Procedures to identify mathematical models that explicitly yield optimal (maximum accuracy) solutions for samples were widely studied in the past century, with literatures emerging in fields such as symbolic logic, discrete mathematics, operations research, mathe­matical programming, set theory, decision-making, systems engineering, algo­rithms, automated manufacturing, com­puter science, machine intelligence, finance, transpor­tation science, man­agement science, and numerical tax­onomy. Broad-spec­trum consensus among disparate experts indicates that predic­tive accu­racy is an objective function worthy of being optimized.

In the Optimal (or “optimizing”) Data Analysis (ODA) statistical paradigm, an optimization algorithm is first utilized to identify the model that explicitly maximizes predictive accuracy for the sample, and then the resulting optimal performance is evaluated in the context of an application-specific exact statistical architec­ture. Discovered in 1990, the first and most basic ODA model was a distribution-free machine learning algorithm used to make maximum accuracy classifications of observations into one of two categories (pass or fail) on the basis of their score on an ordered attribute (test score). When the first book on ODA was writ­ten in 2004 a cornucopia of in­disputable evidence had already amassed demonstrating that statistical models identified by ODA were more flexible, transpar­ent, intuitive, accurate, par­simonious, and generalizable than competing models instead identified using an unin­tegrated menagerie of legacy statistical meth­ods. Understanding of ODA methodology skyrocketed over the next decade, and 2014 produced the development of novometric theory – the conceptual analogue of quan­tum mechanics for the statistical analysis of classical data. Maximizing Predictive Accu­racy was written as a means of organizing and making sense of all that has so-far been learned about ODA, through November of 2015.


The perfect bound (softcover) textbook measures 8.5” wide, 11.5” tall, and 0.94” thick, and is typeset in Calibri size 10 font. There are 12 chapters and 408 pages (29 color), including 93 illustrations, 207 tables, and 491 references.

ISBN-10: 0-692-70092-7

ISBN-13: 978-0-692-70092-1

DOI: 10.13140/RG.2.1.1368.3286

The book unfolds in four sections: Introduction (with three chapters: Pragmatic Considerations; Fundamental Concepts; Methodological Matters); Bivariate Methods (Categorical Attributes, Ordered Attributes); Linear Multiattribute Methods (General Linear Models; Maximum-Likelihood Models; Explicitly Optimal Models; Statistical Confounding); and Non-Linear Multiattribute Methods (Hierarchically Optimal CTA; Enumerated Optimal CTA; Globally Optimal CTA).

For researchers exploring ODA for the first time, the most appreciated aspect will likely be the intellectually transparent, intuitive presentation involving minimal use of a few simple equations: the optimal, maximum-accuracy para­digm is clear in its derivation, application, computation, interpretation, and dissemination. For researchers that use ODA in their work, the most appreciated reward is unquestionably the unmatched flexibility, simplicity, and accuracy of the statistical models – and their generaliza­bility across time and sample. ODA accommodates all metrics, requires no distributional assump­tions, allows for analytic weighting of individual observations, explicitly maximizes predictive accu­racy (overall, or normed against chance), and supports multiple methods of assessing validity. Finally, amply illustrated in Maximizing Predictive Accuracy, conducting maximum-accuracy statistical analysis is astonishingly straightforward, simple, and fast using commercially-available special-purpose software.


The first review of Maximizing Predictive Accu­racy is published in Journal of Evaluation in Clinical Practice.

“This new book by Paul R. Yarnold and Robert C. Soltysik, Maximizing Predictive Accuracy, represents the culmination of over 30 years of research and development into this highly innovative modeling approach. For researchers with a conventional statistics background, ODA (and by extension CTA), offer a bridge between the familiar (a statistical basis for determining “significance”) and the “not-so-familiar” (machine learning, and more broadly, data mining). The ways in which these techniques can be applied are too numerous to count. It is only a matter of time until these tools will replace conventional methods for use in everything from clinical trials to applications in everyday practice. Only the limits of the human imagination pose a constraint for the application of the maximize-accuracy paradigm.” Ariel Linden, DrPH, President, Linden Consulting Group, LLC, Ann Arbor, MI, and Research Scientist, Division of General Internal Medicine, Medical School, University of Michigan, Ann Arbor, MI

