A new approach to introductory statistics Nathan Tintle Hope College

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

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

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

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

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

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

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

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

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

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

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

Key other changes Cycling Cycling Projects Projects Case studies Case studies Research Articles Research Articles Power Power

Key other changes Pedagogy Pedagogy Typical class period Typical class period

Example from the curriculum Chapter 2 Chapter 2 (pdf is available at (pdf is available at

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

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

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

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

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

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

Textbook website First two chapters - 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)

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