Introduction to Statistical Investigations

Introduction to Statistical Investigations, Second Edition provides a unified framework for explaining variation across study designs and variable types, helping students increase their statistical literacy and appreciate the indispensable role of statistics in scientific research. Requiring only basic algebra as a prerequisite, the program uses the immersive, simulation-based inference approach for which the author team is known. Students engage with various aspects of data collection and analysis using real data and clear explanations designed to strengthen multivariable understanding and reinforce concepts.

Each chapter follows a coherent six-step statistical exploration and investigation method (ask a research question, design a study, explore the data, draw inferences, formulate conclusions, and look back and ahead) enabling students to assess a variety of concepts in a single assignment. Challenging questions based on research articles strengthen critical reading skills, fully worked examples demonstrate essential concepts and methods, and engaging visualizations illustrate key themes of explained variation. The end-of-chapter investigations expose students to various applications of statistics in the real world using real data from popular culture and published research studies in variety of disciplines. Accompanying examples throughout the text, user-friendly applets enable students to conduct the simulations and analyses covered in the book.

PRELIMINARIES

Introduction to Statistical

Investigations 1

SECTION P.1 Introduction to the Six-Step Method 2

SECTION P.2 Exploring Data 6

SECTION P.3 Exploring Random Processes 10

UNIT 1 FOUR PILLARS OF INFERENCE: STRENGTH, SIZE, BREADTH, AND CAUSE 21

CHAPTER 1 Significance: How Strong Is the Evidence? 22

SECTION 1.1 Introduction to Chance Models 23

SECTION 1.2 Measuring the Strength of Evidence 35

SECTION 1.3 Alternative Measure of Strength of Evidence 46

SECTION 1.4 What Impacts Strength of Evidence? 53

SECTION 1.5 Inference for a Single Proportion: Theory-Based Approach 63

CHAPTER 2 Generalization: How Broadly Do the Results Apply? 102

SECTION 2.1 Sampling from a Finite Population 103

SECTION 2.2 Inference for a Single Quantitative Variable 120

SECTION 2.3 Errors and Significance 138

CHAPTER 3 Estimation: How Large Is the Effect? 163

SECTION 3.1 Statistical Inference: Confidence Intervals 164

SECTION 3.2 2SD and Theory-Based Confidence Intervals for a Single Proportion 173

SECTION 3.3 2SD and Theory-Based Confidence Intervals for a Single Mean 181

SECTION 3.4 Factors that Affect the Width of a Confidence Interval 187

SECTION 3.5: Cautions When Conducting Inference 194

CHAPTER 4 Causation: Can We Say What Caused the Effect? 231

SECTION 4.1 Association and Confounding 232

SECTION 4.2 Observational Studies versus Experiments 237

UNIT 2 COMPARING TWO GROUPS 259 CHAPTER 5

Comparing Two Proportions 260

SECTION 5.1 Comparing Two Groups: Categorical Response 261

SECTION 5.2 Comparing Two Proportions: Simulation-Based Approach 267

SECTION 5.3 Comparing Two Proportions: Theory-Based Approach 283

CHAPTER 6 Comparing Two Means 323

SECTION 6.1 Comparing Two Groups: Quantitative Response 324

SECTION 6.2 Comparing Two Means: Simulation-Based Approach 331

SECTION 6.3 Comparing Two Means: Theory-Based Approach 346

CHAPTER 7 Paired Data: One Quantitative Variable 382

SECTION 7.1 Paired Designs 383

SECTION 7.2 Analyzing Paired Data: Simulation-Based Approach 388

SECTION 7.3 Analyzing Paired Data: Theory-Based Approach 399

UNIT 3 ANALYZING MORE GENERAL SITUATIONS 427

CHAPTER 8 Comparing More Than Two Proportions 429

SECTION 8.1 Comparing Multiple Proportions: Simulation-Based Approach 430

SECTION 8.2 Comparing Multiple Proportions: Theory-Based Approach 440

CHAPTER 9 Comparing More Than Two Means 475

SECTION 9.1 Comparing Multiple Means: Simulation-Based Approach 476

SECTION 9.2 Comparing Multiple Means: Theory-Based Approach 485

CHAPTER 10 Two Quantitative Variables 520

SECTION 10.1 Two Quantitative Variables: Scatterplots and Correlation 521

SECTION 10.2 Inference for the Correlation Coefficient: Simulation-Based Approach 529

SECTION 10.3 Least Squares Regression 538

SECTION 10.4 Inference for the Regression Slope: Simulation-Based Approach 547

SECTION 10.5 Inference for the Regression Slope: Theory-Based Approach 552

APPENDIX A Calculation Details 592

APPENDIX B Stratified and Cluster Samples 610

SOLUTIONS TO SELECTED EXERCISES 615

INDEX