You’re not feeling so good, so you go to see your doctor.
She taps your kneecaps, looks in your ears and down your throat, listens to your heart and lungs, and palpates your abdomen. She mutters to herself and makes some notes. She leaves and in a few minutes a nurse comes in. “I need to draw some blood for a test Dr. Filomena wants.” You make your arm available and wince as the needle goes in. The syringe fills and the nurse withdraws the needle. He tells you to get dressed and leaves. Moments later, you’re in the doctor’s office. The test has been completed.
Dr. F explains to you that she thinks you have Burgdorfer syndrome (a disease that does not exist as far as I know. I made it up for illustration purposes). She tells you that it afflicts approximately one percent of the population and the test she has used to diagnose it has an accuracy rate of around 90%. She says that it’s easy to treat — you just take a medication called Tamoxifolate for the rest of your life.
You tell her you’d rather not go on a permanent medication like that and ask if there are any other options.
She says there aren’t and that since the test gave you a positive result, you have a 90% chance of having the disease (since that’s the accuracy rate of the test), and you should take the prescription she offers and get it filled.
Foreboding in your heart, you leave the doctor’s office wondering whether she’s right about your chances of having the disease. Assume her numbers about the prevalence of the disease in the population (1%) and the accuracy of the test (90%) are correct. Is your chance of having the disease, given a positive test result, really 90%? What do you think? Tell me in the comments. I’ll have an answer for you tomorrow.