The Big Picture

Ed230B/C

Linear Statistical Models

The Big Picture

Between-Subjects Designs
Completely Randomized Design -- CR-4

A

a1 a2 a3 a4

s 1
...
s 8 s 9
...
s16 s17
...
s24 s25
...
s32

Y_ij = μ + α_j + ε_i(j)
Can test hypotheses about:
A main effects
Completely Randomized Factorial Design -- CRF-42

A

a1 a2 a3 a4

B b1 s 1
...
s 8 s 9
...
s16 s17
...
s24 s25
...
s32

b2 s33
...
s40 s41
...
s48 s49
...
s56 s57
...
s64

Y_ijk = μ + α_j + β_k + αβ_jk + ε_i(jk)
Can test hypotheses about:
A main effects
B main effects
AB interaction
Completely Randomized Factorial Design -- CRF-422

A

a1 a2 a3 a4

C c1 B b1 s 1
...
s 4 s 5
...
s 8 s 9
...
s12 s13
...
s16

b2 s17
...
s20 s21
...
s24 s25
...
s28 s29
...
s32

c2 B b1 s33
...
s36 s37
...
s40 s41
...
s44 s45
...
s48

b2 s49
...
s52 s53
...
s56 s57
...
s60 s61
...
s64

Y_ijkl = μ + α_j + β_k + γ_l + αβ_jk + αγ_jl + βγ_kl + αβγ_jkl + ε_i(jkl)*
Can test hypotheses about:
A main effects
B main effects
C main effects
AB interaction
AC interaction
BC interaction
ABC interaction
Within-Subjects Designs
Randomized Block Design -- RB-4

A

a1 a2 a3 a4

s 1
...
s 8 s 1
...
s 8 s 1
...
s 8 s 1
...
s 8

Y_ij = μ + α_j + π_i + ε_ij
Can test hypotheses about:
A main effects
Randomized Block Factorial Design -- RBF-42

A

a1 a2 a3 a4

B b1 s 1
...
s 8 s 1
...
s 8 s 1
...
s 8 s 1
...
s 8

b2 s 1
...
s 8 s 1
...
s 8 s 1
...
s 8 s 1
...
s 8

Y_ijk = μ + α_j + β_k + αβ_jk + π_i + ε_ijk
Can test hypotheses about:
A main effects
B main effects
AB interaction
Mixed-Subjects Designs
Split-Plot Factorial Design -- SPF-2.4

A

a1 a2 a3 a4

B b1 s 1
...
s 8 s 1
...
s 8 s 1
...
s 8 s 1
...
s 8

b2 s 9
...
s16 s 9
...
s16 s 9
...
s16 s 9
...
s16

Y_ijk = μ + β_j + π_i(j) + α_k + αβ_jk + απ_ik(j) + ε_ijk
Can test hypotheses about:
A main effects
B main effects
AB interaction

Nested Design -- CRH-24(A)

A

a1 a2

B b1 s 1
...
s 8

b2 s 9
...
s16

b3 s 17
...
s24

b4 s 25
...
s32

Y_ijk = μ + α_j + β_k(j) + ε_i(jk)*
Can test hypotheses about:
A main effects
B main effects

Linear Statistical Models Course

Phil Ender, 17sep10, 12Feb98