Teaching introductory statistics

With Active Learning, Statistical Investigation Process, and Simulation-based inference

Johnson County Community College

September 18, 2025

Motivation

• The flow of the semester
• Questions while studying for the final exam
• Technology + Active Learning advanced 🡪 more equitable/inclusive environments
• Our view of statistics vs. our students’

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The consequence

• Few students ever leave our course seeing statistics as this

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The consequence

• The better students may get a fuzzy impression

The consequence

• All too many noses stay too close to the canvas, and see disconnected details

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GAISE guidelines (2016): Guidelines for Assessment and Instruction in Statistics Education

• 1. Teach statistical thinking.
• Teach statistics as an investigative process of problem-solving and decision making.
• Give students experience with multivariable thinking.
• 2. Focus on conceptual understanding.
• 3. Integrate real data with a context and purpose.
• 4. Foster active learning.
• 5. Use technology to explore concepts and analyze data.
• 6. Use assessments to improve and evaluate student learning.

GAISE guidelines (2025 updates; in process):

Ten Recommendations for Statistics and Data Science

1. Teach statistics and data science as iterative processes of gleaning insights from data to inform evidence-based decisions.

2. Emphasize effective written and oral communication of results from data, with attention to the scope and limitations of conclusions.

3. Focus on conceptual understanding rather than algebraic manipulation and formulas.

4. Integrate real data with a context and purpose throughout the course.  Select data that are meaningful and engaging to the students. 

5. Encourage multivariable thinking. 

GAISE guidelines (2025 updates; in process):

Ten Recommendations for Statistics and Data Science

6. Incorporate software/apps to explore concepts and work with data.

7. Emphasize responsible and ethical conduct in the collection and use of data and in their analysis.

8. Employ evidence-based pedagogies that actively engage students in the learning process.

9. Use a variety of formative and summative assessments to improve teaching and learning.

10. Implement a course design that uses inclusive strategies to foster a sense of belonging. 

GAISE vs. the “real world”

• If GAISE is primarily about how to teach statistics (pedagogy), then the question is whether it has implications on what we teach (content)

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• Of course it does!

Unifying concepts – the cathedral of statistics�

The statistical investigation process (6-steps)

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The 4 pillars of statistics (causality, generalizability, estimation, inference)

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Simulation-based inference (generalizable method for inference that works in any application; tactile; concrete) (the 3S – statistic, simulate, strength of evidence)

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Single proportion inference with SBI �

Dolphin communication study under a contract with the Navy. The navy still has a marine mammal program.

• Dolphins and sea lions
• Ship and harbor protection
• Mine detection
• Equipment recovery

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Can dolphins communicate abstract ideas?

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Buzz

Doris

Step 1: Learn the Signals

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Step 1: Learn the Signals

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Step 2: Experiment

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Squeak !

Doris

Buzz

� What we observed

• In one set of trials, Buzz chose the correct button 15 out of 16 times.
• Based on the results, do you think dolphins can communicate abstract ideas?
• Talk with 1-2 people near you
• What do you think your students would say? What do you say?

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• Refined question: Do you think Buzz knew which button to push or is he guessing?
• What sort of results would lead you to think he is just guessing? Is he understanding?

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https://www.youtube.com/watch?v=yKWtJVbStoc&feature=youtu.be

Possible Explanations

• There are two possible reasons why Buzz chose the correct button so many times.
• He is randomly guessing which button to push and got 15 out of 16 correct just by chance.
• He is doing something other than guessing and was understanding what Doris was telling him.
• We want to model the random guessing and see how Buzz’s result fits in this model.
• How might we model the situation where Buzz is guessing (our chance model)?

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� Applet demonstration

• www.isi-stats.com
• ISI Applets>Intro course
• One proportion

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Simulation vs. Real Study

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� Three S Strategy

• Statistic: Compute the statistic from the observed data.
• Simulate: Identify a model that represents a chance explanation. Repeatedly simulate values of the statistic that could have happened when the chance model is true and form a distribution.
• Strength of evidence: Consider whether the value of the observed statistic is unlikely to occur the chance model is true.

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More Doris and Buzz

• In a follow-up study, the researcher put a wooden barricade down the middle of the pool. Buzz pushed the correct button 16/28 times.
• Research question?
• Apply the 3S strategy.

Overview

• Moving from informal to formal inference
• Laying a ground work of the 3-S and other key ideas
• The 6-step statistical investigation process

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6-steps

• Nearly always talk about �the six-steps

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Apply 6-steps to Doris and Buzz��

• Step 1. Ask a research question?
• Can dolphins communicate in an abstract manner?
• Step 2. Design a study and collect data.
• Train dolphins to test a specific research conjecture: Buzz pushes the correct button more often than he would without communication
• Observational units: Buzz’s attempts; Variable: Whether or not Buzz pushes the correct button (categorical; two levels
• Step 3. Explore the data
• Sample of 16 attempts
• 15/16 correct attempts; 0.9375 correct (sample proportion – the statistic)

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Apply 6-steps to Doris and Buzz��

• Step 4. Draw inferences beyond the data
• 3-S process (Statistic, Simulate, Strength of evidence)
• Overall selection process (random process of choosing a button) (parameter)
• Simulation result is that the statistic (15/16) is not the kind of thing that would happen very often if Buzz were just guessing
• Step 5. Formulate conclusions
• Does this study prove Buzz and Doris can communicate? (Causation)
• Does this suggest that all dolphins can communicate? (Generalizability)
• Step 6. Look back and ahead
• Limitations and opportunities for future studies– assumptions of study design (reflections; time of day; Doris🡪Buzz)

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Key take aways

• Students have a natural intuition that 15/16 is not typical when guessing
• Coin flipping (50/50 chance model) is a tactile scaffold that students naturally think of to model guessing (chance)
• Starting by confirming intuition is accessible to students of many backgrounds and provides a firm foundation for moving forward
• Students can explain this thinking with no prior statistical coursework
• Giving them a familiar logic they can return to throughout the course
• Bridges to theory-based approaches

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Table of contents for Intro to Stat. Invest.

• Preliminaries
• Unit 1: Four pillars of inference
• Chapter 1: Significance
• Chapter 2: Generalization
• Chapter 3: Estimation
• Chapter 4: Causation
• Unit 2: Comparing two groups
• Chapter 5: Comparing two proportions
• Chapter 6: Comparing two means
• Chapter 7: Paired data

• Unit 3: Analyzing more general situations
• Chapter 8: Comparing more than two proportions
• Chapter 9: Comparing more than two means
• Chapter 10: Two quantitative variables

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• Beyond unit 4: Have all of the content for a ‘second course’ in statistics with Units 1-3 as a pre-requisite (Intermediate Statistical Investigations)

Moving forward throughout the course

• Key ideas of significance, estimation, generalizability and causality early in the course (Ch 1-5)
• Application to increasingly complex sets of data as the course progresses (Ch 6-11)
• Get all the same learning objectives as a ‘typical’ introductory statistics course
• Do so in a manner that builds a firmer foundation and deeper conceptual understanding of key statistical ideas (e.g., understanding logic of inference when doing theory-based tests)

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Resources

• www.isi-stats.com
• https://sites.google.com/view/eaapost/home (faculty development resources; all free)
• Ongoing NSF-supported EAPost faculty development program related to things you’ve heard here
• Reach out for details: nathan.tintle@isi-stats.com