Detailed Table of Contents.

(Contents for Chapters 11 – 15 are preliminary.)

Preface.

Part One: Welcome to the World of Statistics.

Discovering Statistics

by Daniel T. Larose, Ph.D.

Chapter One: Why Should I Study Statistics?

Section 1.1 Welcome to Discovering Statistics Section 1.2 Data Stories Illustrating The World of Statistics Chapter One Exercises Try This in Class! Chapter One In-Class Activities

Chapter Two: The Nature of Statistics

Vista: Where we are coming from, and where we are headed… Chapter Two Objectives Chapter Two Case Study: Does Friday the 13th Change Human Behavior? Section 2.1 What is Statistics?

Section 2.1.1 Examples of Statistics Section 2.1.2 A Statistical Literacy Quiz Section 2.1 Exercises

Section 2.2 Descriptive Statistics: The Building Blocks of Data Analysis Section 2.2.1 Elements and Variables Section 2.2.2 Qualitative and Quantitative Variables Section 2.2 Exercises

Section 2.3 Inferential Statistics: How Do We Get There From Here? Section 2.3.1 Populations and Samples Section 2.3.2 Statistical Inference Section 2.3.3 Census Section 2.3 Exercises

Chapter Two Glossary Try This in Class! Chapter Two In-Class Activities

Chapter Three: Gathering Data

Vista: Where we are coming from, and where we are headed… Chapter Three Objectives Chapter Three Case Study: How could the experts have been so wrong? Section 3.1 Sources of Data: Where Can I Find That Information?

Section 3.1.1 Printed Sources Section 3.1.2 Electronic Sources Section 3.1 Exercises

Section 3.2 Surveys and Questionnaires: Careful What You Ask For Section 3.2.1 Selection Bias Section 3.2.2 Questionnaire Design Section 3.2 Exercises

Section 3.3 Sampling Methods Section 3.3.1 What is a Random Sample, and Why Do We Need It? Section 3.3.2 Further Sampling Methods Section 3.3 Exercises

Section 3.4 Statistical Studies Section 3.4.1 Outcomes and Explanations Section 3.4.2 Experimental Studies Section 3.4.3 Observational Studies Section 3.4 Exercises

Chapter Three Glossary Try This in Class! Chapter Three In-Class Activities

Part Two: Descriptive Statistics.

Chapter Four: Describing Data Graphically

Vista: Where we are coming from, and where we are headed… Chapter Objectives Chapter Four Case Study: The Caesar Cipher Section 4.1 Summarizing Qualitative Data

Section 4.1.1 Frequency Distributions Section 4.1.2 Relative Frequency Distributions Section 4.1.3 How to Use SPSS to Summarize Qualitative Data Section 4.1 Exercises

Section 4.2 Summarizing Quantitative Data Section 4.2.1 Histograms Section 4.2.2 Using SPSS to Summarize Quantitative Data Section 4.2.3 Stem-and-Leaf Displays Section 4.2.4 Symmetry and Skewness Section 4.2 Exercises

Section 4.3 Summarizing Graphically the Relationship Between Two Variables Section 4.3.1 Crosstabulations Section 4.3.2 Scatter Diagrams Section 4.3.3 Using SPSS to Summarize Graphically the Relationship Between

Two Variables Section 4.3 Exercises

Chapter Four Glossary Try This in Class! Chapter Four In-Class Activities

Chapter Five: Describing Data Numerically

Vista: Where we are coming from, and where we are headed… Chapter Five Objectives Case Study: Bills Introduced in the Early Congresses Section 5.1 Where is the Middle?

Section 5.1.1 The Mean Section 5.1.2 The Median Section 5.1.3 The Mode Section 5.1.4 The Weighted Mean Section 5.1 Exercises

Section 5.2 How Spread Out is the Data? Section 5.2.1 The Range Section 5.2.2 The Mean Absolute Deviation Section 5.2.3 The Standard Deviation and Variance Section 5.2 Exercises

Section 5.3 Applications: How Can I Use These Measures? Section 5.3.1 Percentile Section 5.3.2 Z-score Section 5.3.3 Empirical rule Section 5.3.4 Chebyshev’s Rule Section 5.3 Exercises

Section 5.4 Robust Measures: Section 5.4.1 The Quartiles Section 5.4.2 The Five-Number Summary, Section 5.4.2 The Box Plot

Section 5.5 Summarizing Numerically the Relationship Between Two Variables Section 5.5.1 The Correlation Coefficient Section 5.5.2 Interpreting the Correlation Coefficient Section 5.5 Exercises

Section 5.6 How to Use SPSS to Summarize Data Numerically Section 5.6 Exercises

Chapter Five Glossary Try This in Class! Chapter Five In-Class Activities

Part Three: Probability and Distributions.

