Essential Statistics

This book is ideal for a one-semester course in statistics, offering a streamlined presentation of Introductory Statistics: Exploring the World through Data, by Gould/Ryan.

Exploring the World through Data

We live in a data-driven world, and the goal of this text is to teach students how to access and analyze these data critically. Authors Rob Gould, Colleen Ryan, and Rebecca Wong want students to develop a "data habit of mind" because learning statistics is  an essential life skill that extends beyond the classroom.and Regardless of their math backgrounds, students will learn how to think about data and how to reason using data. With a clear, unintimidating writing style and carefully chosen pedagogy, this text makes data analysis accessible to all students.

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Robert L. Gould (Ph.D., University of California–San Diego) is a leader in the statistics education community. He has served as chair of the American Statistical Association’s Committee on Teacher Enhancement, has served as chair of the ASA’s Statistics Education Section, and was a co-author of the Guidelines for Assessment in Instruction on Statistics Education (GAISE) College Report. As the associate director of professional development for CAUSE (Consortium for the Advancement of Undergraduate Statistics Education), he has worked closely with the American Mathematical Association of Two-Year Colleges (AMATYC) to provide traveling workshops and summer institutes in statistics. He also presented an AMATYC summer institute in 2009. For over ten years, he has served as Vice-Chair of Undergraduate Studies at the UCLA Department of Statistics, and he is Director of the UCLA Center for the Teaching of Statistics. In 2012, Rob was elected Fellow of the American Statistical Association.

Colleen N. Ryan has taught statistics, chemistry, and physics to diverse community college students for decades. She taught at Oxnard College from 1975 to 2006, where she earned the Teacher of the Year Award. Colleen currently teaches statistics part time at California Lutheran University. She often designs her own lab activities. Her passion is to discover new ways to make statistical theory practical, easy to understand, and sometimes even fun. Colleen earned a B.A. in physics from Wellesley College, an M.A.T. in physics from Harvard University, and an M.A. in chemistry from Wellesley College. Her first exposure to statistics was with Frederick Mosteller at Harvard. In her spare time, she sings with the Oaks Chamber Singers, has been an avid skier in the past, and enjoys time with her family.

Rebecca K. Wong has taught mathematics and statistics at West Valley College for more than twenty years. She enjoys designing activities to help students actively explore statistical concepts and encouraging students to apply those concepts to areas of personal interest. Rebecca earned a B.A. in mathematics and psychology from the University of California—Santa Barbara, an M.S.T. in mathematics from Santa Clara University, and an Ed.D. in Educational Leadership from San Francisco State University. She has been recognized for outstanding teaching by the National Institute of Staff and Organizational Development and the California Mathematics Council of Community Colleges. When not teaching, Rebecca is an avid reader and enjoys hiking trails with friends.

Preface

Index of Applications

1. Introduction to Data

            Case Study–Deadly Cell Phones?

1.1 What Are Data?

1.2 Classifying and Storing Data

1.3 Organizing Categorical Data

1.4 Collecting Data to Understand Causality

            Exploring Statistics–Collecting a Table of Different Kinds of Data

2. Picturing Variation with Graphs

            Case Study–Student-to-Teacher Ratio at Colleges

2.1 Visualizing Variation in Numerical Data

2.2 Summarizing Important Features of a Numerical Distribution

2.3 Visualizing Variation in Categorical Variables

2.4 Summarizing Categorical Distributions

2.5 Interpreting Graphs

            Exploring Statistics–Personal Distance

3. Numerical Summaries of Center and Variation

            Case Study–Living in a Risky World

3.1 Summaries for Symmetric Distributions

3.2 What’s Unusual? The Empirical Rule and z-Scores

3.3 Summaries for Skewed Distributions

3.4 Comparing Measures of Center

3.5 Using Boxplots for Displaying Summaries

            Exploring Statistics–Does Reaction Distance Depend on Gender?

4. Regression Analysis: Exploring Associations between Variables

            Case Study–Catching Meter Thieves

4.1 Visualizing Variability with a Scatterplot

4.2 Measuring Strength of Association with Correlation

4.3 Modeling Linear Trends

4.4 Evaluating the Linear Model

            Exploring Statistics–Guessing the Age of Famous People

5. Modeling Variation with Probability

            Case Study–SIDS or Murder?

5.1 What Is Randomness?

5.2 Finding Theoretical Probabilities

5.3 Associations in Categorical Variables

5.4 Finding Empirical Probabilities

            Exploring Statistics–Let’s Make a Deal: Stay or Switch?

6. Modeling Random Events: The Normal and Binomial Models

            Case Study–You Sometimes Get More Than You Pay For

6.1 Probability Distributions Are Models of Random Experiments

6.2 The Normal Model

6.3 The Binomial Model (optional)

            Exploring Statistics–ESP with Coin Flipping

7. Survey Sampling and Inference

            Case Study–Spring Break Fever: Just What the Doctors Ordered?

7.1 Learning about the World through Surveys

7.2 Measuring the Quality of a Survey

7.3 The Central Limit Theorem for Sample Proportions

7.4 Estimating the Population Proportion with Confidence Intervals

7.5 Comparing Two Population Proportions with Confidence

            Exploring Statistics–Simple Random Sampling Prevents Bias

8. Hypothesis Testing for Population Proportions

            Case Study–Dodging the Question

8.1 The Essential Ingredients of Hypothesis Testing

8.2 Hypothesis Testing in Four Steps

8.3 Hypothesis Tests in Detail

8.4 Comparing Proportions from Two Populations

            Exploring Statistics–Identifying Flavors of Gum through Smell

9. Inferring Population Means

            Case Study–Epilepsy Drugs and Children

9.1 Sample Means of Random Samples

9.2 The Central Limit Theorem for Sample Means

9.3 Answering Questions about the Mean of a Population

9.4 Hypothesis Testing for Means

9.5 Comparing Two Population Means

9.6 Overview of Analyzing Means

            Exploring Statistics–Pulse Rates

10. Analyzing Categorical Variables and Interpreting Research

            Case Study–Popping Better Popcorn

10.1 The Basic Ingredients for Testing with Categorical Variables

10.2 Chi-Square Tests for Associations between Categorical Variables

10.3 Reading Research Papers

            Exploring Statistics–Skittles

Appendix A Tables

Appendix B Check Your Tech Answers

Appendix C Answers to Odd-Numbered Exercises

Appendix D Credits

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