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The Nature of Statistics (Dover Books on Mathematics)
Statistics is not merely numbers but a body of methods for making wise decisions in the face of uncertainty, and this book teaches readers to interpret statistical claims skillfully through real-world examples rather than technical figuring.
A profile of this book is on the way.
What it’s about
Wallis and Roberts strip statistics of its forbidding mathematical mystique and reveal it as a lively branch of scientific method and intelligent problem-solving. Through a wealth of vivid, real-world examples drawn from war, business, medicine, the social sciences, and the humanities, the authors show how statistics participates in the full cycle of inquiry—observation, hypothesis, prediction, and verification—and how the same core ideas of sampling, randomness, variability, and measurement underlie problems that look utterly different on the surface. The book teaches the reader to navigate between blind gullibility and blind distrust by cataloging the many ways statistics is misused and by demonstrating, through extended case studies on psychoses, vitamins, and rain-making, what careful statistical work actually requires. It is a guide to living with statistics without actually figuring—cultivating the open-minded skepticism and clear thinking that let any intelligent person evaluate statistical evidence.
The through-line
- Who it’s for
- An intelligent layperson, administrator, executive, scientist, or citizen who wants to understand and evaluate statistical claims without becoming a technical statistician.
- The problem
- Statistical claims surround them in business, government, science, and daily life, but they cannot tell valid uses from misuses. They oscillate between feeling duped when others quote statistics at them and feeling ignorant when they distrust statistics entirely.
- The plan
- Recognize statistics as a method of decision-making under uncertainty, not just figures.
- Study effective real-world uses to see how statistics integrates with subject matter.
- Learn the catalog of common misuses to spot fallacies in the wild.
- Grasp the core ideas of samples, populations, variability, and randomness.
- Always ask how numbers relate to the real world and how the data were obtained.
- The payoff
- The reader interprets statistics skillfully, neither gullible nor dismissive, and gains knowledge available only through good statistics. · They can specify what data and tables they need and judge whether evidence supports the conclusions drawn from it. · They avoid being misled by bad statistics in their administrative, scientific, or civic decisions.
See our guide
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Additional reading
- Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences · Cohen, J., & Cohen, P.
The book recommends this text for its excellent, accessible narrative discussions on regression, particularly for explanatory purposes in the social sciences.
- Classical and Modern Regression with Applications · Myers, R.
Cited as an excellent resource for its modern approach to regression analysis, especially its strong treatment of regression diagnostics for checking assumptions and identifying influential data points.
- Multivariate Statistical Methods in Behavioral Research · Bock, R. D.
This text is frequently cited by the author for more advanced or technical explanations of concepts in MANOVA, repeated measures, and step-down analysis.
- The Analysis of Covariance and Alternatives · Huitema, B.
Recommended as a very comprehensive and thorough text for readers wishing to gain a deeper understanding of Analysis of Covariance (ANCOVA).
- Structural Equations with Latent Variables · Bollen, K. A.
The guest-authored chapter on SEM heavily references this book as a key source for understanding fundamental concepts like model identification.
- Hierarchical Linear Models: Applications and Data Analysis Methods · Raudenbush, S., & Bryk, A.
The guest-authored chapter on Hierarchical Linear Modeling (HLM) cites this as the seminal text on the topic and the basis for the HLM software.
- Applied Discriminant Analysis · Huberty, C.
The chapter on Discriminant Analysis introduces this book as an excellent, current, and very thorough resource on the topic.
- Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan · John Kruschke
Recommended for reading 'During this book' to get additional information and a different perspective on Bayesian statistics and modeling.
- Regression and Other Stories · Andrew Gelman, Jennifer Hill, & Aki Vehtari
Recommended for reading 'During this book' as a supplementary text for a broader understanding of regression and Bayesian modeling.
- Statistical Rethinking: A Bayesian Course with Examples in R and Stan · Richard McElreath
Recommended for reading 'After this book' as a next step for readers who have mastered the concepts and wish to deepen their understanding of Bayesian modeling.