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• About this Book
• Cover Page
• Title Page
• Copyright
• Brief Contents
• About the Authors
• Contents
• To Teachers: About This Book
• Preface
• To Students: What Is Statistics?
• Applications
• Data Table Index
• Beyond the Basics Index
• Part I Looking at Data
• Chapter 1 Looking at Data—Distributions
• Introduction
• 1.1 Data
• Key characteristics of a data set
• Section 1.1 Summary
• Section 1.1 Exercises
• 1.2 Displaying Distributions with Graphs
• Categorical variables: Bar graphs and pie charts
• Quantitative variables: Stemplots and histograms
• Histograms
• Examining distributions
• Dealing with outliers
• Time plots
• Section 1.2 Summary
• Section 1.2 Exercises
• 1.3 Describing Distributions with Numbers
• Measuring center: The mean
• Measuring center: The median
• Comparing the mean and the median
• Measuring spread: The quartiles
• The five-number summary and boxplots
• The 1.5 × IQR rule for suspected outliers
• Measuring spread: The standard deviation
• Properties of the standard deviation
• Choosing measures of center and spread
• Changing the unit of measurement
• Section 1.3 Summary
• Section 1.3 Exercises
• 1.4 Density Curves and Normal Distributions
• Density curves
• Measuring center and spread for density curves
• Normal distributions
• The 68–95–99.7 rule
• Standardizing observations
• Normal distribution calculations
• Using the standard Normal table
• Inverse Normal calculations
• Normal quantile plots
• Beyond the Basics: Density estimation
• Section 1.4 Summary
• Section 1.4 Exercises
• Chapter 1 Exercises
• Chapter 2 Looking at Data—Relationships
• Introduction
• 2.1 Relationships
• Examining relationships
• Section 2.1 Summary
• Section 2.1 Exercises
• 2.2 Scatterplots
• Interpreting scatterplots
• The log transformation
• Adding categorical variables to scatterplots
• Scatterplot smoothers
• Categorical explanatory variables
• Section 2.2 Summary
• Section 2.2 Exercises
• 2.3 Correlation
• The correlation r
• Properties of correlation
• Section 2.3 Summary
• Section 2.3 Exercises
• 2.4 Least-Squares Regression
• Fitting a line to data
• Prediction
• The least-squares regression line
• Facts about least-squares regression
• Correlation and regression
• Interpretation of r2
• Section 2.4 Summary
• Section 2.4 Exercises
• 2.5 Cautions about Correlation and Regression
• Extrapolation
• Residuals
• The distribution of the residuals
• Outliers and influential observations
• Beware of the lurking variable
• Beware of correlations based on averaged data
• Beware of restricted ranges
• Beyond the Basics: Data mining
• Section 2.5 Summary
• Section 2.5 Exercises
• 2.6 Data Analysis for Two-Way Tables
• The two-way table
• Joint distribution
• Marginal distributions
• Describing relations in two-way tables
• Conditional distributions
• Simpson’s paradox
• Section 2.6 Summary
• Section 2.6 Exercises
• 2.7 The Question of Causation
• Explaining association
• Establishing causation
• Section 2.7 Summary
• Section 2.7 Exercises
• Chapter 2 Exercises
• Chapter 3 Producing Data
• Introduction
• 3.1 Sources of Data
• Anecdotal data
• Available data
• Sample surveys and experiments
• Section 3.1 Summary
• Section 3.1 Exercises
• 3.2 Design of Experiments
• Comparative experiments
• Randomization
• Randomized comparative experiments
• How to randomize
• Randomization using software
• Randomization using random digits
• Cautions about experimentation
• Matched pairs designs
• Block designs
• Section 3.2 Summary
• Section 3.2 Exercises
• 3.3 Sampling Design
• Simple random samples
• How to select a simple random sample
• Stratified random samples
• Multistage random samples
• Cautions about sample surveys
• Beyond the Basics: Capture-recapture sampling
• Section 3.3 Summary
• Section 3.3 Exercises
• 3.4 Ethics
• Institutional review boards
• Informed consent
• Confidentiality
• Clinical trials
• Behavioral and social science experiments
• Section 3.4 Summary
• Section 3.4 Exercises
• Chapter 3 Exercises
• Part II Probability and Inference
• Chapter 4 Probability: The Study of Randomness
• Introduction
• 4.1 Randomness
• The language of probability
• Thinking about randomness
• The uses of probability
• Section 4.1 Summary
• Section 4.1 Exercises
• 4.2 Probability Models
• Sample spaces
