After writing my last post, where I casually mentioned that probability and statistics are probably the single most important topics left out of the current standard math curriculum, I read the most recent entry at Cognitive Daily. They’re concerned that people don’t know probability, too. For an alarming example, they turn to a recent study on doctor-patient relationships.
In a course on noise and data analysis conducted in the astronomy department, we had to tackle problems like:
One test for a deadly, rare disease is 97% accurate. The disease is genetic and only about 1% of the population has it. The only treatment for this disease is expensive, but effective if you actually have the disease and potentially deadly if not you don’t. What would you do if your test results came back positive?
The correct answer, of course, is to take the test again. Even though the test is pretty accurate, because almost no one has the disease, the inaccuracy of the test will be responsible for most of the postive readings; false positives will far outnumber positives reported because disease is actually present. But because of the high accuracy of the test, the likelihood that you will get several false positives is low. The more times you test positive, the better the chances are you actually have the disease. And with the scenario I’ve presented, it’s worth your time to take the test again.
We also did astronomy in this class, too.