Lecture on Statistics and Simpson's Paradox

Introduction

• Evaluation of success in medical treatments and social programs often based on population impact.
• Example scenario involves treatment of disease in both people and cats.
  • Treated: 1 cat and 4 people, 1 cat and 1 person recover, 3 people die.
  • Untreated: 4 cats and 1 person, 3 cats recover, 1 person and 1 cat die.

Outcome Analysis

• Treated Animals:
  • 100% of treated cats survive.
  • 25% of treated humans survive.
• Untreated Animals:
  • 75% of untreated cats survive.
  • 0% of untreated humans survive.
• Aggregated Data:
  • 40% of all treated individuals survive.
  • 60% of all untreated individuals survive.

Simpson's Paradox

• Statistical paradox where conclusions vary based on data segregation.
• Statistics alone can't solve the paradox; understanding causality is essential.
• Example Analysis:
  • If humans are more severely affected and more likely to be treated, lower survival rates in treated group can still mean treatment helps.
  • If treatment access is biased (e.g., cost reasons), survival rates may indicate treatment ineffectiveness.

Importance of Experiment Design

• Controlled experiments should avoid external causal influences.
• Uncontrolled experiments must account for outside biases.

Example: Education Comparison

• Wisconsin vs. Texas standardized test scores.
• Overall scores higher in Wisconsin, but Texas students perform better when broken down by race.
• Socioeconomic factors affect overall results.

Graphical Representation

• Graphs can illustrate Simpson's paradox: separate trends differ from overall trend.
• Example: Money and happiness in people vs. cats.

Conclusion

• Paradoxes like Simpson's paradox highlight the need for context in data interpretation.
• Statistics can be straightforward if context aligns with data.

Additional Resources

• Practice is key in understanding subjects deeply.
• Sponsor: Brilliant.org offers courses in probability, logic, and quantitative finance.
  • Example puzzles to solve.
  • Use URL brilliant.org/minutephysics for more information.