• Probability rules
• Assigning probabilities: Finite number of outcomes
• Assigning probabilities: Equally likely outcomes
• Independence and the multiplication rule
• Applying the probability rules
• Section 4.2 Summary
• Section 4.2 Exercises
• 4.3 Random Variables
• Discrete random variables
• Continuous random variables
• Normal distributions as probability distributions
• Section 4.3 Summary
• Section 4.3 Exercises
• 4.4 Means and Variances of Random Variables
• The mean of a random variable
• Statistical estimation and the law of large numbers
• Thinking about the law of large numbers
• Beyond the Basics: More laws of large numbers
• Rules for means
• The variance of a random variable
• Rules for variances and standard deviations
• Section 4.4 Summary
• Section 4.4 Exercises
• 4.5 General Probability Rules
• General addition rules
• Conditional probability
• General multiplication rules
• Tree diagrams
• Bayes’s rule
• Independence again
• Section 4.5 Summary
• Section 4.5 Exercises
• Chapter 4 Exercises
• Chapter 5 Sampling Distributions
• Introduction
• 5.1 Toward Statistical Inference
• Sampling variability
• Sampling distributions
• Bias and variability
• Sampling from large populations
• Why randomize?
• Section 5.1 Summary
• Section 5.1 Exercises
• 5.2 The Sampling Distribution of a Sample Mean
• The mean and standard deviation of x
• The central limit theorem
• A few more facts related to the sampling distribution of x
• Beyond the Basics: Weibull distributions
• Section 5.2 Summary
• Section 5.2 Exercises
• 5.3 Sampling Distributions for Counts and Proportions
• The binomial distributions for sample counts
• Binomial distributions in statistical sampling
• Finding binomial probabilities
• Binomial mean and standard deviation
• Sample proportions
• Normal approximation for counts and proportions
• The continuity correction
• Binomial formula
• The Poisson distributions for sample counts
• Section 5.3 Summary
• Section 5.3 Exercises
• Chapter 5 Exercises
• Chapter 6 Introduction to Inference
• Introduction
• Overview of inference
• 6.1 Estimating with Confidence
• Statistical confidence
• Confidence intervals
• Confidence interval for a population mean
• How confidence intervals behave
• Choosing the sample size
• Some cautions
• Section 6.1 Summary
• Section 6.1 Exercises
• 6.2 Tests of Significance
• The reasoning of significance tests
• Stating hypotheses
• Test statistics
• P-values
• Statistical significance
• Tests for a population mean
• Two-sided significance tests and confidence intervals
• The P-value versus a statement of significance
• Section 6.2 Summary
• Section 6.2 Exercises
• 6.3 Use and Abuse of Tests
• Choosing a level of significance
• What statistical significance does not mean
• Don’t ignore lack of significance
• Statistical inference is not valid for all sets of data
• Beware of searching for significance
• Section 6.3 Summary
• Section 6.3 Exercises
• 6.4 Inference as a Decision
• Two types of error
• Error probabilities
• The common practice of testing hypotheses
• Section 6.4 Summary
• Section 6.4 Exercises
• Chapter 6 Exercises
• Chapter 7 Inference for Means
• Introduction
• 7.1 Inference for the Mean of a Population
• The t distributions
• One-sample t confidence interval
• The one-sample t test
• Using software
• Matched pairs t procedures
• Robustness of the t procedures
• Inference for non-normal populations
• Beyond the Basics: The bootstrap
• Section 7.1 Summary
• Section 7.1 Exercises
• 7.2 Comparing Two Means
• The two-sample z statistic
• The two-sample t procedures
• The two-sample t confidence interval
• The two-sample t significance test
• Robustness of the two-sample procedures
• Inference for small samples
• The pooled two-sample t procedures
• Section 7.2 Summary
• Section 7.2 Exercises
• 7.3 Sample Size Calculations
• Sample size for confidence intervals
• Power of a significance test
• Section 7.3 Summary
• Section 7.3 Exercises
• Chapter 7 Exercises
• Chapter 8 Inference for Proportions
• Introduction
• 8.1 Inference for a Single Proportion
• Large-sample confidence interval for a single proportion
• Beyond the Basics: Plus four confidence interval for a single proportion
• Significance test for a single proportion
• Choosing a sample size for a confidence interval
