A new approach A new approach to introductory to introductory

statisticsstatisticsNathan TintleNathan Tintle

Hope CollegeHope College

OutlineOutline

Case study: Hope College the past Case study: Hope College the past five yearsfive years

A completely randomization-based A completely randomization-based curriculumcurriculum

The bigger pictureThe bigger picture

Case study: Hope CollegeCase study: Hope College

Five years agoFive years ago 2 courses: algebra-based and calculus-based intro 2 courses: algebra-based and calculus-based intro

statsstats 3 hours of lecture with graphing calculator use; 1 3 hours of lecture with graphing calculator use; 1

hour of computer lab work (algorithmic type labs)hour of computer lab work (algorithmic type labs) Process for changeProcess for change

Curricular changeCurricular change Pedagogical changePedagogical change Infrastructure changeInfrastructure change Client discipline buy-inClient discipline buy-in Math department buy-inMath department buy-in

Case study: Hope CollegeCase study: Hope College Where we are now: Where we are now:

Three coursesThree courses Algebra-based intro statsAlgebra-based intro stats Accelerated intro stats (for AP Stats students and Accelerated intro stats (for AP Stats students and

others)others) Second course in stats (multivariable topics)Second course in stats (multivariable topics) Note: NO Calculus pre-requisite’sNote: NO Calculus pre-requisite’s

New dedicated 30-seat computer lab for New dedicated 30-seat computer lab for statistics (HHMI funded)statistics (HHMI funded)

Buy-in of relevant partiesBuy-in of relevant parties Revolutionary new curriculumRevolutionary new curriculum

Embrace the GAISE pedagogy: active learning, Embrace the GAISE pedagogy: active learning, concept based, real dataconcept based, real data

Changes in contentChanges in content

Content changesContent changes

George Cobb, USCOTS 2005George Cobb, USCOTS 2005 A challengeA challenge

Rossman and Chance 2007 NSF-Rossman and Chance 2007 NSF-CCLI grantCCLI grant ModulesModules

Hope College 2009Hope College 2009 Entire curriculumEntire curriculum

Traditional curriculumTraditional curriculum

Unit 1. Descriptive statistics and Unit 1. Descriptive statistics and sample designsample design

Unit 2. Probability and sampling Unit 2. Probability and sampling distributionsdistributions

Unit 3. Statistical inferenceUnit 3. Statistical inferenceNo multivariable topics;

No second course in statistics without calculus

Curriculum outlineCurriculum outline

Unit 1. (1Unit 1. (1stst course) course) Introduction to inferential statistics Introduction to inferential statistics

using randomization techniquesusing randomization techniques Unit 2. (1Unit 2. (1stst course) course)

Revisiting statistical inference using Revisiting statistical inference using asymptotic approaches, confidence asymptotic approaches, confidence intervals and powerintervals and power

Unit 3. (2Unit 3. (2ndnd course) course) Multivariable statistical inference: Multivariable statistical inference:

Controlling undesired variabilityControlling undesired variabilityRandomization techniques=Resampling techniques=permutation tests

Unit 1.Unit 1.

Ch 1. Introduction to Statistical Ch 1. Introduction to Statistical Inference: One proportionInference: One proportion

Ch 2. Comparing two proportions: Ch 2. Comparing two proportions: Randomization MethodRandomization Method

Ch 3. Comparing two means: Ch 3. Comparing two means: Randomization MethodRandomization Method

Ch 4. Correlation and regression: Ch 4. Correlation and regression: Randomization MethodRandomization Method

Unit 2.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 proportionCh 8. Tests of a single mean and proportion

*Connecting asymptotic tests with the *Connecting asymptotic tests with the randomization approach, confidence randomization approach, confidence intervals and powerintervals and power

Unit 3.Unit 3.

Chapter 9: Introduction to multiple Chapter 9: Introduction to multiple regression (ANCOVA/GLM)regression (ANCOVA/GLM)

Chapter 10: Multiple logistic Chapter 10: Multiple logistic regressionregression

Chapter 11: Multi-factor Chapter 11: Multi-factor experimental designexperimental design

Key ChangesKey Changes

Descriptive statisticsDescriptive statistics Only select topics are taught (e.g. Only select topics are taught (e.g.

boxplots); other topics are reviewed boxplots); other topics are reviewed (based on assessment data; CAOS)(based on assessment data; CAOS)

Study designStudy design Discussed from the beginning and Discussed from the beginning and

emphasized throughout in the context emphasized throughout in the context of its impact on inferenceof its impact on inference

