A new approach to introductory statistics

1. A new approach to introductory statistics Nathan Tintle Hope College

2. Outline • Case study: Hope College the past five years • A completely randomization-based curriculum • The bigger picture

3. Case study: Hope College • Five years ago • 2 courses: algebra-based and calculus-based intro stats • 3 hours of lecture with graphing calculator use; 1 hour of computer lab work (algorithmic type labs) • Process for change • Curricular change • Pedagogical change • Infrastructure change • Client discipline buy-in • Math department buy-in

4. Case study: Hope College • Where we are now: • Three courses • Algebra-based intro stats • Accelerated intro stats (for AP Stats students and others) • Second course in stats (multivariable topics) • Note: NO Calculus pre-requisite’s • New dedicated 30-seat computer lab for statistics (HHMI funded) • Buy-in of relevant parties • Revolutionary new curriculum • Embrace the GAISE pedagogy: active learning, concept based, real data • Changes in content

5. Content changes • George Cobb, USCOTS 2005 • A challenge • Rossman and Chance 2007 NSF-CCLI grant • Modules • Hope College 2009 • Entire curriculum

6. Traditional curriculum • Unit 1. Descriptive statistics and sample design • Unit 2. Probability and sampling distributions • Unit 3. Statistical inference No multivariable topics; No second course in statistics without calculus

7. Curriculum outline • Unit 1. (1st course) • Introduction to inferential statistics using randomization techniques • Unit 2. (1st course) • Revisiting statistical inference using asymptotic approaches, confidence intervals and power • Unit 3. (2nd course) • Multivariable statistical inference: Controlling undesired variability Randomization techniques=Resampling techniques=permutation tests

8. Unit 1. • Ch 1. Introduction to Statistical Inference: One proportion • Ch 2. Comparing two proportions: Randomization Method • Ch 3. Comparing two means: Randomization Method • Ch 4. Correlation and regression: Randomization Method

9. Unit 2. • Ch 5. Correlation and regression: revisited* • Ch 6. Comparing means: revisited* • Ch 7. Comparing proportions: revisited* • Ch 8. Tests of a single mean and proportion *Connecting asymptotic tests with the randomization approach, confidence intervals and power

10. Unit 3. • Chapter 9: Introduction to multiple regression (ANCOVA/GLM) • Chapter 10: Multiple logistic regression • Chapter 11: Multi-factor experimental design

11. Key Changes • Descriptive statistics • Only select topics are taught (e.g. boxplots); other topics are reviewed (based on assessment data; CAOS) • Study design • Discussed from the beginning and emphasized throughout in the context of its impact on inference

12. Key Changes • Inference • Starts on day 1; in front of the students throughout the entire semester • Probability and Sampling distributions • More intuitive approach; de-emphasized dramatically

13. Key other changes • Cycling • Projects • Case studies • Research Articles • Power

14. Key other changes • Pedagogy • Typical class period

15. Example from the curriculum • Chapter 2 • (pdf is available at http://math.hope.edu/aasi)

16. Assessment • CAOS • Better learning on inference • Mixed results on descriptive statistics • Increased retention (4-month follow-up)

17. Big picture • Modularity • Advantages: broader impact; flexibility • Disadvantages: can’t fully realize the potential of a randomization-based curriculum • Efficiency of approach allows for cycling over core concepts, quicker coverage of other topics and additional topics are possible

18. Big picture • Resampling methods in general • Permutation tests: Not only a valuable technique practically, but a motivation for inference • Bootstrapping? • Keeping the main thing the main thing • Core logic of statistical inference (Cobb 2007)

19. Big Picture • Motivating concepts with practical, interesting, relevant examples • Capitalizing on students intuition and interest • Real, faculty and/or student-driven, research projects • Danny’s example translated to the traditional Statistics curriculum • One sample Z Test • Calculating probabilities based on the central limit theorem • Art and science of learning from data (Agresti and Franklin 2009)

20. Big Picture • Confidence intervals • Ranges of plausible values under the null hypothesis • “Invert” the test to get the confidence interval • Power • Reinforcing logic of inference • Practical tool

21. Big Picture • The second course • Projects can be student driven or involve students working with faculty in other disciplines • Other efforts • CATALST • West and Woodard • Rossman and Chance • Others

22. Textbook website • http://math.hope.edu/aasi -First two chapters -Email me for copies of other chapters -If interested in pilot testing, please talk to me -Draft of paper in revision at the Journal of Statistics Education is available (assessment results)

23. Acknowledgements • Funding • Howard Hughes Medical Institute Undergraduate Science Education Program (Computer lab, pilot testing and initial curriculum development) • Great Lakes College Association (Assessment and first revision) • Teagle Foundation (second revision this summer) • Co-authors: Todd Swanson and Jill VanderStoep • Others: Allan Rossman, Beth Chance, George Cobb, John Holcomb, Bob delMas