Introductory Statistics

About our authors 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 AMATYC/ASA joint committee, was co-leader of the Two-Year College Data Science Summit hosted by the American Statistical Association, served as chair of the ASA's Statistics Education Section, and was a co-author of the 2005 Guidelines for Assessment in Instruction on Statistics Education (GAISE) College Report. While serving as the Associate Director of Professional Development for CAUSE (Consortium for the Advancement of Undergraduate Statistics Education), he worked closely with the American Mathematical Association of Two-Year Colleges (AMATYC) to provide traveling workshops and summer institutes in statistics. He was the lead principal investigator of the NSF-funded Mobilize Project, which developed and implemented the first high-school level data science course. For over 20 years, he has served as Vice-Chair of Undergraduate Studies at the UCLA Department of Statistics, and 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 and enjoys time with her family.Rebecca K. Wong has taught mathematics and statistics at West Valley College for more than 20 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.

• 1. Introduction to Data 1.1 What Are Data?1.2 Classifying and Storing Data1.3 Investigating Data1.4 Organizing Categorical Data1.5 Collecting Data to Understand Causality2. Picturing Variation with Graphs 2.1 Visualizing Variation in Numerical Data2.2 Summarizing Important Features of a Numerical Distribution2.3 Visualizing Variation in Categorical Variables2.4 Summarizing Categorical Distributions2.5 Interpreting Graphs3. Numerical Summaries of Center and Variation 3.1 Summaries for Symmetric Distributions3.2 What's Unusual? The Empirical Rule and z-Scores3.3 Summaries for Skewed Distributions3.4 Comparing Measures of Center3.5 Using Boxplots for Displaying Summaries<4. Regression Analysis: Exploring Associations between Variables 4.1 Visualizing Variability with a Scatterplot4.2 Measuring Strength of Association with Correlation4.3 Modeling Linear Trends4.4 Evaluating the Linear Model5. Modeling Variation with Probability 5.1 What Is Randomness?5.2 Finding Theoretical Probabilities5.3 Associations in Categorical Variables5.4 Finding Empirical Probabilities6. Modeling Rando Events: The Normal and Binomial Models 6.1 Probability Distributions Are Models of Random Experiments6.2 The Normal Model6.3 The Binomial Model (Optional)7. Survey Sampling and Inference 7.1 Learning about the World through Surveys7.2 Measuring the Quality of a Survey7.3 The Central Limit Theorem for Sample Proportions7.4 Estimating the Population Proportion with Confidence Intervals7.5 Comparing Two Population Proportions with Confidence8. Hypothesis Testing for Population Proportions 8.1 The Essential Ingredients of Hypothesis Testing8.2 Hypothesis Testing in Four Steps8.3 Hypothesis Tests in Detail8.4 Comparing Proportions from Two Populations9. Inferring Population Means 9.1 Sample Means of Rando Samples9.2 The Central Limit Theorem for Sample Means9.3 Answering Questions about the Mean of a Population9.4 Hypothesis Testing for Means9.5 Comparing Two Population Means9.6 Overview of Analyzing Means10. Associations between Categorical Variables 10.1 The Basic Ingredients for Testing with Categorical Variables10.2 The Chi-Square Test for Goodness of Fit10.3 Chi-Square Tests for Associations between Categorical Variables10.4 Hypothesis Tests When Sample Sizes Are Small11. Multiple Comparisons and Analysis of Variance 11.1 Multiple Comparisons11.2 The Analysis of Variance11.3 The ANOVA Test11.4 Post-Hoc Procedures12. Experimental Design: Controlling Variation 12.1 Variation Out of Control12.2 Controlling Variation in Surveys12.3 Reading Research Papers13. Inference without Normality 13.1 Transforming Data13.2 The Sign Test for Paired Data13.3 Mann-Whitney Test for Two Independent Groups13.4 Randomization Tests14. Inference for Regression 14.1 The Linear Regression Model14.2 Using the Linear Model14.3 Predicting Values and Estimating Means