“This book is destined to become a classic in the field of statistics. The unified analytic paradigm of optimally accurate methods that the authors present is the most extraordinary quantitative breakthrough I’ve seen during     my 45 years in the field of statistics. This modern-day analytic paradigm represents a quantum leap beyond the inferential statistical methods of the 19th and 20th century. Had Pearson and Fisher had access to this maximum accuracy distribution-free analytic method, they would have embraced it for its power and precision, its optimal accuracy, its elegant simplicity, and its virtually unlimited applicability. Contemporary statisticians ought to do the same, for this is truly the wave of the future.” Fred B. Bryant, PhD, Professor, Department of Psychology, Loyola University, Chicago


Preface     xi
Acknowledgments     xii
Chapter 1 Pragmatic Considerations     1
Chapter 2 Fundamental Concepts     9
Chapter 3 Methodological Matters     40
Chapter 4 UniODA with Categorical Attributes     72
Chapter 5 UniODA with Ordered Attributes     99
Chapter 6 Optimized General-Linear Models     142
Chapter 7 Optimized Maximum-Likelihood Models     158
Chapter 8 Explicitly Optimal Linear Models     173
Chapter 9 Identifying and Ameliorating Statistical Confounding     183
Chapter 10 Hierarchically Optimal Classification Tree Analysis     231
Chapter 11 Enumerated Optimal Classification Tree Analysis     251
Chapter 12 Globally Optimal Statistical Analysis     261
Appendix A: UniODA and MegaODA Command Syntax     298
Appendix B: MegaODA Time Trials     306
Appendix C: CTA Command Syntax     312
Appendix D: Troubleshooting ODA Software     319
Appendix E: Weather Prediction Results     320
Chapter References     338
Alphabetical References     362
Index     388
About the Authors     396



Statistical models are useful to the extent that they provide accurate predictions and facilitate valid inferences. UniODA is the only software providing a univariate statistical model that explicitly achieves maximum predictive accuracy for any given sample, data configuration, and hypothesis.

  • The most comprehensive exposition of the ODA (maximum-accuracy) paradigm.
  • Self-contained, stands alone, everything needed to conduct analyses quickly, with a minimum of effort.
  • Explained conceptually without equations, using many clear, easy-to-understand examples.
  • The only software enabling manual classification tree analysis (CTA) to be conducted, and offering researchers pin-point control “inside” CTA models, for model exploration and fine-tuning.
  • Maximum-accuracy alternatives to t-test, logistic regression, chi-square, ANOVA, Mann-Whitney U, kappa, phi, discriminant analysis, autocorrelation, Markov analysis, log-linear model, probit analysis, and to a host of other traditional parametric and non-parametric statistical procedures.
  • Hold-out (cross-generalizability) and leave-one-out (jackknife) validity analysis; weighting by prior odds and/or by cost or return; exploratory or confirmatory hypothesis testing; and multiple sample analysis for diagnosing and circumventing Simpson’s paradox—all possible for every analysis.
  • Maximum-accuracy psychometric analyses, including parallel forms, split-half, inter-rater, test-retest, and intraclass reliability analyses; discriminant, convergent, and construct validity analyses; and multidimensional analysis of structure underlying bias in reliability and validity data.
  • Software Review:
  • To Purchase (USA):
  • To Purchase (UK)


MegaODA offers the UniODA algorithm adapted for use with big data.

  • Accommodates samples of up to 3,000,000 observations.
  • No limit on the number of attributes that can be analyzed.
  • Command syntax is the same as in UniODA and CTA


CTA is the only statistical software that provides a multivariable model that explicitly achieves maximum predictive accuracy —for any given sample, data configuration, and hypothesis.

  • The only statistical software system that conducts maximum-accuracy classification tree analyses, or CTA.
  • Self-contained, stands alone, everything needed to conduct analyses quickly, with a minimum of effort.
  • Many clear, easy-to-understand examples available in Maximizing Classification Accuracy, and at
  • This unique statistical software will easily and routinely identify richer, more meaningful effects in your data than all other statistical software systems, combined.
  • For a few example models see Gallery at, and articles in the ODA eJournal and in a host of other journals (see the Publications page).


BOOK: A copy- and write-protected PDF copy of Maximizing Predictive Accuracy is available for $24.95 (USD). The PDF will be sent via eMail when payment is verified by PayPal.

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BOOK and MegaODA software: A zip file containing MegaODA software and the PDF copy of Maximizing Predictive Accuracy is available for $49.95 (USD). The zip file will be sent via eMail when payment is verified by PayPal.

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BOOK and MegaODA and CTA software: A zip file containing MegaODA and CTA software and the PDF copy of Maximizing Predictive Accuracy is available for $149.95 (USD). The zip file will be sent via eMail when payment is verified by PayPal.

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