Minitab Technical Support Document Basic Rules and Guidelines for Specifying ANOVA Models in MINITAB This document was designed by: Ben Cromwell Manager Advanced Integrated Technologies Group, Inc.
RULE 1: The top level factor and all crossed factors will be listed individually. RULE 2: Crossed factors will be listed as interactions interaction s of other higher level factors. Note that the "interactions" include both crossed and nested factors (see rule 3 for nested relationships). RULE 3: All nested factors factors must be expressed expressed in terms terms of their "parent" "parent" factors. All nested parents must be listed.
Simple Examples
Exam ple 1: All Factors Crossed
Note that this is a factorial factorial design. The model is simply the main effects and interactions that you'd normally expect to get.
F a c to rs
S c h e m a tic
Temperature
T 60
Operator
O p1
Gage
Op 2
T 90
Op 3
G1
G2
Supplier
O p4
G3
S1
Batch
S1
S2
S1
Temperature Operator Gage Temperature*Operator Temperature*Gage Operator*Gage Temperature*Operator*Gage
Note that with a nested d esign, the nested lower levels do not stand on their own. That is, they must be expressed "within" the level level above
Exam ple 2: Nested Factors
S am p le
T 75
M in ita b M o d e l
B1
B2
S2
S1
Supplier Batch(Supplier) Sam ple(Supplier ple(Supplier Batch)
S2
B3
S2
B4
S1
B1
S2
S1
B2
S2
S1
B3
B4
S2
S1
S2
S1
S2
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Minitab Technical Support Document Basic Rules and Guidelines for Specifying ANOVA Models in MINITAB Complex Examples
Examp le 3: Nested & Crossed Factors
Layout
L1
Operator
O1
O2
Fixture
L2
O3
O4
F1
O5
O6
F2
O7
O8
Layout Operator(Layout) Fixture Layout*Fixture Fixture*Operator(Layout)
F3
Examp le 4: Nested & Crossed Factors A
A1
B
B1
B2
C
B3
B4
C1
D
E
A2
E1
E2
E3
B5
B6
C2
B7
B8
A C C* A C*B(A) B(A) D(A B) E(A B D)
C3
D1
D2
D3
D4
D5
D6
E4
E5
E6
E7
E8
E9
E1 0
E11
E12
Page 2 Contact Tech Support: Tel: E-mail: Web:
US Office – Minitab Inc. +1-814-231-2682
[email protected] http://www.minitab.com/support/
UK Office – Minitab Ltd. +44 (0) 24 7643 7507
[email protected] http://www.minitab.com/support/
French Office – Minitab SARL +33 1 55 33 12 64
[email protected] http://www.minitab.fr
