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Prosecutor’s Fallacy and Mammograms Case Study

Author(s): Carrie Diaz Eaton1, Sadie Kriegler

Unity College

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Summary:
An introduction to Prosecutor’s Fallacy, and False Positives/Negatives. By Dr. Diaz Eaton, Bates College, for use in DCS 105A, and inspired by Calling Bull & Calculated Risks.

Description

In this lab students will do the following: 1) Explain probability concepts such as Bayes Theorem, conditional probabilities, false positives and false negatives. 2) Explore how representation in the data set can affect interpretation of p-values. 3) Practice automating repetitive calculations through spreadsheets (and optional challenge - through R syntax and RStudio).

The Case Study itself has students analyze mammogram screening data from a large study in Germany. Calculate probabilities and conditional probabilities, then interpret the results to understand the real-world implications of screening policies.

Students will utilize the following... 

  • Spreadsheets: Organize data and perform calculations.
  • Visualizations: Use tree and box diagrams to simplify probability calculations.

In practice, I have students read the Case Study and the first couple of pages in advance of class and then students work in groups, and get "checked off" in class as complete during class or later in office hours or with a grader. 

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