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The Analysis of Means: A Graphical Method for Comparing Means, Rates, and Proportions

Peter R. Nelson, Peter S. Wludyka, and Karen A. F. Copeland
Publication Date: 
Number of Pages: 
ASA-SIAM Series on Statistics and Applied Probability 18
[Reviewed by
Gudmund R. Iversen
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Traditionally, analysis of variance (ANOVA) has been the statistical method used to examine differences between means across groups, in spite of its misleading name. ANOVA provides a value of the F-variable that makes it possible to conclude that one or more means are different from each other, without specifying which means are different. The analysis of means (ANOM) provides a direct comparison of the group means, giving a graph of the overall mean and boundaries around this mean. Any group mean falling outside the boundaries is significantly different from the overall mean.

This book provides an excellent introduction to ANOM, and it should be part of every statistician's library. It is well written and covers a wide range of methods, such as ANOM for one-factor, multifactor and incomplete multifactor studies. ANOM methods can be used for means, proportions and Poisson data. Each analysis has a numerical example and a discussion of the substantive meaning of the analysis results. The book does not cover the derivation of formulas and tables needed for ANOM.

In addition to the lucid presentation of the different types of analyses, the authors also provide excellent explanations of statistical concepts, as they are needed. For example, their introduction of the statistical p-value is actually understandable and does not lead the uninitiated reader to believe that it has anything to do with a probability of the null hypothesis being true.

Gudmund R. Iversen holds a PhD in statistics from Harvard University and is Professor Emeritus of Statistics at Swarthmore College, where he taught statistics for many years. He can be reached at

 Preface; Introduction; Chapter 1: One-Factor Balanced Studies; Chapter 2: One-Factor Unbalanced Studies; Chapter 3: Testing for Equal Variances; Chapter 4: Complete Multi-Factor Studies; Chapter 5: Incomplete Multi-Factor Studies; Chapter 6: Axial Mixture Designs; Chapter 7: Heteroscedastic Data; Chapter 8: Distribution-Free Techniques; Appendix A: Figures; Appendix B: Tables; Appendix C: SAS Examples; References; Index.