This book is probably not what you're expecting since most O'Reilly Nutshell books assume you already have thorough knowledge of a subject and you are just looking for "cues" in case you forget something. This book is more of a "Head First" type of book in that it assumes no prior knowledge of the subject. Since O'Reilly is planning a Head First book on Statistics, I'd like to see the difference between this book and that one.
This book focuses on using and understanding statistics in a research or applications context, not as a discrete set of mathematical techniques but as part of the process of reasoning with numbers. It integrates the discussion of issues such as measurement and data management into an introductory statistics text. It serves as an introductory statistics book that is compact, inexpensive, and easy for beginners to understand without being condescending or overly simplistic.
The audience for this book includes students taking introductory statistics classes in high schools, colleges, and universities, professionals who need to learn statistics as part of their current jobs, and finally people who are interested in learning about statistics out of intellectual curiosity.
The book focuses on statistical reasoning. In particular, the book focuses on thinking about data, and using statistics to aid in that process.
The book is organized into four parts: introductory material (Chapters 1-6) that lays the necessary foundation for the chapters that follow; elementary inferential statistical techniques (Chapters 7-11); more advanced techniques (Chapters 12-16); and specialized techniques (Chapters 17-19). The following is the detailed table of contents:
Chapter 1, Basic Concepts of Measurement - Discusses foundational issues for statistics, including levels of measurement, operationalization, proxy measurement, random and systematic error, measures of agreement, and types of bias. Statistics demonstrated include percent agreement and kappa.
Chapter 2, Probability - Introduces the basic vocabulary and laws of probability, including trials, events, independence, mutual exclusivity, the addition and multiplication laws, and conditional probability. Procedures demonstrated include calculation of basic probabilities, permutations and combinations, and Bayes's theorem.
Chapter 3, Data Management - Discusses practical issues in data management, including procedures to troubleshoot an existing file, methods for storing data electronically, data types, and missing data.
Chapter 4, Descriptive Statistics and Graphics - Explains the differences between descriptive and inferential statistics and between populations and samples, and introduces common measures of central tendency and variability and frequently used graphs and charts. Statistics demonstrated include mean, median, mode, range, interquartile range, variance, and standard deviation. Graphical methods demonstrated include frequency tables, bar charts, pie charts, Pareto charts, stem and leaf plots, boxplots, histograms, scatterplots, and line graphs.
Chapter 5, Research Design - Discusses observational and experimental studies, common elements of good research designs, the steps involved in data collection, types of validity, and methods to limit or eliminate the influence of bias.
Chapter 6, Critiquing Statistics Presented by Others - Offers guidelines for reviewing the use of statistics, including a checklist of questions to ask of any statistical presentation and examples of when legitimate statistical procedures may be manipulated to appear to support questionable conclusions.
Chapter 7, Inferential Statistics - Introduces the basic concepts of inferential statistics, including probability distributions, independent and dependent variables and the different names under which they are known, common sampling designs, the central limit theorem, hypothesis testing, Type I and Type II error, confidence intervals and p-values, and data transformation. Procedures demonstrated include converting raw scores to Z-scores, calculation of binomial probabilities, and the square-root and log data transformations.
Chapter 8, The t-Test - Discusses the t-distribution, the different types of t-tests, and the influence of effect size on power in t-tests. Statistics demonstrated include the one-sample t-test, the two independent samples t-test, the two repeated measures t-test, and the unequal variance t-test.
Chapter 9, The Correlation Coefficient - Introduces the concept of association with graphics displaying different strengths of association between two variables, and discusses common statistics used to measure association. Statistics demonstrated include Pearson's product-moment correlation, the t-test for statistical significance of Pearson's correlation, the coefficient of determination, Spearman's rank-order coefficient, the point-biserial coefficient, and phi.
Chapter 10, Categorical Data - Reviews the concepts of categorical and interval data, including the Likert scale, and introduces the R x C table. Statistics demonstrated include the chi-squared tests for independence, equality of proportions, and goodness of fit, Fisher's exact test, McNemar's test, gamma, Kendall's tau-a, tau-b, and tau-c, and Somers's d.
Chapter 11, Nonparametric Statistics - Discusses when to use nonparametric rather than parametric statistics, and presents nonparametric statistics for between-subjects and within-subjects designs. Statistics demonstrated include the Wilcoxon Rank Sum and Mann-Whitney U tests, the median test, the Kruskal-Wallis H test, the Wilcoxon matched pairs signed rank test, and the Friedman test.
Chapter 12, Introduction to the General Linear Model - Introduces linear regression and ANOVA through the concept of the General Linear Model, and discusses assumptions made when using these designs. Statistical procedures demonstrated include simple (bivariate) regression, one-way ANOVA, and post-hoc testing.
Chapter 13, Extensions of Analysis of Variance - Discusses more complex ANOVA designs. Statistical procedures demonstrated include two-way and three-way ANOVA, MANOVA, ANCOVA, repeated measures ANOVA, and mixed designs.
Chapter 14, Multiple Linear Regression - Extends the ideas introduced in Chapter 12 to models with multiple predictors. Topics covered include relationships among predictor variables, standardized coefficients, dummy variables, methods of model building, and violations of assumptions of linear regression, including nonlinearity, autocorrelation, and heteroscedasticity.
Chapter 15, Other Types of Regression - Extends the technique of regression to data with binary outcomes and nonlinear models, and discusses the problem of overfitting a model.
Chapter 16, Other Statistical Techniques - Demonstrates several advanced statistical procedures, including factor analysis, cluster analysis, discriminant function analysis, and multidimensional scaling, including discussion of the types of problems for which each technique may be useful.
Chapter 17, Business and Quality Improvement Statistics - Demonstrates statistical procedures commonly used in business and quality improvement contexts. Analytical and statistical procedures covered include construction and use of simple and composite indexes, time series, the minimax, maximax, and maximin decision criteria, decision making under risk, decision trees, and control charts.
Chapter 18, Medical and Epidemiological Statistics - Introduces concepts and demonstrates statistical procedures particularly relevant to medicine and epidemiology. Concepts and statistics covered include the definition and use of ratios, proportions, and rates, measures of prevalence and incidence, crude and standardized rates, direct and indirect standardization, measures of risk, confounding, the simple and Mantel-Haenszel odds ratio, and precision, power, and sample size calculations.
Chapter 19, Educational and Psychological Statistics - Introduces concepts and statistical procedures commonly used in the fields of education and psychology. Concepts and procedures demonstrated include percentiles, standardized scores, methods of test construction, the true score model of classical test theory, reliability of a composite test, measures of internal consistency including coefficient alpha, and procedures for item analysis. An overview of item response theory is also provided.
Two appendixes cover topics that are a necessary background to the material covered in the main text, and a third provides references to supplemental reading.