1 / 23

A new approach to introductory statistics

A new approach to introductory statistics. Nathan Tintle Hope College. Outline. Case study: Hope College the past five years A completely randomization-based curriculum The bigger picture. Case study: Hope College. Five years ago 2 courses: algebra-based and calculus-based intro stats

javier
Download Presentation

A new approach to introductory statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related