False positive paradox
Okay kiddo, let's imagine you and your friends are playing a game of hide and seek. You're the seeker and you want to catch all your friends so you search for them in every nook and cranny in the house. But sometimes, you might accidentally think you found one of your friends and yell out "Gotcha!" only to realize that you didn't actually catch them, and they were just hiding somewhere else.
Now imagine that instead of playing hide and seek, we're talking about a test. Let's say you have a test for a very rare disease, which only affects 1 in 1000 people. That means that if there were 1000 people taking the test, only one person would have the disease.
But sometimes, even when someone doesn't have the disease, the test might show a positive result. This is called a false positive. It's kind of like when you thought you found your friend hiding but it turned out they weren't actually there.
Now, here's where things get a little tricky. Let's say you tested 10,000 people for the rare disease. That means that out of those 10,000 people there should be about 10 people who actually have the disease. However, the test is not perfect, and it might show a false positive in some people who don't actually have the disease. Let's say that the test has a 1% chance of giving a false positive.
So, out of those 10,000 people, there would be 10 people with the actual disease and 99 false positive results. That means that out of the 109 people who tested positive, only 10 actually have the disease! That's a very small percentage!
This is what we call the false positive paradox. Even when a test is very accurate, if it's used on a large number of people in a population where the disease is rare, there's a greater chance that a positive result is a false positive.
So, just like with your game of hide and seek, sometimes you might think you found what you were looking for, but it turns out it was just a mistake.
Now imagine that instead of playing hide and seek, we're talking about a test. Let's say you have a test for a very rare disease, which only affects 1 in 1000 people. That means that if there were 1000 people taking the test, only one person would have the disease.
But sometimes, even when someone doesn't have the disease, the test might show a positive result. This is called a false positive. It's kind of like when you thought you found your friend hiding but it turned out they weren't actually there.
Now, here's where things get a little tricky. Let's say you tested 10,000 people for the rare disease. That means that out of those 10,000 people there should be about 10 people who actually have the disease. However, the test is not perfect, and it might show a false positive in some people who don't actually have the disease. Let's say that the test has a 1% chance of giving a false positive.
So, out of those 10,000 people, there would be 10 people with the actual disease and 99 false positive results. That means that out of the 109 people who tested positive, only 10 actually have the disease! That's a very small percentage!
This is what we call the false positive paradox. Even when a test is very accurate, if it's used on a large number of people in a population where the disease is rare, there's a greater chance that a positive result is a false positive.
So, just like with your game of hide and seek, sometimes you might think you found what you were looking for, but it turns out it was just a mistake.
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