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Publisher:

Chapman & Hall/CRC

Publication Date:

2011

Number of Pages:

840

Format:

Hardcover

Price:

89.95

ISBN:

9781439834565

Category:

Textbook

[Reviewed by , on ]

Robert W. Hayden

03/16/2012

This is an interesting and valuable book, though perhaps not for the audience suggested by the title. Let’s first describe what makes it interesting and valuable. Topical coverage is for a year-long introductory course similar to that often found in business departments but with more on ANOVA and its generalizations, and nothing on time series or quality control. What makes the book unusual is that, for most of the techniques described, the author provides a critique of the traditional methods and offers a multitude of alternatives. He also provides copious references to the literature and programs for the R statistical programming language with which to carry out both the traditional and alternative methods. In the limited areas where I have followed this literature, the author cites the right papers and makes defensible recommendations, if not always the same ones I would make.

Those of us teaching college-level mathematics continually struggle with getting students to learn to check the truth of the hypotheses of a theorem before applying said theorem. For that reason, we should be sympathetic to the notion of applying the same policy in statistics. Wilcox reports on the many things that can go wrong when the assumptions of statistical inference procedures are not met. By gathering a mass of results on that topic into a single volume with references, alternative procedures and supporting software, the author has provided a valuable service to those interested is these issues, which should probably include anyone teaching the techniques covered in this book. The writing is clear but terse, as suits mathematicians. Despite the title, example applications come from a variety of fields. As a result, the material on topics included in most one-semester courses is largely discipline-independent. That is true for other parts of the book as well, th ough there we have more variability among disciplines in what topics need covering.

Wilcox is perhaps an outlier in his extreme skepticism of traditional methods, but that is welcome in contrast with the starry-eyed optimism that pervades introductory textbooks. The methods he suggests are not the norm today among neither statisticians nor users of statistics, though the vast number of papers Wilcox cites indicates awareness of problems. It is common among statisticians to try both traditional and alternative methods and to feel safe if they agree and counsel caution if they do not. I see no reason to question Wilcox in technical issues. Any disagreement is over whether the failings of traditional methods suggests they should be carefully used or rarely used. Mathematicians will also be comforted to know that the author has a B.A. and M.A. in mathematics. Any disagreement is likely to be over the implications of the research rather than the accuracy with which the author reports it.

Now let’s consider this book as a textbooks for beginners — in the case of the author’s classes, psychology graduate students who may not have taken an undergraduate statistics course. That audience may well be overwhelmed by the vast number of procedures described. Imagine the usual topics increased by nearly an order of magnitude as each technique comes with 6-12 alternatives. Very often there is not a clear choice among them, and though the author counsels judging each situation on its own merits, he does not offer much advice on how to do that. Often the best technique depends on population characteristics that are hard to judge from a sample. Too often the existing research is inconclusive. Experts are comfortable with this, but beginners need some idea of current best practice while the experts hash out what current best practice will be for the next generation.

Like too many older books, this one concentrates almost all its attention on selecting and implementing an inference technique. I think most statisticians would suggest that the inference technique be chosen as part of the study design, and that choices such as how to measure the effect of interest be made compatible with the inference procedure — or the inference procedure compatible with the desired measurement. Wilcox pretty much ignores anything that happens before the data arrive at the computing center. Although he pays lip service to random sampling as an assumption for most of the techniques, he gives no guidance on how to take a random sample, and ignores how experiments or observational studies that do not involve random sampling are to be analyzed. The datasets are always assumed without comment to be random samples though that often seems implausible. Unfortunately, such design issues create problems that dwarf those caused by choice of hypothesis test, and students need to know about this. (See Simmons,Joseph P., Leif D. Nelson and Uri Simonsohn, “False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant.” *Psychological Science*, October 2011.)

My copy had hard covers, but the pages appeared to be glued in like a paperback rather than sewn, perhaps not a good idea in a book of over 800 pages. It is hard to be sure about that, but the book did arrive starting to split out a few pages in from the end, and almost immediately began to split out a few pages in from the front. We can hope this was just one bad sample.

Recommended to those with a solid background in traditional statistical inference who want a highly competent and comprehensive statement of the cases against traditional statistical inference techniques. Not recommended as a textbook or book for beginners.

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.

