 15 33
PERSON 5 16 24 16 34
(SUBJECT) 6 17 25 17 35
7 18 26 18 36
8 19 27 19 37
9 20 28 20 38
10 21 29 21 39
Models (simple, without subject-by-treatment interactions):
ANOVA:--
For persons i = 1,2,…,10; levels j of A, j = 0,1; and levels k of B, k = 0,1,
y(ijk) = m + p(i) + a(j) + b(k) + (ab)(jk) + e(ijk)
Multiple regression:--
For I = 1,2, . . . , 40,
y(i) = d + b1S1(i) + b2S2(i) . . . + b9S9(i) + aA(i) + bB(i) + gG(i) + e(i)
that is, constant + subject variables + A variable + B variable + Interaction variable + error.
TREATMENT
Subject (1) a b ab
1 12 14 15 19
2 13 15 16 9
3 14 8 14 18
4 15 16 18 17
5 16 17 19 16
6 17 20 20 24
7 18 19 21 25
8 19 22 22 26
9 20 18 23 12
10 21 24 24 28
TREATMENT VALUES OF CONTRASTS
Subject (1) a b ab (1) A B
1 12 14 15 19 60 6 8
2 13 15 16 9 53 -5 -3
3 14 8 14 18 54 -2 10
4 15 16 18 17 66 0 4
5 16 17 19 16 68 -2 2
6 17 20 20 24 81 7 7
7 18 19 21 25 83 5 9
8 19 22 22 26 89 7 7
9 20 18 23 12 73 -13 -3
10 21 24 24 28 97 7 7
CONTRASTS
1 1 1 1 1
A -1 1 -1 1
B -1 -1 1 1
AB 1 -1 -1 1
AB
2
-9
10
-2
-4
1
3
1
-9
1
Data in stacked form Data in form for analysis by multiple regression
Person A B Y S1 S2 S3 S4 S5 S6 S7 S8 S9 A B G Y
1 0 0 12 1 0 0 0 0 0 0 0 0 0 0 0 12
1 1 0 14 1 0 0 0 0 0 0 0 0 1 0 0 14
1 0 1 15 1 0 0 0 0 0 0 0 0 0 1 0 15
1 1 1 19 1 0 0 0 0 0 0 0 0 1 1 1 19
2 0 0 13 0 1 0 0 0 0 0 0 0 0 0 0 13
2 1 0 15 0 1 0 0 0 0 0 0 0 1 0 0 15
2 0 1 16 0 1 0 0 0 0 0 0 0 0 1 0 16
2 1 1 9 0 1 0 0 0 0 0 0 0 1 1 1 9
3 0 0 14 0 0 1 0 0 0 0 0 0 0 0 0 14
3 1 0 8 0 0 1 0 0 0 0 0 0 1 0 0 8
3 0 1 14 0 0 1 0 0 0 0 0 0 0 1 0 14
3 1 1 18 0 0 1 0 0 0 0 0 0 1 1 1 18
4 0 0 15 0 0 0 1 0 0 0 0 0 0 0 0 15
4 1 0 16 0 0 0 1 0 0 0 0 0 1 0 0 16
4 0 1 18 0 0 0 1 0 0 0 0 0 0 1 0 18
4 1 1 17 0 0 0 1 0 0 0 0 0 1 1 1 17
5 0 0 16 0 0 0 0 1 0 0 0 0 0 0 0 16
5 1 0 17 0 0 0 0 1 0 0 0 0 1 0 0 17
5 0 1 19 0 0 0 0 1 0 0 0 0 0 1 0 19
5 1 1 16 0 0 0 0 1 0 0 0 0 1 1 1 16
6 0 0 17 0 0 0 0 0 1 0 0 0 0 0 0 17
6 1 0 20 0 0 0 0 0 1 0 0 0 1 0 0 20
6 0 1 20 0 0 0 0 0 1 0 0 0 0 1 0 20
6 1 1 24 0 0 0 0 0 1 0 0 0 1 1 1 24
7 0 0 18 0 0 0 0 0 0 1 0 0 0 0 0 18
7 1 0 19 0 0 0 0 0 0 1 0 0 1 0 0 19
7 0 1 21 0 0 0 0 0 0 1 0 0 0 1 0 21
7 1 1 25 0 0 0 0 0 0 1 0 0 1 1 1 25
8 0 0 19 0 0 0 0 0 0 0 1 0 0 0 0 19
8 1 0 22 0 0 0 0 0 0 0 1 0 1 0 0 22
8 0 1 22 0 0 0 0 0 0 0 1 0 0 1 0 22
8 1 1 26 0 0 0 0 0 0 0 1 0 1 1 1 26
9 0 0 20 0 0 0 0 0 0 0 0 1 0 0 0 20
9 1 0 18 0 0 0 0 0 0 0 0 1 1 0 0 18
9 0 1 23 0 0 0 0 0 0 0 0 1 0 1 0 23
9 1 1 12 0 0 0 0 0 0 0 0 1 1 1 1 12
10 0 0 21 0 0 0 0 0 0 0 0 0 0 0 0 21
10 1 0 24 0 0 0 0 0 0 0 0 0 1 0 0 24
10 0 1 24 0 0 0 0 0 0 0 0 0 0 1 0 24
10 1 1 28 0 0 0 0 0 0 0 0 0 1 1 1 28