• Choosing a sample size for a significance test
• Section 8.1 Summary
• Section 8.1 Exercises
• 8.2 Comparing Two Proportions
• Large-sample confidence interval for a difference in proportions
• Beyond the Basics: Plus four confidence interval for a difference in proportions
• Significance test for a difference in proportions
• Choosing a sample size for two sample proportions
• Beyond the Basics: Relative risk
• Section 8.2 Summary
• Section 8.2 Exercises
• Chapter 8 Exercises
• Part III Topics in Inference
• Chapter 9 Inference for Categorical Data
• Introduction
• 9.1 Sources of Data
• The hypothesis: No association
• Expected cell counts
• The chi-square test
• Computations
• Computing conditional distributions
• The chi-square test and the z test
• Beyond the Basics: Meta-analysis
• Section 9.1 Summary
• Section 9.1 Exercises
• 9.2 Goodness of Fit
• Section 9.2 Summary
• Section 9.2 Exercises
• Chapter 9 Exercises
• Chapter 10 Inference for Regression
• Introduction
• 10.1 Simple Linear Regression
• Statistical model for linear regression
• Preliminary data analysis and inference considerations
• Revisiting the simple linear regression model
• Estimating the regression parameters
• Estimating the regression parameters
• Confidence intervals and significance tests
• Confidence intervals for mean response
• Prediction intervals
• Transforming variables
• Beyond the Basics: Nonlinear regression
• Section 10.1 Summary
• Section 10.1 Exercises
• 10.2 More Detail about Simple Linear Regression
• Analysis of variance for regression
• The ANOVA F test
• Calculations for regression inference
• Inference for correlation
• Section 10.2 Summary
• Section 10.2 Exercises
• Chapter 10 Exercises
• Chapter 11 Multiple Regression
• Introduction
• 11.1 Inference for Multiple Regression
• Population multiple regression equation
• Data for multiple regression
• Multiple linear regression model
• Estimation of the multiple regression parameters
• Confidence intervals and significance tests for regression coefficients
• ANOVA table for multiple regression
• Squared multiple correlation R2
• Section 11.1 Summary
• Section 11.1 Exercises
• 11.2 A Case Study
• Preliminary analysis
• Relationships between pairs of variables
• Fitting a multiple regression model
• Interpretation of results
• Examining the residuals
• Refining the model
• Considering other sets of explanatory variables
• Test for a collection of regression coefficients
• Beyond the Basics: Regression trees
• Section 11.2 Summary
• Section 11.2 Exercises
• Chapter 11 Exercises
• Chapter 12 One-Way Analysis of Variance
• Introduction
• 12.1 Inference for One-Way Analysis of Variance
• The one-way ANOVA setting
• Comparing means
• The two-sample t statistic
• An overview of ANOVA
• The ANOVA model
• Estimates of population parameters
• Testing hypotheses in one-way ANOVA
• The ANOVA table
• The F test
• Software
• Beyond the Basics: Testing the equality of spread
• Section 12.1 Summary
• Section 12.1 Exercises
• 12.2 Comparing the Means
• Contrasts
• Multiple comparisons
• Simultaneous confidence intervals
• Power of the one-way ANOVA F test
• Section 12.2 Summary
• Section 12.2 Exercises
• Chapter 12 Exercises
• Chapter 13 Two-Way Analysis of Variance
• Introduction
• 13.1 The Two-Way ANOVA Modell
• Advantages of two-way ANOVA
• The two-way ANOVA model
• Main effects and interactions
• Section 13.1 Summary
• Section 13.1 Exercises
• 13.2 Inference for Two-Way ANOVA
• The two-way ANOVA table
• Carrying out a two-way ANOVA
• Section 13.2 Summary
• Section 13.2 Exercises
• Chapter 13 Exercises
• Companion Chapters
• Chapter 14 Logistic Regression
• Introduction
• 14.1 The Logistic Regression Model
• Binomial distributions and odds
• Odds for two groups
• Model for logistic regression
• Fitting and interpreting the logistic regression model
• Section 14.1 Summary
• Section 14.1 Exercises
• 14.2 A Case Study
• Confidence intervals and significance tests
• Inference for multiple logistic regression
• Section 14.2 Summary
• Section 14.2 Exercises
• Chapter 14 Exercises
• Notes and Data Sources
• Chapter 15 Nonparametric Rank Tests
• Introduction
• 15.1 Inference for One-Way Analysis of Variance
• The rank transformation
• The Wilcoxon rank sum test
• The Normal approximation
• What hypotheses does Wilcoxon test?
