Emphasizing the conceptual development of statistical ideas, STATISTICAL IDEAS AND METHODS actively engages students and explains topics in the context of excellent examples and case studies. This text balances the spirit of statistical literacy with statistical methodology taught in the introductory statistics course. Jessica Utts and Robert Heckard built the book on two learning premises: (1) New material is much easier to learn and remember if it is related to something interesting or previously known; (2) New material is easier to learn if you actively ask questions and answer them for yourself. More than any other text available, STATISTICAL IDEAS AND METHODS motivates students to develop their statistical intuition by focusing on analyzing data and interpreting results as opposed to focusing on mathematical formulation. STATISTICAL IDEAS AND METHODS provides the exciting coverage from the authors' acclaimed MIND ON STATISTICS along with coverage of additional discrete random variables, nonparametric tests of hypotheses, multiple regression, two-way analysis of variance, and ethics.
Jessica Utts is a Professor of Statistics at the University of California at Davis, where she joined the faculty in 1978. She received her B.A. in Math and Psychology at SUNY Binghamton, and her M.A. and Ph.D. in Statistics at Penn State University. She is the author of SEEING THROUGH STATISTICS (3rd edition, 2005) and the co-author with Robert Heckard of STATISTICAL IDEAS AND METHODS (1st edition, 2006) both published by Duxbury Press. She is also the Editor-in-Chief of CYBERSTATS, an interactive online introductory statistics course. Jessica has been active in the Statistics Education community at the high school and college level. She served as a member and then chaired the Advanced Placement Statistics Development Committee for six years, and was a member of the American Statistical Association task force that produced the GAISE (Guidelines for Assessment and Instruction in Statistics Education) recommendations for Elementary Statistics courses. She is the recipient of the Academic Senate Distinguished Teaching Award and the Magnar Ronning Award for Teaching Excellence, both at the University of California at Davis. She is also a Fellow of the American Statistical Association, the Institute of Mathematical Statistics and the American Association for the Advancement of Science. Beyond statistics education Jessica's major contributions have been in applying statistics to a variety of disciplines, most notably to parapsychology, the laboratory study of psychic phenomena. She has appeared on numerous television shows, including Larry King Live, ABC Nightline, CNN Morning News and 20/20, and most recently appears in a documentary included on the DVD with the movie "Suspect Zero."
Robert F. Heckard is a senior lecturer in statistics at the Pennsylvania State University, where he has taught for over 30 years. He has taught introductory and intermediate applied statistics to more than 15,000 college students. Bob has been awarded several grants to develop multimedia and web-based instructional materials for teaching statistical concepts. He is the co-author of STATISTICAL IDEAS AND METHODS (1st edition, 2006, Duxbury Press) and is a co-author of CYBERSTATS, a web-based introductory course. As a consultant, he is active in the statistical analysis and design of highway safety research and has frequently been a consultant in cancer treatment clinical trials.
1. STATISTICS SUCCESS STORIES AND CAUTIONARY TALES. What is Statistics? Seven Statistical Stories with Morals. The Common Elements in the Seven Stories. 2. TURNING DATA INTO INFORMATION. Raw Data. Types of Data. Summarizing One or Two Categorical Variables. Finding Information in Quantitative Data. Pictures for Quantitative Data. Numerical Summaries of Quantitative Variables. Bell-Shaped Distributions of Numbers. 3. GATHERING USEFUL INFORMATION. Description or Decision? Using Data Wisely. Speaking the Language of Research Studies. Designing a Good Experiment. Designing a Good Observational Study. Difficulties and Disasters in Experiments and Observational Studies. 4. SAMPLING: SURVEYS AND HOW TO ASK QUESTIONS. The Beauty of Sampling. Sampling Methods. Difficulties and Disasters in Sampling. How to Ask Survey Questions. 5. RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES. Looking for Patterns with Scatterplots. Describing Linear Patterns with a Regression Line. Measuring Strength and Direction with a Regression Line. Why Answers May Not Make Sense. Correlation Does Not Prove Causation. 6. RELATIONSHIPS BETWEEN CATEGORICAL VARIABLES. Displaying Relationships between Categorical Variables. Risk, Relative Risk, Odds Ratio, and Increased Risk. Misleading Statistics about Risk. The Effect of a Third Variable and Simpson's Paradox. Assessing the Statistical Significance of a 2 x 2 Table. 7. PROBABILITY. Random Circumstances. Interpretations of Probability. Probability Definitions and Relationships. Basic Rules for Finding Probabilities. Strategies for Finding Complicated Probabilities. Using Simulation to Estimate Probabilities. Coincidences and Intuitive Judgments about Probability 8. RANDOM VARAIBLES. What is a Random Variable? Discrete Random Variables. Expectations for Random Variables. Binomial Random Variables. Continuous Random Variables. Normal Random Variables. Approximating Binominal Distribution Probabilities. Sums, Differences, and Combinations of Random Variables. 9. MEANS AND PROPORTIONS AS RANDOM VARIABLES. Understanding Dissimilarity among Samples. Sampling Distributions for Sample Proportions. What to Expect of Sample Means. What to Expect in Other Situations: Central Limit Theorem. Sampling Distribution for Any Statistic. Standardized Statistics. Student's t-Distribution: Replacing o with s. Statistical Inference. 10. ESTIMATING PROPORTIONS WITH CONFIDENCE. The Language and Notation of Estimation. Margin of Error. Confidence Intervals. Calculating a Margin of Error for 95% Confidence. General Theory of Confidence Intervals for a Proportion. Choosing a Sample Size for a Survey. Using Confidence Intervals to Guide Decisions. 11. TESTING HYPOTHESES ABOUT PROPORTIONS. Formulating Hypothesis Statements. The Logic of Hypothesis Testing: What if the Null is True? Reaching a Conclusion about the Two Hypotheses. Testing Hypotheses about a Proportion. The Role of Sample Size in Statistical Significance. Real Importance versus Statistical Significance. What Can Go Wrong: The Two Types of Errors. 12. MORE ABOUT CONFIDENCE INTERVALS. Examples of Different Estimation Situations. Standard Errors. Approximate 95% Confidence Intervals. General Confidence Intervals for One Mean or Paired Data. General Confidence Intervals for the Difference Between Two Means (Independent Samples). The Difference between Two Proportions (Independent Samples). Understanding Any Confidence Interval. 13. MORE ABOUT SIGNIFICANCE TESTS. The General Ideas of Significance Testing. Testing Hypotheses about One Mean or Paired Data. Testing the Difference Between Two Means (Independent Samples). Testing the Difference between Two Population Proportions. The Relationship between Significance Tests and Confidence Intervals. The Two Types of Errors and Their Probabilities. Evaluating Significance in Research Reports. 14. MORE ABOUT REGRESSION. Sample and Population Regression Models. Estimating the Standard Deviation for Regression. Inference about the Linear Regression Relationship. Predicting the Value y for an Individual. Estimating the Mean y at a Specified x. Checking for Conditions for Using regression Models for Inference. 15. MORE ABOUT CATEGORICAL VARIABLES. The Chi-Square Test for Two-Way Tables. Analyzing 2 x 2 Tables. Testing Hypotheses about One Categorical Variable: Goodness of Fit. 16. ANALYSIS OF VARIANCE. Comparing Means with the ANOVA F-Test. Details of One-Way Analysis of Variance. Other Methods for Comparing Populations. Two-Way Analysis of Variance. 17. ADDITIONAL DISCRETE RANDOM VARIABLES. Hypergeometric Distribution. Poisson Distribution. Multinomial Distribution. 18. NONPARAMETRIC TESTS OF HYPOTHESES. The Sign Test. The Two-Sample Rank-Sum Test. The Wilcoxon Signed-Rank Test. The Kruskal-Wallis Test. 19. MULTIPLE REGRESSION. The Multiple Linear Regression Model. Inference about Multiple Regression Models. Checking Conditions for Multiple Linear Regression. 20. TWO-WAY ANALYSIS OF VARIANCE. Assumptions and Models for Two-Way ANOVA. Testing for Main Effects and Interactions. 21. ETHICS. Ethical Treatment of Human and Animal Participants. Assurance of Data Quality. Appropriate Statistical Analysis. Fair Reporting of Results. 22. TURNING INFORMATION INTO WISDOM.Beyond the Data. Transforming Uncertainty into Wisdom. Making Personal Decisions. Control of Societal Risks. Understanding Our World. Getting to Know You. Words to the Wise.