Introductory Statistics Exploring the World Through Data

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 2009, Rob was elected president of the Southern California Chapter 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.

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 Private and Public 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 with Simulations

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

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 Margin of Error and Sample Size for Proportions (Optional)

Exploring Statistics: Simple Random Sampling Prevents Bias

8. Hypothesis Testing for Population Proportions

Case Study: Does Watching Violent TV as a Child Lead to Violent Behavior as an Adult?

8.1 The Main Ingredients of Hypothesis Testing

8.2 Characterizing p-values

8.3 Hypothesis Testing in Four Steps

8.4 Comparing Proportions from Two Populations

8.5 Understanding Hypothesis Testing

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 Comparing Two Population Means

9.5 Overview of Analyzing Means

Exploring Statistics: Pulse Rates

10. Associations between Categorical Variables

Case Study: Popping Better Popcorn

10.1 The Basic Ingredients for Testing with Categorical Variables

10.2 The Chi-Square Test for Goodness of Fit

10.3 Chi-Square Tests for Associations between Categorical Variables

10.4 Hypothesis Tests When Sample Sizes Are Small

Exploring Statistics: Skittles

11. Multiple Comparisons and Analysis of Variance

Case Study: Seeing Red

11.1 Multiple Comparisons

11.2 The Analysis of Variance

11.3 The ANOVA Test

11.4 Post-Hoc Procedures

Exploring Statistics: Recovery Heart Rate

12. Experimental Design: Controlling Variation

Case Study: Does Stretching Improve Athletic Performance?

12.1 Variation Out of Control

12.2 Controlling Variation in Surveys

12.3 Reading Research Papers

Exploring Statistics: Reporting on Research Activities

13. Inference without Normality

Case Study: Electric Rays

13.1 Transforming Data

13.2 The Sign Test for Paired Data

13.3 Mann-Whitney Test for Two Independent Groups

13.4 Randomization Tests

Exploring Statistics: Balancing on One Foot

14. Inference for Regression

Case Study: Building a Better Oyster Shucker

14.1 The Linear Regression Model

14.2 Using the Linear Model

14.3 Predicting Values and Estimating Means

Exploring Statistics: Older and Slower?

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