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Monday, August 15, 2005
About statistics
Base Rates
The analysis becomes complicated if more or less than half the people in your situation have Disease X. The proportion of the people having the disease is called the base rate. It is very important to consider the base rate when classifying people. As the saying does, "if you hear hoofs, think horse not zebra" since you are more likely to encounter a horse than a zebra (at least in most places.)
Assume that Disease X is a rare disease, and only 2% of people in your situation have it. How does that affect the probability that you have it? Or, more generally, what is the probability that someone who tests positive actually has the disease. Lets consider what would happen if one million people were tested. Out of these one million people, 2% or 20,000 people would have the disease. Of these 20,000 with the disease, the test would accurately detect it in 99% of them. This means that 19,800 cases would be accurately identified. Now lets consider the 98% of the one million people (980,000) who do not have the disease. Since the false positive rate is 0.09, 9% of these 980,000 people will test positive for the disease. This is a total of 88,200 people incorrectly diagnosed.
Basic Concept
The analysis becomes complicated if more or less than half the people in your situation have Disease X. The proportion of the people having the disease is called the base rate. It is very important to consider the base rate when classifying people. As the saying does, "if you hear hoofs, think horse not zebra" since you are more likely to encounter a horse than a zebra (at least in most places.)
Assume that Disease X is a rare disease, and only 2% of people in your situation have it. How does that affect the probability that you have it? Or, more generally, what is the probability that someone who tests positive actually has the disease. Lets consider what would happen if one million people were tested. Out of these one million people, 2% or 20,000 people would have the disease. Of these 20,000 with the disease, the test would accurately detect it in 99% of them. This means that 19,800 cases would be accurately identified. Now lets consider the 98% of the one million people (980,000) who do not have the disease. Since the false positive rate is 0.09, 9% of these 980,000 people will test positive for the disease. This is a total of 88,200 people incorrectly diagnosed.
Basic Concept
