Introduction to the Practice of Statistics, Ninth Edition by Moore, David S. -- Read -- Imperial Library of Trantor

Index

Cover Title Copyright Brief Contents Contents To Teachers: About This Book To Students: What Is Statistics? About the Authors 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 Data analysis in action: Don’t hang up on me 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 Mean versus 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 Least-squares regression Interpreting the regression line Facts about least-squares regression Correlation and regression Another view of r2

Section 2.4 Summary Section 2.4 Exercises 2.5 Cautions about Correlation and Regression

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 x̅ The central limit theorem A few more facts

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

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 Power and Inference as a Decision

Power Increasing the power Inference as 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 The one-sample t confidence interval The one-sample t test Matched pairs t procedures Robustness of the t procedures

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 Software approximation for the degrees of freedom The pooled two-sample t procedures

Section 7.2 Summary Section 7.2 Exercises 7.3 Additional Topics on Inference

Choosing the sample size Inference for non-Normal populations

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: The 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: The 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 Inference for Two-Way Tables

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 Estimating the regression parameters Checking model assumptions 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 Regression on high school grades Interpretation of results Examining the residuals Refining the model Regression on SAT scores Regression using all variables Test for a collection of regression coefficients

Beyond the Basics: Multiple logistic regression 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

Data for one-way ANOVA 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 Power

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 Model

Advantages of two-way ANOVA The two-way ANOVA model Main effects and interactions

13.2 Inference for Two-Way ANOVA

The ANOVA table for two-way ANOVA

Chapter 13 Summary Chapter 13 Exercises

Tables Answers to Odd-Numbered Exercises Notes and Data Sources Index

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