Introductory Statistics Exploring the World Through Data, 3rd edition By Robert Gould, Colleen Ryan [PDF] [eBook]

Introductory Statistics: Exploring the World Through Data Contents Preface About This Book What’s New in the Third Edition Approach Coverage Organization Features Pearson MyLab MyLab Statistics Online Course fo ...

Introductory Statistics: Exploring the World Through Data Contents Preface About This Book What’s New in the Third Edition Approach Coverage Organization Features Pearson MyLab MyLab Statistics Online Course for Introductory Statistics: Exploring the World Through Data, 3e (Access Code Required) Resources for Success Instructor Resources Index of Applications Biology Business and Economics Crime and Corrections Education Employment Entertainment Environment Finance Food and Drink Games General Interest Health Law Politics Psychology Social Issues Sports Surveys and Opinion Polls Technology Transportation Chapter 1 Introduction to Data 1.1 What Are Data? What Is Data Analysis? 1.2 Classifying and Storing Data Two Types of Variables Coding Categorical Data with Numbers Storing Your Data 1.3 Investigating Data 1.4 Organizing Categorical Data 1.5 Collecting Data to Understand Causality Anecdotes Observational Studies Controlled Experiments Sample Size Random Assignment Blinding Placebos Extending the Results Statistics in the News Chapter Review Key Terms Learning Objectives Summary Sources Section Exercises Section 1.2 Section 1.3 Section 1.4 Section 1.5 Chapter Review Exercises Guided Exercises Chapter 2 Picturing Variation with Graphs 2.1 Visualizing Variation in Numerical Data Dotplots Histograms Relative Frequency Histograms Stemplots 2.2 Summarizing Important Features of a Numerical Distribution Shape Symmetric or Skewed? How Many Mounds? Do Extreme Values Occur? Center Why Not the Mode? Variability Describing Distributions 2.3 Visualizing Variation in Categorical Variables Bar Charts Bar Charts versus Histograms Pie Charts 2.4 Summarizing Categorical Distributions The Mode Variability Describing Distributions of Categorical Variables 2.5 Interpreting Graphs Misleading Graphs The Future of Statistical Graphics Chapter Review Key Terms Learning Objectives Summary Sources Section Exercises Sections 2.1 and 2.2 Sections 2.3 and 2.4 Section 2.5 Chapter Review Exercises Guided Exercises Chapter 3 Numerical Summaries of Center and Variation 3.1 Summaries for Symmetric Distributions The Center as Balancing Point: The Mean Visualizing the Mean The Mean in Context Calculating the Mean for Small Data Sets Calculating the Mean for Larger Data Sets Measuring Variation with the Standard Deviation Visualizing the Standard Deviation The Standard Deviation in Context Calculating the Standard Deviation Variance, a Close Relative of the Standard Deviation 3.2 What’s Unusual? The Empirical Rule and z-Scores The Empirical Rule z-Scores: Measuring Distance from Average Visualizing z-Scores Using z-Scores in Context Calculating the z-Score 3.3 Summaries for Skewed Distributions The Center as the Middle: The Median Visualizing the Median The Median in Context Calculating the Median Measuring Variability with the Interquartile Range Visualizing the IQR The Interquartile Range in Context Calculating the Interquartile Range Finding the Range, Another Measure of Variability 3.4 Comparing Measures of Center Look at the Shape First The Effect of Outliers Many Modes: Summarizing Center and Spread Comparing Two Groups with Different-Shaped Distributions 3.5 Using Boxplots for Displaying Summaries Investigating Potential Outliers Horizontal or Vertical? Using Boxplots to Compare Distributions Things to Watch for with Boxplots Finding the Five-Number Summary Numerical Summaries and the Data Cycle Chapter Review Key Terms Learning Objectives Summary Formulas Sources Section Exercises Section 3.1 Section 3.2 Section 3.3 Section 3.4 Section 3.5 Chapter Review Exercises Guided Exercises Questions Question Chapter 4 Regression Analysis: Exploring Associations between Variables 4.1 Visualizing Variability with a Scatterplot Recognizing Trend Seeing Strength of Association Identifying Shape Writing Clear Descriptions of Associations Asking Statistical Questions About Regression 4.2 Measuring Strength of Association with Correlation Visualizing the Correlation Coefficient The Correlation Coefficient in Context More Context: Correlation Does Not Mean Causation! Finding the Correlation Coefficient