Introduction to Statistics and Data Analysis

Roxy Peck is emerita associate dean of the College of Science and Mathematics and professor of statistics emerita at California Polytechnic State University, San Luis Obispo. As a faculty member at Cal Poly from 1979 until 2009, Dr. Peck served for six years as chair of the statistics department before becoming associate dean, a position she held for 13 years. She received an M.S. in mathematics and a Ph.D. in applied statistics from the University of California, Riverside. Dr. Peck is nationally known in the area of statistics education, and she was presented with the Lifetime Achievement Award in Statistics Education at the U.S. Conference on Teaching Statistics in 2009. In 2003, she received the American Statistical Association’s Founder’s Award, recognizing her contributions to K-12 and undergraduate statistics education. She is a fellow of the American Statistical Association and an elected member of the International Statistics Institute. Dr. Peck served for five years as the chief reader for the Advanced Placement (AP) Statistics Exam and has chaired the American Statistical Association’s Joint Committee with the National Council of Teachers of Mathematics on Curriculum in Statistics and Probability for Grades K-12 and the Section on Statistics Education. In addition to her texts in introductory statistics, Dr. Peck is co-editor of STATISTICAL CASE STUDIES: A COLLABORATION BETWEEN ACADEME AND INDUSTRY and is a member of the editorial board for STATISTICS: A GUIDE TO THE UNKNOWN, 4TH EDITION. Outside of the classroom, she likes to travel and spends her spare time reading mystery novels. Dr. Peck also collects Navajo rugs and travels to Arizona and New Mexico whenever she can find the time. For over 25 years, Chris Olsen taught statistics at George Washington High School in Cedar Rapids, Iowa, and currently teaches at Grinnell College. Chris is a past member (twice) of the AP Statistics Test Development Committee and has been a table leader at the AP Statistics reading for 14 years. He is a long-time consultant to the College Board and has led workshops and institutes for AP Statistics teachers in the United States and internationally. Chris was the Iowa recipient of the Presidential Award for Excellence in Science and Mathematics Teaching in 1986, a regional awardee of the IBM Computer Teacher of the Year in 1988 and received the Siemens Award for Advanced Placement in Mathematics in 1999. Chris is a frequent contributor to, and is moderator of, the AP Teacher Community online. He is currently a member of the editorial board of Teaching Statistics. Chris graduated from Iowa State University with a major in mathematics and philosophy, and while acquiring graduate degrees at the University of Iowa, he concentrated on statistics, computer programming and psychometrics. In his spare time, he enjoys reading and hiking. He and his wife have a daughter, Anna, a Caltech graduate in Civil Engineering.

• 1. THE ROLE OF STATISTICS AND THE DATA ANALYSIS PROCESS: Why Study Statistics? The Nature and Role of Variability. Statistics and the Data Analysis Process. Types of Data and Some Simple Graphical Displays.2. COLLECTING DATA SENSIBLY: Statistical Studies: Observation and Experimentation. Sampling. Simple Comparative Experiments. More on Experimental Design. Interpreting and Communicating the Results of Statistical Analyses. More on Observational Studies: Designing Surveys (online).3. GRAPHICAL METHODS FOR DESCRIBING DATA: Displaying Categorical Data: Comparative Bar Charts and Pie Charts. Displaying Numerical Data: Stem-and-Leaf Displays. Displaying Numerical Data: Frequency Distributions and Histograms. Displaying Bivariate Numerical Data. Bivariate and Multivariable Graphical Displays. Interpreting and Communicating the Results of Statistical Analyses.4. NUMERICAL METHODS FOR DESCRIBING DATA: Describing the Center of a Data Set. Describing Variability in a Data Set. Summarizing a Data Set: Boxplots. Interpreting Center and Variability: Chebyshev’s Rule, the Empirical Rule, and z Scores. Interpreting and Communicating the Results of Statistical Analyses.5. SUMMARIZING BIVARIATE DATA: Correlation. Linear Regression: Fitting a Line to Bivariate Data. Assessing the Fit of a Line. Nonlinear Relationships and Transformations. Interpreting and Communicating the Results of Statistical Analyses. Logistic Regression (online).6. PROBABILITY: Chance Experiments and Events. Definition of Probability. Basic Properties of Probability. Conditional Probability. Independence. Some General Probability Rules. Estimating Probabilities Empirically Using Simulation.7. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS: Random Variables. Probability Distributions for Discrete Random Variables. Probability Distributions for Continuous Random Variables. Mean and Standard Deviation of a Random Variable. Binomial and Geometric Distributions. Normal Distributions. Checking for Normality and Normalizing Transformations. Using the Normal Distribution to Approximate a Discrete Distribution.8. SAMPLING VARIABILITY AND SAMPLING DISTRIBUTIONS: Statistics and Sampling Variability. The Sampling Distribution of a Sample Mean. The Sampling Distribution of a Sample Proportion.9. ESTIMATION USING A SINGLE SAMPLE: Point Estimation. Large-Sample Confidence Interval for a Population Proportion. Confidence Interval for a Population Mean. Interpreting and Communicating the Results of Statistical Analyses. Bootstrap Confidence Intervals for a Population Proportion (optional). Bootstrap Confidence Intervals for a Population Mean (optional).10. HYPOTHESIS TESTING USING A SINGLE SAMPLE: Hypotheses and Test Procedures. Errors in Hypothesis Testing. Large-Sample Hypothesis Tests for a Population Proportion. Hypothesis Tests for a Population Mean. Power and Probability of Type II Error. Interpreting and Communicating the Results of Statistical Analyses. Exact Binomial Test and Randomization Test for a Population Proportion (optional). Randomization Test for a Population Mean (optional).11. COMPARING TWO POPULATIONS OR TREATMENTS: Inferences Concerning the Difference Between Two Population or Treatment Means Using Independent Samples. Inferences Concerning the Difference Between Two Population or Treatment Means Using Paired Samples. Large-Sample Inferences Concerning the Difference Between Two Population or Treatment Proportions. Interpreting and Communicating the Results of Statistical Analyses. Randomization-Based Inference for a Difference in Proportions (optional). Randomization-Based Inference for a Difference in Means (optional).12. THE ANALYSIS OF CATEGORICAL DATA AND GOODNESS-OF-FIT TESTS: Chi-Square Tests for Univariate Data. Tests for Homogeneity and Independence in a Two-way Table. Interpreting and Communicating the Results of Statistical Analyses.13. SIMPLE LINEAR REGRESSION AND CORRELATION: INFERENTIAL METHODS: Simple Linear Regression Model. Inferences ab