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A new approach to introductory statistics

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Title: 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-requisites
  • 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 techniquesResampling
techniquespermutation 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 cant 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
  • Dannys 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
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