Understanding the Correlation Coefficient 4.3 Modeling Linear Trends The Regression Line Review: Equation of a Line Visualizing the Regression Line Regression in Context Finding the Regression Line Interpreting the Regression Line Choosing x and y: Order Matters The Regression Line Is a Line of Averages Interpreting the Slope Interpreting the Intercept 4.4 Evaluating the Linear Model Pitfalls to Avoid Don’t Fit Linear Models to Nonlinear Associations Correlation Is Not Causation Beware of Outliers Regressions of Aggregate Data Don’t Extrapolate! The Origin of the Word Regression (Regression toward the Mean) The Coefficient of Determination, r2, Measures ­Goodness of Fit Chapter Review Key Terms Learning Objectives Summary Sources Section Exercises Section 4.1 Section 4.2 Section 4.3 Section 4.4 Chapter Review Exercises Guided Exercises Chapter 5 Modeling Variation with Probability 5.1 What Is Randomness? Theoretical, Empirical, and Simulation-Based Probabilities 5.2 Finding Theoretical Probabilities Facts about Theoretical Probabilities Finding Theoretical Probabilities with Equally Likely Outcomes Combining Events with “AND” and “OR” Using “OR” to Combine Events Mutually Exclusive Events 5.3 Associations in Categorical Variables Conditional Probabilities “Given That” versus “AND” Finding Conditional Probabilities Flipping the Condition Independent and Dependent Events Intuition about Independence Sequences of Independent and Associated Events Independent Events Watch Out for Incorrect Assumptions of Independence Associated Events with “AND” 5.4 Finding Empirical and Simulated Probabilities Designing Simulations Summary of Steps for a Simulation The Law of Large Numbers How Many Trials Should I Do in a Simulation? What If My Simulation Doesn’t Give the Theoretical Value I Expect? Some Subtleties with the Law Streaks: Tails Are Never “Due.” How Common Are Streaks? Chapter Review Key Terms Learning Objectives Summary Sources Section Exercises Section 5.1 Section 5.2 Section 5.3 Section 5.4 Chapter Review Exercises Guided Exercises Chapter 6 Modeling Random Events: The Normal and Binomial Models 6.1 Probability Distributions Are Models of Random Experiments Discrete Probability Distributions Can Be Tables or Graphs Discrete Distributions Can Also Be Equations Continuous Probabilities Are Represented as Areas under Curves Finding Probabilities for Continuous-Valued Outcomes 6.2 The Normal Model Visualizing the Normal Distribution Center and Spread The Mean and the Standard Deviation of a Normal Distribution Finding Normal Probabilities Finding Probability with Technology Without Technology: Apply The Empirical Rule Without Technology: The Standard Normal Finding Measurements from Percentiles for the Normal Distribution Appropriateness of the Normal Model 6.3 The Binomial Model Visualizing the Binomial Distribution Finding Binomial Probabilities Finding (Slightly) More Complex Probabilities Finding Binomial Probabilities by Hand The Formula The Shape of the Binomial Distribution: Center and Spread Interpreting the Mean and the Standard Deviation Surveys: An Application of the Binomial Model Chapter Review Key Terms Learning Objectives Summary Formulas Sources Section Exercises Section 6.1 Section 6.2 Section 6.3 Chapter Review Exercises Guided Exercises Question Question Chapter 7 Survey Sampling and Inference 7.1 Learning about the World through Surveys Survey Terminology What Could Possibly Go Wrong? The Problem of Bias Measurement Bias Sampling Bias Simple Random Sampling Saves the Day Sampling in Practice 7.2 Measuring the Quality of a Survey Using Simulations to Understand the Behavior of Estimators Simulation 1: Statistics Vary from Sample to Sample Simulation 2: The Size of the Population Does Not Affect ­Precision Simulation 3: Large Samples Produce More Precise Estimators Finding the Bias and the Standard Error Real Life: We Get Only One Chance 7.3 The Central Limit Theorem for Sample Proportions Meet the Central Limit Theorem for Sample Proportions Checking Conditions for the Central Limit Theorem Using the Central Limit Theorem 7.4 Estimating the Population Proportion with Confidence Intervals Setting the Confidence Level Selecting a Margin of Error Reality Check: Finding a Confidence Interval When p Is Not Known Interpreting Confidence Intervals Planning a Study: Finding the Sample Size 7.5 Comparing Two Population Proportions with Confidence What’s the Difference? Confidence