Key ChangesKey Changes

InferenceInference Starts on day 1; in front of the students Starts on day 1; in front of the students

throughout the entire semesterthroughout the entire semester

Probability and Sampling Probability and Sampling distributionsdistributions More intuitive approach; de-emphasized More intuitive approach; de-emphasized

dramaticallydramatically

Key other changesKey other changes CyclingCycling

ProjectsProjects

Case studiesCase studies

Research ArticlesResearch Articles

PowerPower

Key other changesKey other changes

PedagogyPedagogy Typical class periodTypical class period

Example from the Example from the curriculumcurriculum

Chapter 2Chapter 2 (pdf is available at (pdf is available at

http://math.hope.edu/aasihttp://math.hope.edu/aasi) )

AssessmentAssessment

CAOSCAOS Better learning on inferenceBetter learning on inference Mixed results on descriptive statisticsMixed results on descriptive statistics Increased retention (4-month follow-up)Increased retention (4-month follow-up)

Big pictureBig picture

ModularityModularity Advantages: broader impact; flexibilityAdvantages: broader impact; flexibility Disadvantages: can’t fully realize the Disadvantages: can’t fully realize the

potential of a randomization-based potential of a randomization-based curriculumcurriculum Efficiency of approach allows for cycling Efficiency of approach allows for cycling

over core concepts, quicker coverage of over core concepts, quicker coverage of other topics and additional topics are other topics and additional topics are possiblepossible

Big pictureBig picture

Resampling methods in generalResampling methods in general Permutation tests: Not only a valuable Permutation tests: Not only a valuable

technique practically, but a motivation for technique practically, but a motivation for inferenceinference

Bootstrapping?Bootstrapping?

Keeping the main thing the main thingKeeping the main thing the main thing Core logic of statistical inference (Cobb Core logic of statistical inference (Cobb

2007)2007)

Big PictureBig Picture

Motivating concepts with practical, Motivating concepts with practical, interesting, relevant examplesinteresting, relevant examples Capitalizing on students intuition and interestCapitalizing on students intuition and interest Real, faculty and/or student-driven, research Real, faculty and/or student-driven, research

projectsprojects Danny’s example translated to the traditional Danny’s example translated to the traditional

Statistics curriculumStatistics curriculum One sample Z TestOne sample Z Test Calculating probabilities based on the central limit Calculating probabilities based on the central limit

theoremtheorem Art and science of learning from data (Agresti Art and science of learning from data (Agresti

and Franklin 2009)and Franklin 2009)

Big PictureBig Picture

Confidence intervalsConfidence intervals Ranges of plausible values under the Ranges of plausible values under the

null hypothesisnull hypothesis ““Invert” the test to get the confidence Invert” the test to get the confidence

intervalinterval

PowerPower Reinforcing logic of inferenceReinforcing logic of inference Practical toolPractical tool

Big PictureBig Picture

The second courseThe second course Projects can be student driven or Projects can be student driven or

involve students working with faculty in involve students working with faculty in other disciplinesother disciplines

Other effortsOther efforts CATALSTCATALST West and WoodardWest and Woodard Rossman and ChanceRossman and Chance OthersOthers

Textbook websiteTextbook website

http://math.hope.edu/aahttp://math.hope.edu/aasisi

-First two chapters-First two chapters-Email me for copies of -Email me for copies of

other chaptersother chapters-If interested in pilot -If interested in pilot

testing, please talk to metesting, please talk to me-Draft of paper in revision -Draft of paper in revision

at the Journal of Statistics at the Journal of Statistics Education is available Education is available (assessment results)(assessment results)

AcknowledgementsAcknowledgements

FundingFunding Howard Hughes Medical Institute Undergraduate Howard Hughes Medical Institute Undergraduate

Science Education Program (Computer lab, pilot Science Education Program (Computer lab, pilot testing and initial curriculum development)testing and initial curriculum development)

Great Lakes College Association (Assessment and Great Lakes College Association (Assessment and first revision)first revision)

Teagle Foundation (second revision this summer)Teagle Foundation (second revision this summer) Co-authors: Todd Swanson and Jill Co-authors: Todd Swanson and Jill

VanderStoepVanderStoep Others: Allan Rossman, Beth Chance, George Others: Allan Rossman, Beth Chance, George

Cobb, John Holcomb, Bob delMasCobb, John Holcomb, Bob delMas