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Dual review of
While the titles do not suggest these books belong together, those titles are clever ones that do not immediately inform us of the actual content. Perplexed is not so much about what we think of as ethics in statistics — informed consent and human subjects advisory panels. Rather, it is about doing good work, with the ethical dimension arising from the fact that shoddy work may cost others money — or their lives. Trial illustrates that point dramatically with a number of serious court cases. But it is not math that is on trial in this book. Rather, mathematical (usually probability) arguments are used in the trials reported as crucial evidence. Perplexed covers a wider range, and greater number, of situations, though there is overlap between the two books in the examples chosen.
Trial treats a short list of examples introduced with a simple explanation of the probability (or sometimes statistics) involved. The presentation favors arithmetic over algebra, and uses plain English and simple examples to convey general points. These explanations get somewhat more involved and drawn out as the chapters progress, though the basic level is appropriate to a determined general reader. Most of these discussions would benefit from additional coverage in class if you were to use this as a supplement. In all cases, the math lesson is brief, and we jump quickly into an exciting court case. Here the authors shine, and the dramatic presentation will grip many readers. (This one read the book in a single sitting.) The authors always finish the story, even when that involves no mathematics. Be warned that some have unhappy endings while others are never resolved. Chapters end by looping back to the original math lesson to make sure readers see its relevance in the situation at hand. Some of the cases have already appeared in numerous statistics textbooks — the yellow convertible in California or the Berkeley graduate admissions data — but here we get not only a much more dramatic presentation, but also a lot more context.
Although mathematicians often rely on applied context both for motivation and as a source of problems for research, the ultimate focus in mathematical thinking is on abstract patterns: the context is part of the irrelevant detail that must be boiled off over the flame of abstraction in order to reveal the previously hidden crystal of pure structure. In mathematics, context obscures structure. Like mathematicians, data analysts also look for patterns, but ultimately, in data analysis, whether the patterns have meaning, and whether they have any value, depends on how the threads of those patterns interweave with the complementary threads of the storyline. In data analysis, context provides meaning. (George W. Cobb and David S Moore, “Mathematics, Statistics, and Teaching,” American Mathematical Monthly, Vol. 104, No. 9 (Nov., 1997), p. 803.)
While real data has (fortunately) become common in introductory statistics textbooks, it is too often presented with such a sketchy context as to make much statistical thinking about the data difficult. Trial presents context in a way that stimulates both thought and interest. As a result, this book needs to be on any teacher’s short list of possible outside readings. Unlike some books for a wide audience, the mathematics is generally sound, though the authors seem to ignore their own warnings about unwarranted assumptions of independence in their analysis of the Puckett case.
Perplexed is at the opposite end of a spectrum in its presentation. The math lessons are often long, with heavy use of symbolism and at a high level of abstraction. The authors say they intend to reach graduate students in the social sciences, but it is hard to imagine many such students prepared to read this material. A very large number of specific examples of statistical issues are treated very briefly, and the link between all the math and the application is left as an exercise for the reader. The text is heavy with parenthetical remarks, footnotes, and long quotations, making it very hard to follow the train of thought.
This book is more valuable as a reference than as something to read for more than a few pages at a time. There is a 40-page bibliography, a six-page author index, a fourteen-page subject index, and a thirteen-page list of sources, plus a 105 page online supplement that consists mostly of legal decisions and recommended reading. (Trial would benefit from at least an index, though admittedly this review is based on an advance copy.) Using all the resources provided by Perplexed, one can assemble a very long list of issues and applications, with readings and references. These could cover a much wider range of applications than are presented in Trial, but it would take a lot of work to turn them into equally engaging reading.
Both books are recommended, but for very different audiences and uses. Trial is likely to engage students and get them thinking, talking and even arguing about the issues involved. Perplexed is more of a resource the statistically sophisticated teacher can mine for material from which to create their own examples to engage students.
After a few years in industry, Robert W. Hayden (bob@statland.org) taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He now teaches statistics online at statistics.com and does summer workshops for high school teachers of Advanced Placement Statistics. He contributed the chapter on evaluating introductory statistics textbooks to the MAA's Teaching Statistics.
Preamble
Introduction
The (Questionable) Use of Statistical Models
TOOLS FROM PROBABILITY AND STATISTICS
Probability Theory: Background and Bayes’ Theorem
The (Mis)assignment of Probabilities
The Probabilistic Generalizations of Logical Fallacies Are No Longer Fallacies
Using Bayes’ Rule to Assess the Consequences of Screening for Rare Events
Bayes’ Rule and the Confusion of Conditional Probabilities
Bayes’ Rule and the Importance of Base Rates
Probability Theory: Application Areas
Some Probability Considerations in Discrimination and Classification
Probability and Litigation
Betting, Gaming, and Risk
Correlation
Illusory Correlation
Ecological Correlation
Restriction of Range for Correlations
Odd Correlations
Measures of Nonlinear Association
Intraclass Correlation
Prediction
Regression toward the Mean
Actuarial Versus Clinical Prediction
Incorporating Reliability Corrections in Prediction
Differential Prediction Effects in Selection
Interpreting and Making Inferences from Regression Weights
The (Un)reliability of Clinical Prediction
The Basic Sampling Model and Associated Topics
Multivariable Systems
Graphical Presentation
Problems with Multiple Testing
Issues in Repeated-Measures Analyses
Matching and Blocking
Randomization and Permutation Tests
Pitfalls of Software Implementations
Sample Size Selection
Psychometrics
Traditional True Score Theory Concepts of Reliability and Validity
Test Fairness
Quotidian Psychometric Insights
Psychometrics, Eugenics, and Immigration Restriction
DATA PRESENTATION AND INTERPRETATION
Background: Data Presentation and Interpretation
Weight-of-the-Evidence Arguments in the Presentation and Interpretation of Data
(Mis)reporting of Data
The Social Construction of Statistics
Adjustments for Groups Not Comparable on a Variable, Such As Age
Inferring Causality
Casuistry
The Bradford-Hill Criteria for Determining a Causal Connection
Some Historical Health and Medical Conceptions of Disease Causality
Medical Error as (the) Causative Factor
Simpson’s Paradox
Meta-Analysis
Statistical Sleuthing and Explanation
Sleuthing Interests and Basic Tools
Survival Analysis
Statistical Sleuthing and the Imposition of the Death Penalty: McCleskey v. Kemp (1987)
EXPERIMENTAL DESIGN AND THE COLLECTION OF DATA
Background: Experimental Design and the Collection of Data
Observational Studies: Interpretation
Observational Studies: Types
Observational Studies: Additional Cautions
Controlled Studies
Controlled Studies: Additional Sources of Bias
The Randomized Response Method
Ethical Considerations in Data Collection
The Nazi Doctor’s Trial and the Nuremberg Code
The National Research Act of 1974
The Declaration of Helsinki
The Federal Rules of Evidence
Junk Science
The Consequences of Daubert and the Data Quality Act (of 2001)
Some Concluding Remarks
Bibliography
Author Index
Subject Index