9780898715927

The Analysis of Means

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  • ISBN13:

    9780898715927

  • ISBN10:

    089871592X

  • Format: Paperback
  • Copyright: 2005-07-30
  • Publisher: Society for Industrial & Applied
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Supplemental Materials

What is included with this book?

  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

Summary

The analysis of means (ANOM) is a graphical procedure used to quantify differences among treatment groups in a variety of experimental design and observational study situations. Key advances in ANOM procedures that have appeared only in technical journals during the last 20 years are included in this first comprehensive modern treatment of the ANOM containing all of the needed information for practitioners to understand and apply ANOM. This book contains examples from a wide variety of fields adapted from real-world applications and data with easy-to-follow, step-by-step instructions. It is front loaded, so potential ANOM users can find solutions to standard problems in the first five chapters. An appendix contains several SASĀ® examples showing the system's ANOM capabilities and how SAS was used to produce selected ANOM decision charts in the book. It will be welcomed by practitioners and statisticians for whom it will serve both as a primer and reference.

Author Biography

Peter R. Nelson (1949 ū 2004), formerly of Clemson University, played a key role in the development of ANOM methods. In addition to authoring journal articles, books, and book chapters, he served as editor and as editorial review board member of the Journal of Quality Technology and as editorial review board member of the American Journal of Mathematical and Management Sciences. Peter was a Fellow of the ASA and ASQ. Peter S. Wludyka is Associate Professor of Statistics at the University of North Florida, Jacksonville, and Director of the UNF Center for Research and Consulting in Statistics. He is also Biostatistical Consultant to the Office of the Dean at the University of Florida Health Sciences Center in Jacksonville, Florida. His paper on analysis of means for variances, co-authored with Peter Nelson, won the Wilcoxon Prize as best applications paper in Technometrics in 1997. Among his publications are a half dozen methodological papers on the ANOM. He has presented talks to SAS user groups on ANOM and routinely uses ANOM in collaborative research and consulting. Karen A. F. Copeland is currently the principal statistician of Boulder Statistics, which provides statistical consulting services to clients in a variety of industry sectors, including the medical device, chemical, medical diagnostic, environmental, consumer product, food product, and tourism sectors. She held academic and industrial positions before becoming an independent consultant. Karen is a co-author of Introductory Statistics for Engineering Experimentation (Academic Press, 2003) as well as an author of peer-reviewed papers. She has developed JMP scripts for using ANOM.

Table of Contents

Preface xi
Introduction
1(10)
ANOM as a Multiple Comparison Procedure
1(7)
History of ANOM
8(2)
This Book
10(1)
One-Factor Balanced Studies
11(24)
Types of Data
11(2)
Normally Distributed Data
13(14)
Assumptions
14(2)
ANOM
16(9)
ANOM p-Values
25(1)
Sample Sizes
25(2)
Binomial Data (ANOM for Proportions)
27(2)
Poisson Data (ANOM for Frequencies or Rates)
29(6)
Chapter 2 Problems
32(3)
One-Factor Unbalanced Studies
35(16)
Normally Distributed Data
35(5)
Binomial Data
40(3)
Poisson Data
43(8)
Chapter 3 Problems
47(4)
Testing for Equal Variances
51(20)
ANOMV for Balanced Studies
51(6)
Critical Values
52(5)
ANOMV with Unequal Sample Sizes
57(2)
ANOMV for Large Samples
59(4)
Equal Sample Sizes
59(2)
Unequal Sample Sizes
61(2)
Robust ANOM for Variance Test
63(5)
Transformations
65(3)
Power and Sample Size Considerations for ANOMV
68(3)
Comments for Practitioners Regarding ANOMV Tests
69(1)
Chapter 4 Problems
69(2)
Complete Multifactor Studies
71(60)
Testing for Interaction
72(14)
The ANOVA Test for Interaction
75(6)
Using ANOM to Test for Interaction
81(5)
ANOM for a Two-Way Layout
86(10)
When There Is No AB Interaction
86(2)
When There Is an AB Interaction
88(3)
With Only One Observation per Cell
91(4)
Randomized Block Designs
95(1)
Practitioner's Summary of Two-Way ANOM
96(13)
Two-Factor ANOM for Binomial and Poisson Data
109(6)
ANOM for Higher-Order Layouts
115(16)
Chapter 5 Problems
127(4)
Incomplete Multifactor Studies
131(16)
Latin Squares
131(3)
Graeco--Latin Squares
134(2)
Balanced Incomplete Block Designs
136(6)
Youden Squares
142(5)
Axial Mixture Designs
147(6)
Heteroscedastic Data
153(10)
The One-Way Layout
153(3)
Higher-Order Layouts
156(7)
Distribution-Free Techniques
163(18)
Robust Variance Tests
163(2)
The Odd Sample Size Case
163(2)
ANOM-Type Randomization Tests
165(6)
RANDANOMV-R: A Randomization Test Version of ANOMV
165(1)
Appropriateness of and Drawbacks to RANDANOMV-R
166(1)
UBRANDANOMV-R: More General Randomization Test for Variances
167(3)
Comparisons Among HOV Tests
170(1)
Distribution-Free ANOM Techniques
171(10)
Rank Tests
171(3)
Transformed Ranks
174(1)
A Randomization Test
175(2)
Comparison of the Three Procedures
177(1)
Note on Randomization Tests
178(1)
Chapter 9 Problems
178(3)
Appendix A Figures
181(14)
ANOM Power Curves
181(4)
ANOMV Power Curves
185(4)
HANOM Power Curves
189(6)
Appendix B Tables
195(32)
Balanced ANOM Critical Values h(α; k, v)
196(5)
Sample Sizes for ANOM
201(9)
Unbalanced ANOM Critical Values m(α; k, v)
210(4)
ANOMV Critical Values
214(6)
Sample Sizes for ANOMV
220(1)
ANOM Critical Values g(α; (I, J), v) for Two-Factor Interactions
221(3)
HANOM Critical Values H(α; k, v)
224(3)
Appendix C SAS Examples
227(12)
Introduction
227(1)
Examples from Chapter 2
227(1)
Examples from Chapter 3
228(1)
Examples from Chapter 5
228(11)
References 239(6)
Index 245

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