Intervals for Two Population Proportions Checking Conditions Interpreting Confidence Intervals for Two Proportions Random Assignment versus Random Sampling Chapter Review Key Terms Learning Objectives Summary Sources Section Exercises Section 7.1 Section 7.2 Section 7.3 Section 7.4 Section 7.5 Chapter Review Exercises Guided Exercises Chapter 8 Hypothesis ­Testing for Population Proportions 8.1 The Essential Ingredients of Hypothesis Testing Main Ingredient: A Pair of Hypotheses Add In: Making Mistakes Mix with: The Test Statistic Why Is the z-Statistic Useful? The Final Essential Ingredient: Surprise! Hypothesis Testing and the Data Cycle: Asking Questions 8.2 Hypothesis Testing in Four Steps A Few Details Detail for Step 2: Check Conditions to Find Probabilities Detail for Step 3: Calculating the p-Value Detail for Step 4: Making a Decision The Four-Step Approach Step 1: Hypothesize Step 2: Prepare Step 3: Compute to Compare Step 4: Interpret 8.3 Hypothesis Tests in Detail Xtreme Stats! If Conditions Fail Sample Size Is Too Small Samples Are Not Randomly Selected Balancing Two Types of Mistakes So What? Statistical Significance versus Practical Significance Don’t Change Hypotheses! Hypothesis-Testing Logic Confidence Intervals and Hypothesis Tests 8.4 Comparing Proportions from Two Populations Changes to Ingredients: The Hypotheses Changes to Ingredients: The Test Statistic Changes to Ingredients: Checking Conditions Chapter Review Key Terms Learning Objectives Summary Sources Section Exercises Section 8.1 Section 8.2 Section 8.3 Section 8.4 Chapter Review Exercises Guided Exercises Question Question Chapter 9 Inferring Population Means 9.1 Sample Means of Random Samples Accuracy and Precision of a Sample Mean What Have We Demonstrated with These Simulations? 9.2 The Central Limit Theorem for Sample Means Visualizing Distributions of Sample Means Applying the Central Limit Theorem Many Distributions The t-Distribution 9.3 Answering Questions about the Mean of a Population Estimation with Confidence Intervals When Are Confidence Intervals Useful? Checking Conditions Interpreting Confidence Intervals Measuring Performance with the Confidence Level Calculating the Confidence Interval Reporting and Reading Confidence Intervals Understanding Confidence Intervals 9.4 Hypothesis Testing for Means One- and Two-sided Alternative Hypotheses 9.5 Comparing Two Population Means Estimating the Difference of Means with Confidence Intervals (Independent Samples) Interpreting Confidence Intervals of Differences Testing Hypotheses about Two Means Into the Pool Hypotheses: Choosing Sides CI for the Mean of a Difference: Dependent Samples Test of Two Means: Dependent Samples 9.6 Overview of Analyzing Means Don’t Accept the Null Hypothesis Confidence Intervals and Hypothesis Tests Hypothesis Test or Confidence Interval? Chapter Review Key Terms Learning Objectives Summary Formulas Formula 9.1: One-Sample Confidence Interval for Mean Formula 9.2: The One-Sample t-Test for Mean Formula 9.3: Two-Sample Confidence Interval Formula 9.4: Two-Sample t-Test (Unpooled) Sources Section Exercises Section 9.1 Section 9.2 Section 9.3 Section 9.4 Section 9.5 Chapter Review Exercises Guided Exercises Question Question Confidence Interval Question Chapter 10 Associations between Categorical Variables 10.1 The Basic Ingredients for Testing with Categorical Variables 1. The Data 2. Expected Counts Starting with the Physical Abuse Variable Starting with the TV Violence Variable 3. The Chi-Square Statistic 4. Finding the p-Value for the Chi-Square Statistic 10.2 The Chi-Square Test for Goodness of Fit Goodness of Fit 10.3 Chi-Square Tests for Associations between Categorical Variables Tests of Independence and Homogeneity Random Samples and Randomized Assignment Relation to Tests of Proportions 10.4 Hypothesis Tests When Sample Sizes Are Small Combining Categories Advantages and Disadvantages of Combining Categories Fisher’s Exact Test Chapter Review Key Terms Learning Objectives Summary Formulas Expected Counts Chi-Square Statistic Goodness-of-Fit Test Hypotheses Conditions Sampling Distribution Test of Homogeneity and Independence Hypotheses Conditions (Homogeneity) Conditions (Independence) Sampling Distribution Sources Section Exercises Section 10.1 Section 10.2 Section 10.3 Section 10.4 Chapter Review Exercises Guided Exercises Question Question Chapter 11 Multiple Comparisons and Analysis of Variance 11.1 Multiple