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Publisher:

Chapman & Hall/CRC

Publication Date:

2012

Number of Pages:

199

Format:

Paperback

Price:

39.95

ISBN:

9781439877487

Category:

Student Helps

[Reviewed by , on ]

Robert W. Hayden

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

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

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

Summary

Suggested Reading

Inference

Significance Tests, Type I and Type II Errors, Power and the

Power and Sample Size

Student’s

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

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

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