Let's analyze the given data for both the early stage and advanced stage treatments and then look at the aggregated data, step-by-step.
### 1. Early Stage Data Analysis
For the early stage treatment:
- Treatment A:
- Remissions: 5
- Deaths: 1
- Rate ([tex]\( \text{Remissions} / (\text{Remissions} + \text{Deaths}) \)[/tex]): 0.833
- Treatment B:
- Remissions: 10
- Deaths: 4
- Rate: 0.714
### 2. Advanced Stage Data Analysis
For the advanced stage treatment:
- Treatment A:
- Remissions: 4
- Deaths: 6
- Rate: 0.400
- Treatment B:
- Remissions: 1
- Deaths: 4
- Rate: 0.200
### 3. Aggregated Data Analysis
For the aggregated treatments data:
- Treatment A:
- Remissions: 9
- Deaths: 7
- Rate: 0.563
- Treatment B:
- Remissions: 11
- Deaths: 8
- Rate: 0.579
### Conclusion:
- When we look at the early stage, Treatment A has a higher rate of remission (0.833) compared to Treatment B (0.714).
- For the advanced stage, Treatment A again has a higher rate of remission (0.400) compared to Treatment B (0.200).
- However, when we look at the aggregated data, Treatment B has a slightly higher overall remission rate (0.579) compared to Treatment A (0.563).
This scenario is an example of Simpson's Paradox, where treatment B appears to be better when aggregated, even though treatment A appears better in each individual stage (early and advanced).
Thus, the true statement for this scenario is an illustration of Simpson's Paradox.