Comparisons Data for Multiple Comparisons The Problem of Multiple Comparisons One Solution: The Bonferroni Correction Finding the Number of Comparisons Bonferroni Confidence Intervals 11.2 The Analysis of Variance Visualizing It Putting a Number on It ANOVA in Context: A Tour of the ANOVA Table Explained Variation + Unexpected Variation = Total Variation The Mean Sum of Squares In Other Words Relation of Total Sum of Squares to Variance 11.3 The ANOVA Test Finding the p-Value What If Conditions Are Not Satisfied? Carrying Out an ANOVA Test 11.4 Post Hoc Procedures Chapter Review Key Terms Learning Objectives Summary Sources Section Exercises Section 11.1 Section 11.2 Section 11.3 Section 11.4 Chapter Review Exercises Guided Exercises Question Conclusion Question Question Chapter 12 Experimental Design: Controlling Variation 12.1 Variation Out of Control Review of Experimental Basics Statistical Power Blocking Creating Blocks Blocking and Matching 12.2 Controlling Variation in Surveys Review of Sampling Basics Systematic Sampling Stratified Sampling Cluster Sampling 12.3 Reading Research Papers Reading Abstracts Buyer Beware Data Dredging Publication Bias Profit Motive Media Clinical Significance vs. Statistical Significance Chapter Review Key Terms Learning Objectives Summary Sources Section Exercises Section 12.1 Section 12.2 Section 12.3 Guided Practice Chapter 13 Inference without Normality 13.1 Transforming Data Interpreting QQ Plots The Log Transform Analyzing Log-Transformed Data Comparing Means Median or Geometric Mean? 13.2 The Sign Test for Paired Data Overview of the Sign Test Stating Hypotheses Calculating the Test Statistic Finding the p-Value Applying the Sign Test 13.3 Mann-Whitney Test for Two Independent Groups Overview of the Mann-Whitney Test Stating Hypotheses Finding the Test Statistic Finding the p-Value Applying the Mann-Whitney Test Sample Size and the Mann-Whitney Test What Can Go Wrong? t-Test or Mann-Whitney Test? 13.4 Randomization Tests Overview of Randomization Tests Stating Hypotheses Finding the p-Value Applying Randomization Tests Chapter Review Key Terms Learning Objectives Summary Sources Section Exercises Section 13.1 Section 13.2 Section 13.3 Section 13.4 Chapter Review Exercises Guided Exercises Chapter 14 Inference for Regression 14.1 The Linear Regression Model Components of the Model Checking the Conditions of the Model Checking Linearity Checking the Constant Standard Deviation (SD) Condition Checking Normality Checking the Independence Condition 14.2 Using the Linear Model Estimators for the Intercept and Slope Hypothesis Tests for Intercept and Slope Confidence Intervals for Intercept and Slope Interpreting Confidence Intervals for Regression 14.3 Predicting Values and Estimating Means What Can Go Wrong? If the Linearity Condition Is Not Satisfied If the Errors Are Not Normal If the Standard Deviation Is Not the Same for All Values of x If the Errors Are Not Independent of Each Other Influential Points Interpreting r-squared Chapter Review Key Terms Learning Objectives Summary Sources Section Exercises Section 14.1 Section 14.2 Section 14.3 Chapter Review Exercises Appendix A: Tables Appendix B Answers to Odd-Numbered Exercises Chapter 1 Section 1.2 Section 1.3 Section 1.4 Section 1.5 Chapter Review Exercises Chapter 2 Sections 2.1 and 2.2 Sections 2.3 and 2.4 Chapter Review Exercises Chapter 3 Section 3.1 Section 3.2 Section 3.3 Section 3.4 Section 3.5 Chapter Review Exercises Chapter 4 Section 4.1 Section 4.2 Section 4.3 Section 4.4 Chapter Review Exercises Chapter 5 Section 5.1 Section 5.2 Section 5.3 Section 5.4 Chapter Review Exercises Chapter 6 Section 6.1 Section 6.2 Section 6.3 Chapter Review Exercises Chapter 7 Section 7.1 Section 7.2 Section 7.3 Section 7.4 Section 7.5 Chapter Review Exercises Chapter 8 Section 8.1 Section 8.2 Section 8.3 Section 8.4 Chapter Review Exercises Chapter 9 Section 9.1 Section 9.2 Section 9.3 Section 9.4 Section 9.5 Chapter Review Exercises Chapter 10 Section 10.1 Section 10.2 Section 10.3 Section 10.4 Chapter Review Exercises Chapter 11 Section 11.1 Section 11.2 Section 11.3 Section 11.4 Chapter Review Exercises Chapter 12 Section 12.1 Section 12.2 Section 12.3 Chapter 13 Section 13.1 Section 13.2 Section 13.3 Section 13.4 Chapter Review Exercises Chapter 14 Section 14.1 Section 14.2 Section 14.3 Chapter Review Exercises Appendix C: Credits Photo Credits 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