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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

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)
• 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
• 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
• 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

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