Transcript slides - Project MOSAIC

A new approach to
introductory statistics
Nathan Tintle
Hope College
Outline
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Case study: Hope College the past five years
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A completely randomization-based curriculum
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The bigger picture
Case study: Hope College
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Five years ago
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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
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Curricular change
Pedagogical change
Infrastructure change
Client discipline buy-in
Math department buy-in
Case study: Hope College
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Where we are now:
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Three courses
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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
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Embrace the GAISE pedagogy: active learning, concept based, real
data
Changes in content
Content changes
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George Cobb, USCOTS 2005
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Rossman and Chance 2007 NSF-CCLI grant
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A challenge
Modules
Hope College 2009
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Entire curriculum
Traditional curriculum
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Unit 1. Descriptive statistics and sample design
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Unit 2. Probability and sampling distributions
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Unit 3. Statistical inference
No multivariable topics;
No second course in statistics without calculus
Curriculum outline
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Unit 1. (1st course)
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Unit 2. (1st course)
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Introduction to inferential statistics using
randomization techniques
Revisiting statistical inference using asymptotic
approaches, confidence intervals and power
Unit 3. (2nd course)
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Multivariable statistical inference: Controlling
undesired variability
Randomization techniques=Resampling techniques=permutation tests
Unit 1.
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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
Unit 2.
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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
Unit 3.
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Chapter 9: Introduction to multiple regression
(ANCOVA/GLM)
Chapter 10: Multiple logistic regression
Chapter 11: Multi-factor experimental design
Key Changes
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Descriptive statistics
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Only select topics are taught (e.g. boxplots); other
topics are reviewed (based on assessment data;
CAOS)
Study design
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Discussed from the beginning and emphasized
throughout in the context of its impact on inference
Key Changes
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Inference
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Starts on day 1; in front of the students throughout
the entire semester
Probability and Sampling distributions
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More intuitive approach; de-emphasized dramatically
Key other changes
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Cycling
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Projects
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Case studies
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Research Articles
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Power
Key other changes
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Pedagogy
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Typical class period
Example from the curriculum
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Chapter 2
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(pdf is available at http://math.hope.edu/aasi)
Assessment
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CAOS
Better learning on inference
 Mixed results on descriptive statistics
 Increased retention (4-month follow-up)
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Big picture
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Modularity
Advantages: broader impact; flexibility
 Disadvantages: can’t fully realize the potential of a
randomization-based curriculum
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Efficiency of approach allows for cycling over core
concepts, quicker coverage of other topics and additional
topics are possible
Big picture
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Resampling methods in general
Permutation tests: Not only a valuable technique
practically, but a motivation for inference
 Bootstrapping?
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Keeping the main thing the main thing
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Core logic of statistical inference (Cobb 2007)
Big Picture
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Motivating concepts with practical, interesting, relevant
examples
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Capitalizing on students intuition and interest
Real, faculty and/or student-driven, research projects
Danny’s example translated to the traditional Statistics
curriculum
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One sample Z Test
Calculating probabilities based on the central limit theorem
Art and science of learning from data (Agresti and Franklin
2009)
Big Picture
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Confidence intervals
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Ranges of plausible values under the null hypothesis
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“Invert” the test to get the confidence interval
Power
Reinforcing logic of inference
 Practical tool
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Big Picture
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The second course
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Projects can be student driven or involve students
working with faculty in other disciplines
Other efforts
CATALST
 West and Woodard
 Rossman and Chance
 Others
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Textbook website
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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)
Acknowledgements
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Funding
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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