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Modern Statistics for the Social and Behavioral Sciences: A Practical Introduction

Publisher: 
Chapman & Hall/CRC
Number of Pages: 
840
Price: 
89.95
ISBN: 
9781439834565

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.

Date Received: 
Wednesday, August 10, 2011
Reviewable: 
Yes
Include In BLL Rating: 
No
Rand Wilcox
Publication Date: 
2011
Format: 
Hardcover
Category: 
Textbook
Robert W. Hayden
03/16/2012

INTRODUCTION
Samples versus Populations
Software
R Basics

NUMERICAL AND GRAPHICAL SUMMARIES OF DATA
Basic Summation Notation
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

PROBABILITY AND RELATED CONCEPTS
Basic Probability
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 AND CONFIDENCE INTERVALS
Random Sampling
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

HYPOTHESIS TESTING
The Basics of Hypothesis Testing
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

REGRESSION AND CORRELATION
The Least Squares Principle
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

BOOTSTRAP METHODS
Bootstrap-t Method
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

COMPARING TWO INDEPENDENT GROUPS
Student’s T Test
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 TWO DEPENDENT GROUPS
The Paired T Test
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

ONE-WAY ANOVA
Analysis of Variance for Independent Groups
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

TWO-WAY AND THREE-WAY DESIGNS
Basics of a Two-Way ANOVA Design
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 MORE THAN TWO DEPENDENT GROUPS
Comparing Means in a One-Way Design
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-Way ANOVA, Independent Groups

SOME MULTIVARIATE METHODS
Location, Scatter, and Detecting Outliers
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

ROBUST REGRESSION AND MEASURES OF ASSOCIATION
Robust Regression Estimators
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

BASICMETHODS FOR ANALYZING CATEGORICAL DATA
Goodness of Fit
A Test of Independence
Detecting Differences in the Marginal Probabilities6
Measures of Association
Logistic Regression
Exercises

ANSWERS TO SELECTED EXERCISES
TABLES
BASIC MATRIX ALGEBRA
REFERENCES
Index

Publish Book: 
Modify Date: 
Friday, March 16, 2012

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