ANOVA Basic Rules

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 techsupport@minitab.com http://www.minitab.com/support/

UK Office – Minitab Ltd. +44 (0) 24 7643 7507 techsupport@minitab.co.uk http://www.minitab.com/support/

French Office – Minitab SARL +33 1 55 33 12 64 support@minitab.fr http://www.minitab.fr