Teaching Statistical Thinking with GAISE: Statistical Investigation Process, Multivariable Thinking, Simulation-Based Inference

Beth Chance, Karen McGaughey, Soma Roy

Cal Poly – San Luis Obispo

bchance@calpoly.edu

kmcgaugh@calpoly.edu

soroy@calpoly.edu

Workshop goals

• Help faculty to teach introductory statistics effectively in accordance with GAISE recommendations by:
• Immersing participants in hands-on activities for introducing students to statistical concepts, particularly with regard to:
• Statistical investigation process
• Multivariable thinking
• Simulation-based inference

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Acknowledgement

• This workshop is supported by a grant from the National Science Foundation’s IUSE (Improving Undergraduate STEM Education) program
• Expanding and assessing the art and practice of statistical thinking (#2235355)
• More information (and workshop materials!) can be found at: https://sites.google.com/view/eaapost

Schedule for Today

• Quick introductions (name, where and what teach)
• Introduction (GAISE Guidelines), Starting the course
• Multivariable thinking
• Statistical significance (simulation-based inference)
• Sampling (Collecting data/Making inferences)
• Lunch
• Confidence intervals
• Random assignment (Collecting data/Making inferences)

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Schedule for Tomorrow

• Comparing multiple groups
• Inference for two quantitative variables
• More complicated models
• Working with larger data sets
• Implementation advice

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What else will you see?

• Real research studies, Classroom ready materials
• Freely available applets that:
• Provide more intuition, visualizations of concepts, ease of use
• Make simulations more concrete
• Easily transition from simulation to theory
• Assessment ideas
• Project ideas

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Workshop Materials

• PowerPoint slides and handouts located at:

https://tinyurl.com/c5fbd4p9

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Brief History of Statistics Education

• 1923: Mathematical Association of America (MAA) recommends that statistics be in included as part of the junior and senior high math curriculums
• 1944: American Statistical Association (ASA) developed the Committee on Training Statisticians
• 1960-1961: Statistics taught as part of Continental Classroom
• 1967: ASA/NCTM joint committee on K-12 statistics and probability education
• 1970s: Experiential learning, Applications, “data analysis” (Tukey)
• Cal Poly graduates its first statistics major
• 1980s: Quantitative literacy
• 1990: TI-80 graphing calculator

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Any one vitally concerned with the teaching of high school pupils and observant of the rapidly growing public need for some knowledge of quantitative method in social problems must be asking what portions of statistical method can be brought within the comprehension of high school boys and girls, and in what way these can best be presented to them. (Walker 1931)

1990s: Calls for reform

1992

• (1992)

1995

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Brief History of Statistics Education

• 1997: First Advanced Placement Statistics Exam offered
• 1997: 7,667 → 2017: 217,000
• 2012: Common Core statistics standards grades 6-12
• 2014: “Active learning increases student performance in science, engineering, and mathematics” (Freeman et al., PNAS)
• 1990-2015: Statistics enrollments more than tripled, 35% at two-year colleges

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(2009)

Brief history of statistics education

• The TI-80 calculator came out in 1990 and quickly caught on in high school mathematics classes and started to be used more and more in statistics
• Consensus curriculum in 1990s
• Descriptive Statistics
• Probability/Design/Sampling Distributions
• Inference (testing and intervals)
• As the 1990s went on and into the early 2000s textbooks seemed to incorporate more real data, real studies, but the basic curriculum did not seem to change much

GAISE Guidelines

• Guidelines for Assessment and Instruction in Statistics Education
• https://www.amstat.org/education/guidelines-for-assessment-and-instruction-in-statistics-education-(gaise)-reports
• Recommendations for teaching introductory statistics at college level
• Comparable guidelines at PreK-12 level
• Endorsed by the American Statistical Association
• Originally written in 2005, revised in 2016, currently under revision

GAISE recommendations

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.

New Recommendations (probably)

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.
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. 

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GAISE recommendations (2025)

• Ten Recommendations for Statistics and Data Science
• Student Learning Outcomes for Introductory Statistics
• Sections on Data Science

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George Cobb

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• 2005 United States Conference on Teaching Statistics <https://escholarship.org/uc/item/6hb3k0nz>
• He talked about what we currently do and contrasted that with what was important to teach in an introductory statistics class
• We too often “teach a curriculum in which the most important ideas are often made to seem secondary.”
• “We need a new curriculum, centered not on the normal distribution, but on the logic of inference.”
• Before computers, there was no alternative. Now there is no excuse.