Chapter Six: Probability

Vista: Where we are coming from, and where we are headed…Chapter Six ObjectivesChapter Six Case Study: The Monty Hall Problem and Bayes' RuleSection 6.1 Introducing Probability

Section 6.1.1 The Language of UncertaintySection 6.1.2 The Building Blocks of ProbabilitySection 6.1.3 How to Assign Probabilities to OutcomesSection 6.1 Exercises

Section 6.2 EventsSection 6.2.1 The Tree DiagramSection 6.2.2 Counting RuleSection 6.2.3 How to Assign Probabilities to EventsSection 6.2 Exercises

Section 6.3 Combining Events and their ProbabilitiesSection 6.3.1 The Complement of an EventSection 6.3.2 The Union and Intersection of Two EventsSection 6.3.3 The Addition LawSection 6.3.4 Mutually Exclusive EventsSection 6.3 Exercises

Section 6.4 Conditional ProbabilitySection 6.4.1 Discovering Conditional ProbabilitySection 6.4.2 Independent EventsSection 6.4.3 The Multiplication LawSection 6.4.4 Sampling with Replacement and Sampling without

ReplacementSection 6.4 Exercises

Section 6.5 Bayes' Theorem for Updating ProbabilitiesSection 6.5.1 Prior Probabilities and Posterior ProbabilitiesSection 6.5.2 Bayes' Theorem: General Form and Tabular MethodSection 6.5.3 Solving the Monty Hall Problem using Bayes'

TheoremSection 6.5 Exercises

Chapter Six GlossaryTry This in Class! Chapter Six In-Class Activities

Chapter Seven: Discrete Distributions

Vista: Where we are coming from, and where we are headed…Chapter Seven ObjectivesChapter Seven Case Study: At What Age Do Youngsters Drink their First Beer?Section 7.1 Random Variables

Section 7.1.1 Discrete Random VariablesSection 7.1.2 Continuous Random VariablesSection 7.1 Exercises

Section 7.2 Discrete Probability DistributionsSection 7.2.1 Discrete Probability Distribution as a TableSection 7.2.2 Discrete Probability Distribution as a GraphSection 7.2 Exercises

Section 7.3 Expectation and VariabilitySection 7.3.1 Expected Value of a Discrete Random VariableSection 7.3.2 Variability of a Discrete Random VariableSection 7.3 Exercises

Section 7.4 The Binomial DistributionSection 7.4.1 The Binomial ExperimentSection 7.4.2 The Binomial Probability FormulaSection 7.4.3 The Binomial TableSection 7.4.4 The Binomial Mean, Variance, and Standard

DeviationSection 7.4 Exercises

Chapter Seven GlossaryTry This in Class! Chapter Seven In-Class Activities

Chapter Eight: Continuous Distributions

Vista: Where we are coming from, and where we are headed…Chapter Eight ObjectivesChapter Eight Case Study: The Story in Her EyesSection 8.1 Continuous Distributions: Don't Count It, Measure It!

Section 8.1.1 Why Continuous? or, How Much Soda is in Your 12-Ounce Can?

Section 8.1.2 Working with Continuous Probability Distributions, or What Two Species Live in This Habitat?

Section 8.1 ExercisesSection 8.2 The Normal Probability Distribution: It's Everywhere!

Section 8.2.1 Properties of the Normal Distribution: Beautiful Bell Shaped SymmetrySection 8.2.2 Drawing a Picture to Solve the Problem: Get Both Sides of Your Brain in on It!Section 8.2 Exercises

Section 8.3 The Standard Normal Distribution: The Keys to the KingdomSection 8.3.1 The Standard Normal Random Variable Z:

What's So Special?Section 8.3.2 Strategies and Techniques for Finding Z Probabilities: The PlayBookSection 8.3.3 How to Find Z Values for a Given Area: Now Do It

Backwards!Section 8.3 Exercises

Section 8.4 Applications of the Normal DistributionSection 8.4.1 Standardizing: Out of Many, OneSection 8.4.2 Finding Probabilities for Applications of the Normal

DistributionSection 8.4.3 Finding Normal Data Values for Specified ProbabilitiesSection 8.4 Exercises

Chapter Eight GlossaryTry This in Class! Chapter Eight In-Class Activities

Part Four: Inferential Statistics for One Population.

