Errors in the interpretation of experiments
A piece from Peter Norvig's excellent article on experimental errors .
Cerebral vasculitis affects one person in a million, and seasonal cold affects every tenth. Suppose we have developed tests for these diseases, which give the correct answer in 99% of cases (both for the sick and for the healthy).
What conclusion should make a doctor, having the following data:
In Nikolai, the test for cerebral vasculitis gave a positive result (the result is correct in 99% of cases).
Sergey has tested for cold for a positive result (the result is correct in 99% of cases).
')
Probably the doctor will decide that most likely both are sick. If you think so too, then your intuition let you down. The chance that Nikolai is sick with vasculitis is 0.01%. This may seem incredible, but it is. Perhaps the following example will help you understand why.
Suppose we have a device for determining the Martians, and it gives the correct answer in 99% of cases. We scan, for example, deputies one by one, the result is always negative. But when it comes to Vladimir Volfovich, the inscription lights up that he is a Martian. Will you believe the device? Probably not, this is exactly the 1% of cases when the device gives the wrong answer.
In the case of vasculitis, our test of 1% error will give a positive result for 10,000 people out of a million, but only one of these 10,000 people will actually be sick.
Cerebral vasculitis affects one person in a million, and seasonal cold affects every tenth. Suppose we have developed tests for these diseases, which give the correct answer in 99% of cases (both for the sick and for the healthy).
What conclusion should make a doctor, having the following data:
In Nikolai, the test for cerebral vasculitis gave a positive result (the result is correct in 99% of cases).
Sergey has tested for cold for a positive result (the result is correct in 99% of cases).
')
Probably the doctor will decide that most likely both are sick. If you think so too, then your intuition let you down. The chance that Nikolai is sick with vasculitis is 0.01%. This may seem incredible, but it is. Perhaps the following example will help you understand why.
Suppose we have a device for determining the Martians, and it gives the correct answer in 99% of cases. We scan, for example, deputies one by one, the result is always negative. But when it comes to Vladimir Volfovich, the inscription lights up that he is a Martian. Will you believe the device? Probably not, this is exactly the 1% of cases when the device gives the wrong answer.
In the case of vasculitis, our test of 1% error will give a positive result for 10,000 people out of a million, but only one of these 10,000 people will actually be sick.
Source: https://habr.com/ru/post/98824/
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