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. A faculty member at Cal Poly from 1979 until 2009, Roxy 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. Roxy 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. Roxy 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, Roxy is also co-editor of “Statistical Case Studies: A Collaboration Between Academe and Industry” and a member of the editorial board for “Statistics: A Guide to the Unknown, 4th Edition.” Outside the classroom, Roxy likes to travel and spends her spare time reading mystery novels. She also collects Navajo rugs and heads to Arizona and New Mexico whenever she can find the time. Chris retired from high school teaching after teaching mathematics at Washington High School, Cedar Rapids, Iowa, for more than 30 years. His teaching load included Advanced Placement Statistics and Calculus, precalculus and an assortment of other classes. He was talked out of retirement and taught Applied Statistics and Experimental Design at Grinnell College in Grinnell, Iowa for 10 years. Chris graduated from Iowa State University majoring in mathematics and philosophy. In his graduate work at the University of Iowa he concentrated on statistics, computer programming, psychometrics, and test development. He is a former member (twice!) of the Advanced Placement Statistics Test Development Committee, was a table leader at the AP Statistics reading for seventeen years and was the moderator of the AP Statistics Teacher Community for 15 years. He has authored or co-authored 3 books and an assortment of materials dedicated to the teaching and learning of statistics. His current Big Project is SPLAT, Statistical Package for Learning and Teaching, a freeware computer program targeted at AP Statistic teachers and students. The late Tom Short was an Associate Professor in the Statistics Program within the Department of Mathematics at West Chester University of Pennsylvania. He also previously held faculty positions at Villanova University, Indiana University of Pennsylvania and John Carroll University. He was a Fellow of the American Statistical Association and received the 2005 Mu Sigma Rho Statistics Education Award. Tom served on the leadership team for readings of the Advanced Placement (AP) Statistics Exam, and on the AP Statistics Development Committee. He also served on the Board of Directors of the American Statistical Association. Tom treasured the time he shared with his four children and the many adventures experienced with his wife, Darlene.

• 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. 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 about the Slope of the Population Regression Line.