A Whistle-Stop Tour of Statistics

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ISBN 9781439877487
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Features

  • Presents an accessible reference to the key concepts in probability and statistics
  • Introduces each concept through bitesize descriptions
  • Presents interesting real-world examples
  • Includes lots of diagrams and graphs to illustrate the topics

Summary

A Whistle-Stop Tour of Statistics introduces basic probability and statistics through bite-size coverage of key topics. A review aid and study guide for undergraduate students, it presents descriptions of key concepts from probability and statistics in self-contained sections.

Features

  • Presents an accessible reference to the key concepts in probability and statistics
  • Introduces each concept through bite-size descriptions and presents interesting real-world examples
  • Includes lots of diagrams and graphs to clarify and illustrate topics
  • Provides a concise summary of ten major areas of statistics including survival analysis and the analysis of longitudinal data

Written by Brian S, Everitt, the author of over 60 statistical texts, the book shows how statistics can be applied in the real world, with interesting examples and plenty of diagrams and graphs to illustrate concepts.

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

Author Bio(s)

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

Editorial 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