Imagine the following situation.
You go to your doctor for a physical examination. You test positive for a spreadable, yet treatable virus-based disease.
You discover that the testing is somewhat accurate. If you have the disease, you will be diagnosed positive 75% of the time and negative 25% of the time. If you don’t have the disease, you will be diagnosed as negative 75% of the time and positive 25% of the time.
You also learn that 1% of the population has this disease. That is, one in one hundred people have contracted this virus.
Given that you tested positive, what are the odds that you have the disease? 75%? 50%? 25%? How concerned should you really be?
Interestingly, there is less than a 3% chance that you actually have the disease.
Here’s how the math works.
Imagine 10,000 people.
100 people will have the disease (1%), of which 75 (75%) will accurately test positive.
9,900 will not have the disease (99%), of which 2,475 (25%) will falsely test positive.
Therefore, of 2,550 people (75+2475) who test positive, only 75 in fact have the disease. 75/2,550 = .0294 which is less than 3%. The rest are false positives.
If this disease is totally treatable if diagnosed, I might be more concerned if I tested negative. 25 people who should be treated won’t be, and those individuals will continue to spread the disease.