Best Practices for Teaching Introductory Statistics in the Modern Classroom, eCOTS workshop

Beth Chance (bchance@calpoly.edu)

eCOTS, 2026

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Step 1: Ask a research question

What is a healthy body temperature?

German physician Carl Wunderlich analyzed a million temperatures from 25,000 patients and in 1869 published that the normal human-body temperature is 98.6⁰ F. But several more recent studies have found that number to be too high, leading to speculation that Dr. Wunderlich was wrong, or that human body temperature has changed over time.

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Activity goals

• Use real data that’s meaningful to students
• Explore data within the context of a genuine research question
• Add to previous knowledge
• Sow the seeds for statistical inference/ thinking
• Scaffold an activity across multiple points of the course

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Step 2: Collect data�

• Leftover “no touch” thermometer
• As students settle in classroom
• Enter responses into google sheet

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Issues to keep in mind

• My temperature gun seems a little wacky
• Infrared temperature guns may have a built-in bias (e.g., article, 98.6 – 0.75)
• Students often note that they have recently…
• Rushed to class
• Woken up
• Laid in the sun
• Been ill
• Any other issues?

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Step 3: Explore data

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Modelling body temps (1 of 2)

• Which distribution do you think is most plausible? Least plausible?
• For a class of students vs. repeated observations on yourself?

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Modelling body �temps (2 of 2)

• Data = truth + random “error”
• What one number would you use to estimate your “true” body temperature?
• How accurate would you think that estimate is?
• What one number would you use to estimate the body temperature of a random Cal Poly student? How accurate?

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Normal distribution

• If believe students’ temperatures follow an approximately normal distribution, then
• approximately 68% of students have an observation within one standard deviation of the mean
• 95% within two standard deviations of the mean

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Step 4: Draw conclusions beyond the data

• Based on our sample, about 95% of healthy temperatures should be between 93.2 and 100.0 ^oF
• Among Cal Poly students
• Assuming the normal distribution pattern
• Assuming we have a reasonable estimate of the standard deviation of temperatures
• Assuming accurate measurements

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Later in the course: Inference for one mean

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Simulation-based inference for one mean

• Goal: generate random samples (of the same size) from a population that has a mean of 98.6, explore sample to sample variation
• Option 1: Sample from theoretical distribution
• Option 2: Bootstrapping
• Option 3: Sample from finite population
• Transition to t-statistic

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Applet demo (1 of 2)

• Sampling from Finite Population applet

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Applet demo (2 of 2)

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• Focus on SD of ….

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Explorations

• Does the shape of the population matter?
• What is the impact of the value of the population standard deviation?
• What is the impact of a change in sample size?
• What is the impact of changing the number of samples?

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2SD interval

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Later in the course

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Possible extensions

• Compare temperatures across groups
• Start introducing distinction between “within group variation” vs. “between group variation”
• How much of the variation in body temperatures is explained by…
• Mackowiak, Wasserman, & Levine (Journal of the American Medical Association, 1992)
• Stanford data across 3 eras
• Protsiv et al., 2020

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