STAT 1404 GNTC Simpsons Paradox Aggregation Hides Trends Discussion

Once three threads are started, everyone else needs to respond to at least one of the posts and try to determine if Simpson’s Paradox is present in their example or not. No more than two or three responses per thread. Note: Just because ChatGPT provided the example does not mean it actually demonstrates Simpson’s paradox. The pictures I’m posting are just the question for this answer you don’t have to worry about it. Everything after this sentence is what you’ll be responding to.

Answer 1

Let’s consider an example involving admission rates to two departments, A and B, at a university over two years. We will use fictional numbers for the sake of illustration:

Year 1:

• Department A:
  • Total Applicants: 800
  • Admitted: 400 (50% admission rate)
• Department B:
  • Total Applicants: 200
  • Admitted: 100 (50% admission rate)

Year 2:

• Department A:
  • Total Applicants: 1,000
  • Admitted: 300 (30% admission rate)
• Department B:
  • Total Applicants: 300
  • Admitted: 200 (66.67% admission rate)

Now, if you look at the admission rates for each department separately, you might conclude that in both years, Department A had a lower admission rate than Department B. However, when you combine the data for both years without considering the yearly breakdown, you get the following:

Combined Data (Year 1 + Year 2):

• Department A:
  • Total Applicants: 1,800
  • Admitted: 700 (38.89% admission rate)
• Department B:
  • Total Applicants: 500
  • Admitted: 300 (60% admission rate)

Surprisingly, when you combine the data, it appears that Department A has a lower admission rate (38.89%) than Department B (60%). This is Simpson’s Paradox in action. The paradox occurs because the proportions of applicants from each department change over time. In Year 2, Department A received more applications, but the admission rate dropped, while Department B received fewer applications but had a higher admission rate.

The paradox highlights the importance of considering the context and potential confounding variables when interpreting data, as aggregating data without considering these factors can lead to misleading conclusions.