• Ties
• Nonparametric rank and t procedures
• Section 15.1 Summary
• Section 15.1 Exercises
• 15.2 The Wilcoxon Signed Rank Test
• The Normal approximation
• Ties
• Testing a hypothesis about the median of a distribution
• Section 15.2 Summary
• Section 15.2 Exercises
• 15.3 The Kruskal-Wallis Test*
• Hypotheses and assumptions
• The Kruskal-Wallis test
• Section 15.3 Summary
• Section 15.3 Exercises
• Chapter 15 Exercises
• Notes and Data Sources
• Chapter 16 Bootstrap Methods and Permutation Tests
• Introduction
• Software
• 16.1 The Bootstrap Idea
• The big idea: Resampling and the bootstrap distribution
• Thinking about the bootstrap idea
• Using software
• Section 16.1 Summary
• Section 16.1 Exercises
• 16.2 First Steps in Using the Bootstrap
• Bootstrap t confidence intervals
• Bootstrapping to compare two groups
• Beyond the Basics: The bootstrap for a scatterplot smoother
• Section 16.2 Summary
• Section 16.2 Exercises
• 16.3 How Accurate Is a Bootstrap Distribution?
• Bootstrapping small samples
• Bootstrapping a sample median
• Section 16.3 Summary
• Section 16.3 Exercises
• 16.4 Bootstrap Confidence Intervals
• Bootstrap percentile confidence intervals
• A more accurate bootstrap confidence interval: BCa
• Confidence intervals for the correlation
• Section 16.4 Summary
• Section 16.4 Exercises
• 16.5 Significance Testing Using Permutation Tests
• Using software
• Permutation tests in practice
• Permutation tests in other settings
• Section 16.5 Summary
• Section 16.5 Exercises
• Chapter 16 Exercises
• Notes and Data Sources
• Chapter 17 Statistics for Quality: Control and Capability
• Introduction
• 17.1 Processes and Statistical Process Control
• Describing processes
• Statistical process control
• x charts for process monitoring
• s charts for process monitoring
• Section 17.1 Summary
• Section 17.1 Exercises
• 17.2 Using Control Charts
• x and R charts
• Additional out-of-control rules
• Setting up control charts
• Comments on statistical control
• Don’t confuse control with capability!
• Section 17.2 Summary
• Section 17.2 Exercises
• 17.3 Process Capability Indexes
• The capability indexes Cp and Cpk
• Cautions about capability indexes
• Section 17.3 Summary
• Section 17.3 Exercises
• 17.4 Control Charts for Sample Proportions
• Control limits for p charts
• Section 17.4 Summary
• Section 17.4 Exercises
• Chapter 17 Exercises
• Notes and Data Sources
• Tables
• Answers to Odd-Numbered Exercises
• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11
• Chapter 12
• Chapter 13
• Chapter 14
• Chapter 15
• Chapter 16
• Chapter 17
• Notes and Data Sources
• Index
• Formulas and Key Ideas
• Back Cover