Introductory Statistics with Randomization and Simulation, authored by David M. Diez, Christopher D. Barr, and Mine Çetinkaya-Rundel, is a comprehensive first edition textbook designed for students and educators in statistics. This resource emphasizes the principles of randomization and simulation, providing a modern approach to statistical inference. Key topics include data collection methods, hypothesis testing, confidence intervals, and linear regression, making it ideal for introductory statistics courses. The textbook is structured with case studies and exercises that enhance understanding of statistical concepts through practical application. Available under a Creative Commons license, it encourages open access to learning materials.

Key Points

  • Explores randomization and simulation techniques for statistical inference
  • Includes case studies and exercises to reinforce statistical concepts
  • Covers essential topics like hypothesis testing and confidence intervals
  • Designed for introductory statistics courses at the undergraduate level
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354 pages
Statistics
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354 pages
Statistics
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Introductory Statistics
with
Randomization and Simulation
First Edition
David M Diez
Quantitative Analyst
Google/YouTube
david@openintro.org
Christopher D Barr
Graduate Student
Yale School of Management
chris@openintro.org
Mine C¸ etinkaya-Rundel
Assistant Professor of the Practice
Department of Statistics
Duke University
mine@openintro.org
Copyright © 2014. First Edition.
This textbook is available under a Creative Commons license. Visit openintro.org for a free
PDF, to download the textbook’s source files, or for more information about the license.
Contents
1 Introduction to data 1
1.1 Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Data basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Overview of data collection principles . . . . . . . . . . . . . . . . . . . . . 9
1.4 Observational studies and sampling strategies . . . . . . . . . . . . . . . . . 13
1.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6 Examining numerical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.7 Considering categorical data . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2 Foundation for inference 61
2.1 Randomization case study: gender discrimination . . . . . . . . . . . . . . . 61
2.2 Randomization case study: opportunity cost . . . . . . . . . . . . . . . . . . 65
2.3 Hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.4 Simulation case studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.5 Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.6 Normal distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.7 Applying the normal model . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
2.8 Confidence intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
2.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3 Inference for categorical data 123
3.1 Inference for a single proportion . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.2 Difference of two proportions . . . . . . . . . . . . . . . . . . . . . . . . . . 128
3.3 Testing for goodness of fit using chi-square (special topic) . . . . . . . . . . 134
3.4 Testing for independence in two-way tables (special topic) . . . . . . . . . . 144
3.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4 Inference for numerical data 163
4.1 One-sample means with the t distribution . . . . . . . . . . . . . . . . . . . 163
4.2 Paired data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
4.3 Difference of two means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
4.4 Comparing many means with ANOVA (special topic) . . . . . . . . . . . . . 184
4.5 Bootstrapping to study the standard deviation . . . . . . . . . . . . . . . . 195
4.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
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FAQs

What are the main topics covered in Introductory Statistics with Randomization and Simulation?
The textbook covers a wide range of topics essential for understanding statistics, including data collection methods, hypothesis testing, and confidence intervals. It also delves into randomization and simulation techniques, which are crucial for modern statistical inference. Additionally, the book addresses linear regression, multiple regression, and logistic regression, providing a comprehensive foundation for students. Each chapter includes practical exercises and case studies to help students apply these concepts effectively.
How does this textbook incorporate randomization in statistical studies?
Randomization is a key theme in this textbook, particularly in the context of experimental design and hypothesis testing. The authors explain how randomization helps eliminate bias in data collection and ensures that the results of statistical tests are valid. Through case studies, students learn how to implement randomization in real-world scenarios, enhancing their understanding of its importance in statistical analysis. The textbook also provides examples of randomized experiments and discusses their implications for drawing conclusions from data.
What exercises are included in the textbook to aid learning?
Each chapter of Introductory Statistics with Randomization and Simulation includes a variety of exercises designed to reinforce the concepts presented. These exercises range from simple problems that test basic understanding to more complex case studies that require critical thinking and application of statistical methods. The exercises encourage students to engage with the material actively, making the learning process more interactive and effective. Solutions and explanations are often provided to help students understand their mistakes and learn from them.
What is the significance of simulation in statistics as discussed in the textbook?
Simulation plays a vital role in the textbook as it allows students to understand complex statistical concepts through practical experimentation. The authors illustrate how simulation can be used to model real-world scenarios, estimate probabilities, and conduct hypothesis tests without relying solely on theoretical distributions. By engaging in simulation exercises, students gain hands-on experience with statistical methods, which enhances their comprehension and prepares them for practical applications in various fields. The textbook emphasizes the power of simulation in making statistical inference more accessible and intuitive.

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