**INTRODUCTION**Samples versus Populations

Software

R Basics

Measures of Location

Measures of Variation or Scale

Detecting Outliers

Histograms

Kernel Density Estimators

Stem-and-Leaf Displays

Skewness

Choosing a Measure of Location

Covariance and Pearson’s Correlation

Exercises

Expected Values

Conditional Probability and Independence

Population Variance

The Binomial Probability Function

Continuous Variables and the Normal Curve

Understanding the Effects of Non-normality

Pearson’s Correlation and the Population Covariance

Some Rules About Expected Values

Chi-Squared Distributions

Exercises

Sampling Distributions

A Confidence Interval for the Population Mean

Judging Location Estimators Based on Their Sampling Distribution

An Approach to Non-normality: The Central Limit Theorem

Student’s t and Non-normality

Confidence Intervals for the Trimmed Mean

Transforming Data

Confidence Interval for the Population Median

A Remark About MOM and M-Estimators

Confidence Intervals for the Probability of Success

Exercises

Power and Type II Errors

Testing Hypotheses about the Mean When σ Is Not Known

Controlling Power and Determining n

Practical Problems with Student’s T Test

Hypothesis Testing Based on a Trimmed Mean

Testing Hypotheses About the Population Median

Making Decisions About Which Measure of Location To Use

Exercises

Confidence Intervals and Hypothesis Testing

Standardized Regression

Practical Concerns About Least Squares Regression and How They Might Be Addressed

Pearson’s Correlation and the Coefficient of Determination

Testing H0: ρ = 0

A Regression Method for Estimating the Median of Y and Other Quantiles

Detecting Heteroscedasticity

Concluding Remarks

Exercises

The Percentile Bootstrap Method

Inferences About Robust Measures of Location

Estimating PowerWhen Testing Hypotheses About a Trimmed Mean

A Bootstrap Estimate of Standard Errors

Inferences about Pearson’s Correlation: Dealing with Heteroscedasticity

Bootstrap Methods for Least Squares Regression

Detecting Associations Even When There Is Curvature

Quantile Regression

Regression: Which Predictors are Best?

Comparing Correlations

Empirical Likelihood

Exercises

Relative Merits of Student’s T Test

Welch’s Heteroscedastic Method for Means

Methods for Comparing Medians and Trimmed Means

Percentile Bootstrap Methods for Comparing Measures of Location

Bootstrap-t Methods for Comparing Measures of Location

Permutation Tests

Rank-Based and Nonparametric Methods

Graphical Methods for Comparing Groups

Comparing Measures of Scale

Methods for Comparing Measures of Variation

Measuring Effect Size

Comparing Correlations and Regression Slopes

Comparing Two Binomials

Making Decisions About Which Method To Use

Exercises

Comparing Robust Measures of Location

Handling Missing Values

A Different Perspective When Using Robust Measures of Location

R Functions loc2dif and l2drmci

The Sign Test

Wilcoxon Signed Rank Test

Comparing Variances

Comparing Robust Measures of Scale

Comparing All Quantiles

Plots for Dependent Groups

Exercises

Dealing with Unequal Variances

Judging Sample Sizes and Controlling Power When Data Are Available

Trimmed Means

Bootstrap Methods

Random Effects Model

Rank-Based Methods

R Function kruskal.test

Exercises

Testing Hypotheses About Main Effects and Interactions

Heteroscedastic Methods for Trimmed Means, Including Means

Bootstrap Methods

Testing Hypotheses Based on Medians

A Rank-Based Method For a Two-Way Design

Three-Way ANOVA

Exercises

Comparing Trimmed Means When Dealing with a One-Way Design

Percentile Bootstrap Methods for a One-Way Design

Rank-Based Methods for a One-Way Design

Comments on Which Method to Use

Between-by-Within Designs

Within-by-Within Design

Three-Way Designs

Exercises

MULTIPLE COMPARISONS

One-Sample Hypothesis Testing

Two-Sample Case

MANOVA

A Multivariate Extension of the Wilcoxon-Mann-Whitney Test

Rank-Based Multivariate Methods

Multivariate Regression

Principal Components

Exercises

Comments on Choosing a Regression Estimator

Testing Hypotheses When Using Robust Regression Estimators

Dealing with Curvature: Smoothers

Some Robust Correlations and Tests of Independence

Measuring the Strength of an Association Based on a Robust Fit

Comparing the Slopes of Two Independent Groups

Tests for Linearity

Identifying the Best Predictors

Detecting Interactions and Moderator Analysis

ANCOVA

Exercises

A Test of Independence

Detecting Differences in the Marginal Probabilities6

Measures of Association

Logistic Regression

Exercises

TABLES

BASIC MATRIX ALGEBRA

REFERENCES

Index

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