A Whistle-Stop Tour of Statistics: 1st Edition (Paperback) book cover

A Whistle-Stop Tour of Statistics

1st Edition

By Brian S. Everitt

Chapman and Hall/CRC

211 pages | 51 B/W Illus.

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pub: 2011-12-01
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Description

The book is intended as a quick source of reference and as an aide-memoir for students taking A-level, undergraduate or postgraduate statistics courses. It includes numerous examples, helping instructors on such courses by providing their students with small data sets with which to work.

Reviews

"I think that Everitt has been quite successful. All the standard topics, such as probability, estimation, hypothesis testing, analysis of variance, and regression, are discussed. The discussion is short, to the point, readable, and reliable. In addition, there are the more ‘advanced’ topics of logistic regression, survival analysis, longitudinal data analysis, and multivariate analysis, thus providing the reader with a short introduction to a wide array of the methods in the statistical arsenal without getting bogged down in detail. … a brief, but good, introduction to statistics. … excellent ‘refresher’ for those who have already experienced an introduction to statistics and want a slightly different approach or point of view."

—David Bellhouse, The American Statistician, November 2014

"For an MAA member, this book might serve as a small desktop encyclopedia of statistics … . 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."

—Robert W. Hayden, MAA Reviews, May 2012

Table of Contents

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

About the Author

Brian Everitt is Retired from King's College London, UK.

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis