Probability Statistics

Question

What probability does this question fall under?

2. A cold and flu study is looking at how two different medications work on sore throats and fever. Results are as follows:

• Sore throat - Medication A: Success rate - 90% (101 out of 112 trials were successful)
• Sore throat - Medication B: Success rate - 83% (252 out of 305 trials were successful)

• Fever - Medication A: Success rate - 71% (205 out of 288 trials were successful)
• Fever - Medication B: Success rate - 68% (65 out of 95 trials were successful)
Analyze the data and explain which one would be the better medication for both a sore throat and a fever.

Answer 1

If we combine the studies medication A had 306 successes out of 400.

 

B had 317 successes out of 400.

 

So if we want to decide which had a better "overall" success rate it would be B.

 

This seems counter-intuitive with the individual test data and is an example of what is called in statistics "Simpson's Paradox."

 

Does this make sense?