Chapter Nine: Sampling Distributions

Section 9.1 Point Estimationo Section 9.1 Exercises

Section 9.2 Sampling Distributionso Section 9.2.1 Variability of Sample Statisticso Section 9.2.2 Sampling Distribution of the Sample Meano Section 9.2 Exercises

Section 9.3 The Central Limit Theoremo Section 9.3 Exercises

Chapter Nine Glossary and Formulas Try This in Class! Chapter Nine In-Class Activities

Chapter Ten: Confidence Intervals and Sample Size

Section 10.1 Confidence intervals for means, large sample caseo Section 10.1.1 Derivation of the Confidence Interval Formulao Section 10.1.2 Large Sample Confidence Intervals for when is knowno Section 10.1.3 Large Sample Confidence Intervals for when is not

knowno Section 10.1.4 Margin of Erroro Section 10.1 Exercises

Section 10.2 Confidence intervals for means, small sample caseo Section 10.2.1 The t Distributiono Section 10.2.2 The Small Sample Confidence Interval for o Section 10.2.3 Using Confidence Intervals to Determine Significanceo Section 10.2 Exercises

Section 10.3 Confidence intervals for proportionso Section 10.3.1 The Sampling Distribution of the Sample Proportiono Section 10.3.2 The Large Sample Confidence Interval for the Population

Proportiono Section 10.3 Exercises

Section 10.4 Sample Size Considerationso Section 10.4.1 Sample Size for Estimating the Population Meano Section 10.4.2 Sample Size for Estimating the Population Proportiono Section 10.4 Exercises

Chapter Ten Glossary and Formulas Try This in Class! Chapter Ten In-Class Activities

Chapter Eleven: Hypothesis Testing

Vista: Where we are coming from, and where we are headed… Chapter Eleven Objectives Chapter Eleven Case Study Section 11.1 An Introduction to Hypothesis Testing

Section 11.1 Exercises Section 11.2 Type I and Type II Errors

Section 11.2 Exercises Section 11.3 Hypothesis Tests About a Population Mean: Large Sample Case

Section 11.3 Exercises Section 11.4 Hypothesis Tests About a Population Mean: Small Sample Case

Section 11.4 Exercises Section 11.5 Hypothesis Tests About a Population Proportion

Section 11.5 Exercises Chapter Eleven Glossary Try This in Class! Chapter Eleven In-Class Activities

Chapter Twelve: Two-Sample Inference

Vista: Where we are coming from, and where we are headed… Chapter Twelve Objectives Chapter Twelve Case Study Section 12.1 Test for Difference in Means: Large Sample

Section 12.1 Exercises Section 12.2 Test for Difference in Means: Small Sample

Section 12.2 Exercises Section 12.3 Paired t-Test

Section 12.3 Exercises Section 12.4 Test for Difference in Proportions

Section 12.4 Exercises Chapter Twelve Glossary Try This in Class! Chapter Twelve In-Class Activities

Chapter Thirteen: Tests for Goodness of Fit and Independence

Vista: Where we are coming from, and where we are headed… Chapter Thirteen Objectives Chapter Thirteen Case Study Section 13.1 Goodness of Fit Test for Multinomial Data

Section 13.1 Exercises Section 13.2 Contingency Tables: Tests of Independence

Section 13.2 Exercises Section 13.3 Goodness of Fit Test for Normal Data

Section 13.3 Exercises Chapter Thirteen Glossary Try This in Class! Chapter Thirteen In-Class Activities

Chapter Fourteen: Analysis of Variance and Experimental Design

Vista: Where we are coming from, and where we are headed… Chapter Fourteen Objectives Chapter Fourteen Case Study Section 14.1 Intuitive Introduction to Analysis of Variance

Section 14.1 Exercises Section 14.2 Nuts and Bolts of Analysis of Variance

Section 14.2 Exercises Section 14.3 Multiple Comparisons

Section 14.3 Exercises Section 14.4 Completely Randomized Design

Section 14.4 Exercises Section 14.5 Randomized Block Design

Section 14.5 Exercises Section 14.6 Factorial Experiments

Section 14.6 Exercises Chapter Fourteen Glossary Try This in Class! Chapter Fourteen In-Class Activities

Chapter Fifteen: Regression and Correlation Analysis

Vista: Where we are coming from, and where we are headed… Chapter Fifteen Objectives Chapter Fifteen Case Study Section 15.1 Intuitive Introduction to Regression Analysis

Section 15.1 Exercises Section 15.2 The Regression Model and Least Squares

Section 15.2 Exercises Section 15.3 Is the Regression Useful?

Section 15.3 Exercises Section 15.4 Testing for the Significance of the Regression Model

Section 15.4 Exercises Section 15.5 Estimation: Confidence Intervals and Prediction Intervals

Section 15.5 Exercises Section 15.6 Correlation Analysis

Section 15.6 Exercises Chapter Fifteen Glossary Try This in Class! Chapter Fifteen In-Class Activities