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George Cobb

• These methods may offer a quicker, less abstract bridge to the logic of inference while also emphasizing the scope of inference (random sampling, random assignment)
• May scaffold the transition to ‘traditional’ (asymptotic; theory-based methods) better than traditional theory/probability theory, etc.
• Normal approximation is found empirically rather than (falling out of the sky)
• This is what Fisher wanted to do, he just couldn’t back in 1936

More changes

• Major changes
• We went from maybe having a computer lab to all students owning laptops. (Or laptop, tablet, phone)�
• Data collection is much more prevalent, and with it the need for data analysis.�
• Statistical practice changed to more computer intensive methods, large datasets, multivariable methods, etc. �
• Recognition of the utility of simulation to enhance student understanding of random processes

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Still more changes

• Other changes directly impacting Stat 101
• Stats increasing in K-12 curriculum both in math classes, newly created stats classes and AP stats�
• Enrollments have skyrocketed (High school, two and four-year colleges)�
• Statistics education research has given us more knowledge of how and what students learn in Stat 101

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• Three things we are going to emphasize in this workshop
• Statistical investigation process
• Multivariable thinking: Not necessarily inference involving more than two variables (at least in the intro course), but just acknowledging that they are there, how we can view them, and seeing that they have an impact.
• Simulation-based inference

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The six steps of the statistical investigation process

Starting the course (~3 days)

Before our Chapter 1 we have a short preliminary section that covers three things:

• An overview of Statistics where students are introduced to the Six Step Statistical Investigation Process
• A quick look at some terms and concepts that are used with quantitative data
• Observation unit and Variable
• An exploration as to what probability is and how we will use it to help us understand Statistics

Robot Touch

Step 1. Ask a Research Question

• In general: Can touch from a humanoid robot evoke similar positive behavioral consequences as human touch?
• More specifically: Are participants in a counseling conversation more likely to comply with a request posed by a robot during conversation when the robot touches their hand?

Robot Touch

• Step 2: Design a study and collect data
• Volunteers were recruited on campus at a European university and received either course credit or monetary compensation. The study was announced as testing a robotic student counselor.
• Participants’ sex was balanced across the conditions.
• . In total, N = 49 subjects participated in the experiment (n = 25 in the touch condition, n = 24 in the no-touch control condition). 

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https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0249554

Robot Touch

Step 3: Explore the data.

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Participants who gave ambiguous answers (e.g., “maybe,” “I don’t know”, n = 6) were excluded from this analysis.

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Robot Touch

Step 4: Draw inferences beyond the data.

• “In support of H1, the test demonstrated that participants who were touched by the robot while it was announcing the course were significantly [Pearson χ² (1, N = 42) = 5.08, p = .02, φ = .35] more compliant (63%, n = 17 out of 21 answered ‘yes’) than participants in the no-touch condition (37%, n = 10 out of 21 answered ‘yes’).”

Robot Touch

Step 5: Formulate conclusions

• “The analyses of participants’ behavior revealed that they mostly reacted by smiling and laughing. Furthermore, participants who were touched by the robot complied significantly more frequently with a request posed by the robot during conversation, and reported better feelings compared to those who were not touched. However, there were no effects of robot touch on subjective evaluations of the robot or on the interaction experience.”

Robot Touch

Step 6: Look back and ahead.

• European graduate students
• Moderate to high technology expertise
• Specific kind of robot, co-speech
• Further validation of subjective measures scales
• Direct comparison to human touch

�Monty Hall Problem

Monty Hall Problem

• A popular TV game show, Let’s Make a Deal, featured a game where there were three doors. Behind one was a really nice prize and behind the other two were much less appealing prizes (like goats).
• If a contestant picked the correct door, he or she would win the car.
• What is the probability that the contestant would win the car under this scenario?

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• https://www.rossmanchance.com/chance/stat217S22/labs/lab0/lab0_1.html

Monty Hall Problem

• After a contestant picked a door, Monty would open up a different door (to show a goat) and then allow the contestant to switch to the unopened door or keep the one that was chosen.
• Should the contestant stick with the original door or switch?
• What is the probability of winning if the contestant stays with the original?
• What is the probability of winning if the contestant switches doors?
• Let’s simulate this.

Applets

• https://www.isi-stats.com/isi2nd/ISIapplets2021.html

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Monty Hall Problem

• The probability of an event is the long-run proportion of times the event would occur if the random process were repeated indefinitely (under identical conditions).

Key Ideas

• Want to expose students to the entire statistical process
• Want students to have preliminary exposure to ideas of variable, observational unit, distribution, model
• Temperature data
• Fan cost index
• Want students to understand what is meant by “probability”