A Whistle-Stop Tour of Statistics

Brian S. Everitt

Publisher:

Chapman & Hall/CRC

Publication Date:

2012

Number of Pages:

199

Format:

Paperback

Price:

39.95

ISBN:

9781439877487

Category:

Student Helps

MAA Review
Table of Contents

[Reviewed by

Robert W. Hayden

, on

05/16/2012

]

The jacket and publisher’s blurb suggest this text might be suitable for students in an introductory statistics course, or even a curious layperson. In fact the level is much higher. Calculus is assumed through defining a function of t as an integral with respect to x in which t is a parameter of the integrand. The Gamma function is assumed to be familiar, as is practical linear algebra through eigenvectors.

The general plan for each chapter is to present the topic at a glossary level and then give an example problem with answer. There is some attention to assumptions but brevity precludes much practical advice. The computational examples suggest an exam on the horizon — a researcher might want more on the uses and weaknesses of the technique than the computations. The level of prior statistical training assumed is unclear, as histograms are explained but we soon get to moment generating functions. Readers are often referred to texts in mathematical statistics for details.

It is a bit hard to place this work in the context of higher education in the United States. The work seems more geared to the British educational system. We might conceptualize this as a study guide for an imaginary examination that all undergraduate statistics majors have to take — sort of a GRE for statistics. It could remind an examinee of material studied some time ago, or alert them to topics they may not have studied at all.

For an MAA member, this book might serve as a small desktop encyclopedia of statistics covering one person’s view of the core of an undergraduate major. For someone with the mathematical prerequisites, it can answer questions such as “What is logistic regression?” with a bit more detail than a dictionary of statistics. (Such a dictionary is among the author’s other publications.) This certainly seems more a reference work than something to be read from cover to cover. This is not a bad book but it is not a book with a clear audience.

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.

Some Basics and Describing Data
Population, Samples and Variables
Types of Variables
Tabulating and Graphing data: Frequency Distributions, Histograms and Dotplots
Summarizing Data: Mean, Variance and Range
Comparing Data from Different Groups Using Summary Statistics and Boxplots
Relationship between Two Variables, Scatterplots and Correlation Coefficients
Types of Studies
Summary
Suggested Reading

Probability
Probability
Odds and Odds Ratios
Permutations and Combinations
Conditional Probabilities and Bayes’ Theorem
Random Variables, Probability Distributions and Probability Density Functions
Expected Value and Moments
Moment-Generating Function
Summary
Suggested Reading

Estimation
Point Estimation
Sampling Distribution of the Mean and the Central Limit Theorem
Estimation by the Method of Moments
Estimation by Maximum Likelihood
Choosing Between Estimators
Sampling Distributions: Student’s t, Chi-Square and Fisher’s F
Interval Estimation, Confidence Intervals
Summary
Suggested Reading

Inference
Inference and Hypotheses
Significance Tests, Type I and Type II Errors, Power and the z-Test
Power and Sample Size
Student’s t-Tests
The Chi-Square Goodness-of-Fit Test
Nonparametric Tests
Testing the Population Correlation Coefficient
Tests on Categorical Variables
The Bootstrap
Significance Tests and Confidence Intervals
Frequentist and Bayesian Inference
Summary
Suggested Reading

Analysis of Variance Models
One-Way Analysis of Variance
Factorial Analysis of Variance
Multiple Comparisons, a priori and post hoc Comparisons
Nonparametric Analysis of Variance
Summary
Suggested Reading

Linear Regression Models
Simple Linear Regression
Multiple Linear Regression
Selecting a Parsimonious Model
Regression diagnostics
Analysis of variance as regression
Summary
Suggested reading

Logistic Regression and the Generalized Linear Model
Odds and odds ratios
Logistic regression
Generalized linear model
Variance function and overdispersion
Diagnostics for GLMs
Summary
Suggested reading

Survival Analysis
Survival data and censored observations
Survivor function, log-rank test and hazard function
Proportional hazards and Cox regression
Diagnostics for Cox regression
Summary
Suggested reading

Longitudinal Data and Their Analysis
Longitudinal data and some graphics
Summary measure analysis
Linear mixed effects models
Missing data in longitudinal studies
Summary
Suggested Reading

Multivariate Data and Their Analysis
Multivariate data
Mean vectors, variances, covariance and correlation matrices
Two multivariate distributions: The multinomial distribution and the multivariate normal distribution
The Wishart distribution
Principal Components Analysis
Summary
Suggested reading